Abstract

Probabilistic mechanical fasteners are used to provide secure, reversible, and repeatable attachments in both nature and industry. Since the first observation of this mechanism in nature, which led to the creation of hook-and-loop fasteners, there has been a multitude of variations on the basic hook-and-loop design. However, few fastener designs have looked back to nature for inspiration in creating novel products or improving existing fasteners. Given the diverse probabilistic mechanical fasteners employed in nature, there is opportunity to further the research and development of these underdeveloped fasteners. To this end, we present a framework which describes the theory, design considerations, modelling, and mechanical testing required to study probabilistic mechanical fasteners. We further provide a comparison of the performance of existing probabilistic mechanical fasteners found in nature and industry as a reference for novel bio-inspired designs. Finally, we discuss current areas of application and future opportunities for fastener innovation.

1 Introduction

The challenge of attachment has inspired a broad range of solutions in both industry and nature. Welding, gluing, and bolting technologies are some of the techniques devised in industry [1]. In nature, examples include mussels secreting sticky foot proteins in salt water [2], gecko footpads utilizing van der Waals forces [3], and some fruit hooks mechanically engaging with the fur or feathers of passing animals [4]. The underlying principles behind these attachment devices can be described as primarily relying upon chemical, physical, or mechanical joining. To date, most research and innovation efforts have been focused on exploring adhesive attachments utilizing suction [5] and chemical bonds [69]. Less attention has been devoted to purely mechanical attachments. Mechanical fastening is a practice that predates civilization, beginning with the invention of basic hooks, arrows, and barbed spears [1]. With the invention of hook-and-loop fasteners in 1955 [10], mechanical fastening technologies expanded to include an immense variety of attachment designs. Since the vast number of fastener elements results in a high likelihood of attachment, these devices are described as probabilistic mechanical fasteners.

Probabilistic mechanical fasteners are comprised of one or two specially designed surfaces with many hooking elements. Those with only one specially designed hooking surface interact with mating surfaces in their environment, which possess a degree of randomness, e.g., a surface covered in asperities of different shapes and sizes. The distribution of spacings between asperities has been found to follow an exponential distribution which drives the likelihood of a hooking element successfully engaging asperities on the mating surface [11]. For fasteners with two specially designed surfaces, such as a typical hook-and-loop fastener, the likelihood of attachment is certain given the high number of elements. Unlike other attachment technologies which involve additional tools and a high level of skill, these fasteners do not require expert precision to achieve secure attachments [12]. Other advantageous characteristics of these fasteners are that they are reversible, repeatable, and durable. These traits allow probabilistic mechanical fasteners to be employed in a multitude of applications including medicine, transportation and storage, apparel, and robotics.

The first artificial probabilistic mechanical fastener was inspired by nature. When the Swiss engineer de-Mestral was out hiking, he noticed tiny hooks of burdock seeds clinging to the fabric of his clothing. This discovery led to the creation of the first hook-and-loop fastener [13]. Since this discovery, there have been many variations of de-Mestral's original design. However, there have been only three bio-inspired designs based on probabilistic mechanical fasteners found in nature—one inspired by Galium aparine leaf hooks [14], the second by insect leg hooks [11,15,16], and the third by hooks surrounding the proboscis of gut parasites [17]. Given the wide popularity and use of these fasteners in industry, there is great potential to create novel products and improve existing designs by studying underutilized probabilistic fasteners found in nature. The focus of this paper is to present a framework to aid in the research and development of novel bio-inspired probabilistic mechanical fasteners.

In Sec. 2, a detailed description of a probabilistic mechanical fastener and the theory behind a successful attachment is described. Recently, the first directional probabilistic mechanical fastener was discovered between the overlapping flight feathers of birds. This discovery motivated our bio-inspired outlook for finding new functional fastener designs. Section 3 presents the design process for a bio-inspired mechanical fastener including fastener element design choices, material and manufacturing options, a modelling framework, mechanical testing, and an overall strength comparison with existing probabilistic fasteners found in nature and industry. In Sec. 4, we discuss current areas of applications and focus on opportunities in the field of robotics. We conclude Sec. 4 with a discussion of alternative design pathways to enhance a probabilistic mechanical fastener by harnessing innovative combinations of physical and bio-inspired principles.

2 Description and Theory of Probabilistic Mechanical Fasteners

Probabilistic fasteners are attachment devices comprised of many hooking elements forming an array. Each hooking element has a probability of attachment and combining many of the hooking elements into a single array provides a high likelihood of attachment [18]. To compare the functional principles of probabilistic fasteners with other biological attachments, we present an overview of the main fastening strategies found in nature as seen in Fig. 1. Successful attachment of probabilistic mechanical fasteners does not require engagement of each individual hooking element, but rather a “sufficient number of contacts” [18,19]. When the hooking elements are brought into contact with a mating surface, the engagement of elements is primarily passive due to the high likelihood of attachment. The bond between the hooking elements and mating surface is unique in that it can be broken and rejoined many times. This is due to the many elements in the array; while some of the connections may destructively fail under loading, there are enough elements to ensure that a “sufficient number” is still functioning for successful reattachment [18,19]. All that is required for joining is to actively bring the fastener elements into contact. As a result, attachment is highly likely based on each element of the array having a high likelihood of attachment. Although the miniscule scale of each hooking element produces only a small contact force, the integrated result of many hooked elements is a secure connection. Together, the hooking elements contribute to make a strong, reversible, and repeatable attachment which requires little precision in aligning the hooking elements with the mating surface.

Fig. 1
Schematic function of eight attachment principles identified in nature [19], including: (a) Wet Adhesion in frog toe pads [20], (b) dry adhesion in gecko toe pads [3], (c) interlocking mechanism in the dragonfly head arrester system [21], (d) clamping of crab pincers [22], (e) suction in octopus tentacles [5,23], (f) friction for hooks on burr leaves [24], (g) hooking between overlapping microstructures in some bird species' flight feathers [25], and (h) spacing in the specialized setae on the shoulder joints of feather mites [24]. While many recent reviews on and innovations in bio-inspired attachment are based on the principles of adhesion and suction [5–9], less attention has been given to attachment devices that rely on passive mechanisms. To fill this gap, our review focuses on probabilistic mechanical fasteners, which are highlighted and outlined in blue. They are based on interlocking, friction, and hooking mechanisms. The unique characteristics of these micropatterned fasteners and their frequent appearance in nature provides unexplored opportunities for creating new bio-inspired fasteners. Drawings of attachment devices modified and reprinted with permission from the Royal Society [19,24]. Animal and plant avatars were hand drawn.
Fig. 1
Schematic function of eight attachment principles identified in nature [19], including: (a) Wet Adhesion in frog toe pads [20], (b) dry adhesion in gecko toe pads [3], (c) interlocking mechanism in the dragonfly head arrester system [21], (d) clamping of crab pincers [22], (e) suction in octopus tentacles [5,23], (f) friction for hooks on burr leaves [24], (g) hooking between overlapping microstructures in some bird species' flight feathers [25], and (h) spacing in the specialized setae on the shoulder joints of feather mites [24]. While many recent reviews on and innovations in bio-inspired attachment are based on the principles of adhesion and suction [5–9], less attention has been given to attachment devices that rely on passive mechanisms. To fill this gap, our review focuses on probabilistic mechanical fasteners, which are highlighted and outlined in blue. They are based on interlocking, friction, and hooking mechanisms. The unique characteristics of these micropatterned fasteners and their frequent appearance in nature provides unexplored opportunities for creating new bio-inspired fasteners. Drawings of attachment devices modified and reprinted with permission from the Royal Society [19,24]. Animal and plant avatars were hand drawn.
Close modal

2.1 Mating Surfaces for Probabilistic Mechanical Fasteners.

The mating surface can have purposefully designed, patterned elements or a degree of randomness in its elements' geometries. A description of the differences between these mating surfaces is shown in Fig. 2. A predetermined, patterned mating surface can have hooking elements identical to the fastening surface, as in self-mating, or it can involve different element geometries meant to engage a hooking surface, such as loops. Probabilistic fasteners in nature most often engage with random mating surfaces encountered in their environment [1719]. In manufacturing, predetermined, patterned mating surfaces are specifically designed and sold together with the fastener surface, as in hook-and-loop type fasteners. For patterned surfaces, where each mating element is designed to engage, the likelihood of attachment is essentially guaranteed [1719]. In contrast, a mating surface with a degree of randomness cannot guarantee a successful attachment. Differences between the likelihood of attachment for patterned and random mating surfaces is illustrated in Fig. 3. Besides the random quality of the mating surface, there are additional factors which impact the likelihood of attachment including: hooking and mating element spatial distributions, variable element strengths, and the angle of the applied load. Therefore, it is worth examining the factors which influence a successful attachment for the purpose of designing probabilistic mechanical fasteners.

Fig. 2
Patterned (a) and random (b) mating surfaces of probabilistic mechanical fasteners. Patterned mating surfaces, (a), are predetermined to engage with the fastener surface featuring hooking elements in a specific fashion. Random mating surfaces, (b), are adapted to engage with hooking fastener surfaces encountered by chance in the environment. In nature, a patterned mating surface can be self-mating, (a(1.i)), or hierarchical, (a(1.ii)). A self-mating surface is identical to the hooking element surface. An example of a self-mating surface in biology is the head-arrester system in dragonflies (Fig. 1(c); [21]). A hierarchical connection involves hooking and mating elements of different scales. Hierarchical connections can be found in wing interlocking devices of insects [19], well-described fastening structures between the barbs of a single feather vane [26], and between the recently discovered directional fastening microstructures of overlapping flight feathers (Fig. 1(g); [25]). Random mating surfaces in biology include surface asperities, (b(1.i)), as well as feather and furry surfaces, (b(1.ii)), which engage with the hooks of insects and plants. Most artificial mating surfaces are patterned and are made of self-mating or loop elements although some artificial hooking element surfaces have been designed to engage with surface asperities (b(2.i)), [11,15,16]. To our knowledge there is currently no artificial equivalent of hair, fur, or feather structures for probabilistic mechanical fasteners. Drawings modified from [15,19] and printed with permission from Sage Publication Inc. Journals [15] and the Royal Society [19]. Image of animal hair is hand drawn.
Fig. 2
Patterned (a) and random (b) mating surfaces of probabilistic mechanical fasteners. Patterned mating surfaces, (a), are predetermined to engage with the fastener surface featuring hooking elements in a specific fashion. Random mating surfaces, (b), are adapted to engage with hooking fastener surfaces encountered by chance in the environment. In nature, a patterned mating surface can be self-mating, (a(1.i)), or hierarchical, (a(1.ii)). A self-mating surface is identical to the hooking element surface. An example of a self-mating surface in biology is the head-arrester system in dragonflies (Fig. 1(c); [21]). A hierarchical connection involves hooking and mating elements of different scales. Hierarchical connections can be found in wing interlocking devices of insects [19], well-described fastening structures between the barbs of a single feather vane [26], and between the recently discovered directional fastening microstructures of overlapping flight feathers (Fig. 1(g); [25]). Random mating surfaces in biology include surface asperities, (b(1.i)), as well as feather and furry surfaces, (b(1.ii)), which engage with the hooks of insects and plants. Most artificial mating surfaces are patterned and are made of self-mating or loop elements although some artificial hooking element surfaces have been designed to engage with surface asperities (b(2.i)), [11,15,16]. To our knowledge there is currently no artificial equivalent of hair, fur, or feather structures for probabilistic mechanical fasteners. Drawings modified from [15,19] and printed with permission from Sage Publication Inc. Journals [15] and the Royal Society [19]. Image of animal hair is hand drawn.
Close modal
Fig. 3
Likelihood of attachment between a hooking surface and its patterned/random mating surface. Successful attachment of a hooking element depends on the spatial distribution of mating elements and on the strength of the connection of each engaged element. For a patterned mating surface, engagement is guaranteed since the spatial and strength distributions are optimized to engage by design. On the other hand, a mating surface with a random spatial and strength distribution is not guaranteed to engage. Statistical models have been developed to explain the likelihood of attachment for claws [27] and spines [15] interacting with rough asperity surfaces. Once the hooking and mating surfaces engage, there are two possibilities for the contact: it can hold or it can fail. These outcomes are described by the expression, P(Hold) + P(Fail) = 1, which is adapted from Ref. [15]. Failure occurs through overload, slip, or simultaneously from both overload and slip. We then assume that P(Slip) and P(Overload) are independent, nonmutually exclusive events as shown above in the Venn Diagrams for Slip and Overload. From these assumptions, we represent P(Fail) as P(Fail) = P(Overload) + P(Slip)—P(Overload ∩ Slip). Substituting this expression into P(Hold) + P(Fail)=1, and rearranging gives P(Overload) + P(Slip)—P (Overload ∩ Slip) = 1—P(Hold). The likelihood of each scenario may evolve if the conditions of the attachment are dynamic. For example, if the loading force causes failure of hooking elements, load sharing will require nonfailed elements to sustain more force which would increase P(Overload). On the other hand, if the connection was displaced so that the hooking element lost its ideal grip on the mating surface, P(Slip) would increase. For both an increase in load and displacement of the hooking element, P(Overload) and P(Slip) would increase. Diagram modified and printed with permission from Sage Publications Inc. Journals [15].
Fig. 3
Likelihood of attachment between a hooking surface and its patterned/random mating surface. Successful attachment of a hooking element depends on the spatial distribution of mating elements and on the strength of the connection of each engaged element. For a patterned mating surface, engagement is guaranteed since the spatial and strength distributions are optimized to engage by design. On the other hand, a mating surface with a random spatial and strength distribution is not guaranteed to engage. Statistical models have been developed to explain the likelihood of attachment for claws [27] and spines [15] interacting with rough asperity surfaces. Once the hooking and mating surfaces engage, there are two possibilities for the contact: it can hold or it can fail. These outcomes are described by the expression, P(Hold) + P(Fail) = 1, which is adapted from Ref. [15]. Failure occurs through overload, slip, or simultaneously from both overload and slip. We then assume that P(Slip) and P(Overload) are independent, nonmutually exclusive events as shown above in the Venn Diagrams for Slip and Overload. From these assumptions, we represent P(Fail) as P(Fail) = P(Overload) + P(Slip)—P(Overload ∩ Slip). Substituting this expression into P(Hold) + P(Fail)=1, and rearranging gives P(Overload) + P(Slip)—P (Overload ∩ Slip) = 1—P(Hold). The likelihood of each scenario may evolve if the conditions of the attachment are dynamic. For example, if the loading force causes failure of hooking elements, load sharing will require nonfailed elements to sustain more force which would increase P(Overload). On the other hand, if the connection was displaced so that the hooking element lost its ideal grip on the mating surface, P(Slip) would increase. For both an increase in load and displacement of the hooking element, P(Overload) and P(Slip) would increase. Diagram modified and printed with permission from Sage Publications Inc. Journals [15].
Close modal

2.2 Theory Behind the Likelihood of Attachment

2.2.1 Background for Examining Failure in a Matrix of Many Elements.

Probabilistic mechanical fasteners consist of many elements which effectively form a single matrix. The first attempts to explain the performance of a matrix with many individual elements examined composites made of fiber bundles [28,29]. Failure of the matrix resulted from failure of individual fibers due to crack formations. Strain mismatches between the individual fibers led to reduced crack strength. Strain mismatches also made fibers more susceptible to slip [28,29]. Later, the stress needed to overcome bonding at the fiber-matrix interface was also determined to influence the overall matrix cracking stress [28,29].

For a matrix of many individual fiber elements, the evolution of fiber failure which leads to overall matrix cracking, has been examined through the concept of load sharing [30,31]. Load sharing is the mechanism through which matrix elements redistribute and share load when a single element fails. Load sharing can be viewed from two perspectives: global load sharing, and local load sharing. Global load sharing assumes that broken fibers do not cause local stress concentrations, and that load lost by failed fibers, n, is transferred equally to all unbroken fibers, nfn. The increase in load for the unbroken fibers is given by the expression [1nfn]Σi=1nΔσi(z), where Δσi(z) is the change in stress that results at a position z along the length of the nonfailed fibers [31]. As all unbroken fibers experience an equal increase in stress, it is further assumed that both the stress at each fiber is the same and the strength distribution along the lengths of all fibers is the same [31]. This assumption is shown in Eq. (1) which can be used to find the resulting stress due to the applied external load and the redistributed stress that results from load sharing. In Eq. (1), the resulting stress is T, the applied external load is σf, and the redistributed stress from load sharing is Δσi(z). The redistributed stress, Δσi(z), depends on the height, z, along the length of a fiber, while the external load, σf, is independent of the height along the fiber [31]. Because the stress on each fiber and the strength distribution along the length, z, of each fiber is assumed to be the same, the resulting stress, T, can be assumed to be the same across the length of the fibers [31]. As a first approximation, Eq. (1) can be used to calculate the resulting stress on a matrix of fibers, or fastener elements, due to an applied external load and stress redistribution resulting from load sharing:
(1)

With the simplified assumptions of global load sharing, criteria for measuring the performance of a matrix can be developed for expressions of fiber pull out lengths, work of pull out, and ultimate tensile stress [30]. In contrast to global load sharing, local load sharing considers local stress concentrations, stress gradients, and localized damage due to notches, holes, or other imperfections [31]. When a fiber is damaged, the stress increases in the region of the failed fiber which propagates damage from one region to another nearby region [31]. There are several models which have been developed to characterize local load sharing, see Curtin [31] and additional references for further explanation of load sharing [3136].

2.2.2 Likelihood of Attachment for Case of Probabilistic Mechanical Fasteners.

For probabilistic fasteners, the criteria for success and failure depends not only on the fracture and load sharing of hooking elements, but also on the likelihood of attachment with a mating surface. Here, we discuss the likelihood of attachment between a spine hooking element and a random asperity mating surface [11,15,16,37]. We present the primary factors that impact successful attachments as a basis for examining the likelihood of attachment for different fastener and mating surfaces. The loading and release of a hooking element with an asperity is described as a loading cycle and consists of four main phases (Fig. 4): approach, surface contact, asperity encounter, and release. Each phase has key factors that impact the likelihood of a successful attachment [11]. These attachment factors are discussed first from the perspective of compliantly supported, rigid spines [11]. Later, we examine how the phases of attachment differ for compliant hooks.

Fig. 4
The loading cycle of a hooking element with a random asperity mating surface. The loading cycle includes four phases: 1—Approach, 2—Surface contact, 3—asperity encounter, and 4—release [38]. After moving with a horizontal (a) and vertical velocity (b), the hooking element (I) contacts with the mating surface (II), which exerts a small normal (c) and shear (d) force at the tip of the hooking element. The hooking element is then dragged until it encounters an asperity (III) at which point the angled (ϕ) loading force (g) tries to pull the hook away from the mating surface in the vertical (y) direction. The vertical pull force is opposed by the normal component of the tangential surface friction force (h), which pulls the hooking element towards the mating surface. In (III), the local surface slope of the asperity (Ψ) combined with the angle of the tip of the hooking element (β) is also shown to be key for fastening function. Eventually the loading force overcomes the normal component of the friction force and the hook is released. Schematic modified and printed with permission from Sage Publications Inc. Journals [15].
Fig. 4
The loading cycle of a hooking element with a random asperity mating surface. The loading cycle includes four phases: 1—Approach, 2—Surface contact, 3—asperity encounter, and 4—release [38]. After moving with a horizontal (a) and vertical velocity (b), the hooking element (I) contacts with the mating surface (II), which exerts a small normal (c) and shear (d) force at the tip of the hooking element. The hooking element is then dragged until it encounters an asperity (III) at which point the angled (ϕ) loading force (g) tries to pull the hook away from the mating surface in the vertical (y) direction. The vertical pull force is opposed by the normal component of the tangential surface friction force (h), which pulls the hooking element towards the mating surface. In (III), the local surface slope of the asperity (Ψ) combined with the angle of the tip of the hooking element (β) is also shown to be key for fastening function. Eventually the loading force overcomes the normal component of the friction force and the hook is released. Schematic modified and printed with permission from Sage Publications Inc. Journals [15].
Close modal

During the approach phase, the hook moves with a horizontal and vertical velocity until it contacts the asperity surface [11]. Here, the approach angle primarily determines the hook's ability to engage with an asperity [11]. If the hook's approach angle is too high, the hook may bend when it reaches the asperity surface. On the other hand, if the hook's approach angle is too low, the hook may slip when it contacts the asperity surface [11]. During the surface contact phase, the spine slides along the surface to find a viable asperity and applies a small positive normal force and may also apply a small shear force to the surface [11]. Factors that determine the probability of latching onto an asperity are loading force, load angle, and the coefficient of friction of the surface [11]. The coefficient of friction of the surface is important, because it determines whether the hook may fail in strength (rough surface) or from slip (smooth surface) [11].

In the asperity encounter phase, the motion of the hook is halted by an asperity [11]. The normal force component due to surface friction pulls the hook towards the mating surface, which opposes the loading force [11]. Contact with an asperity depends on the spatial distribution, slopes, and shapes of the asperities, as well as the relative size of the spine tip radius compared to the average asperity size [11,16]. The spatial distribution of lengths between asperities on a mating surface were first described using an exponential distribution [11]. In Table 1, variations of this general expression are presented for specific cases [15,16]. In addition to asperity spatial distribution, asperity slopes also influence whether or not a hooking element can engage the mating surface [11]. An expression for the minimum usable asperity slope is found in Table 1 [11].

Table 1

Expressions for asperity distributions and usable asperities

Asperity distributionPDF expressionVariables
Asperity spatial distribution [11]
(2)
λ: number of asperities
x: random variable for distance between asperities
Asperity spatial distribution considering asperity length [15]
(3)
Pexp: spacing between asperities
Pint: asperity length
(1α): probability of immediate engagement
α: fit parameter
λ: number of asperities
x: random variable for distance between asperities
Asperity spatial distribution for linearly constrained hook [16]
(4)
ψ: asperity slope. When ψ > 60, distribution is linear and not exponential
Usable asperity slopes [11]
(5)
θmin: minimum usable asperity slope
θload: angle of the applied load
μ: coefficient of friction
Asperity distributionPDF expressionVariables
Asperity spatial distribution [11]
(2)
λ: number of asperities
x: random variable for distance between asperities
Asperity spatial distribution considering asperity length [15]
(3)
Pexp: spacing between asperities
Pint: asperity length
(1α): probability of immediate engagement
α: fit parameter
λ: number of asperities
x: random variable for distance between asperities
Asperity spatial distribution for linearly constrained hook [16]
(4)
ψ: asperity slope. When ψ > 60, distribution is linear and not exponential
Usable asperity slopes [11]
(5)
θmin: minimum usable asperity slope
θload: angle of the applied load
μ: coefficient of friction

Note: This table includes equations which can be used to determine characteristics of a random asperity mating surface. Here, we reference three equations which explain the spatial distribution of asperities, including a general asperity distribution in Eq. (2), a spatial distribution which takes into account the length of the asperities in Eq. (3), and an asperity spatial distribution for the special case of linearly constrained hooks in Eq. (4). These equations are presented as a starting point for readers seeking to research or design fasters which interact with random asperity surfaces. Understanding different expressions for asperity spatial distributions can aid in creating hooking surfaces which are more likely to contact the asperity mating surface. Additionally, we reference an expression for determining which asperities on a random mating surface can sustain a connection with a hooking element based on the asperity's slope.

As the hooking element approaches an asperity, it is critical to consider the size of the hooking element's tip radius—if it is too large, the force of attachment increases, but it misses the chance to engage smaller surface asperities [11]. One solution is to use a higher number of smaller hooks to achieve the same integrated force of attachment and reach the smaller asperities. At some point, however, load sharing is impeded as too many hooking elements will interfere with each other's attachments, blocking some hooking elements from carrying the load [11]. With this unequal distribution of the load, the force ceases to increase with the number of hooks. Relationships between hooking element size and the number of hooking elements is found in Table 2.

Table 2

Expressions for stress, strength, and load sharing in hooking elements

Load on hooking elementScaling relationVariables
Force carried by one hooking element [37]
(6)
F1: force for one hooking element
Fh: max attachment force, see (8)
r: radius of an equivalent circular cross section
R: hook radius of curvature
Force scaling for multiple hook subcontacts [37]
(7)
n: number of subcontacts
F1: force carried by one hook
Fn: force for n subcontacts
β = 0 if r R
β = 2 if r = constant
Bending [37]
(8)
σb: bending stress
r: radius of an equivalent circular cross section
R: hook radius of curvature
Tension [37]
(9)
σt: tensile stress
r: radius of an equivalent circular cross section
R: hook radius of curvature
Nominal Stress [37]
(10)
σh: nominal stress
r: radius of an equivalent circular cross section
R: hook radius of curvature
Hook/asperity contact strength [11]
(11)
r: radius at tip of hooking element
Fhook/asperity: load per hook/asperity contact
Load on hooking elementScaling relationVariables
Force carried by one hooking element [37]
(6)
F1: force for one hooking element
Fh: max attachment force, see (8)
r: radius of an equivalent circular cross section
R: hook radius of curvature
Force scaling for multiple hook subcontacts [37]
(7)
n: number of subcontacts
F1: force carried by one hook
Fn: force for n subcontacts
β = 0 if r R
β = 2 if r = constant
Bending [37]
(8)
σb: bending stress
r: radius of an equivalent circular cross section
R: hook radius of curvature
Tension [37]
(9)
σt: tensile stress
r: radius of an equivalent circular cross section
R: hook radius of curvature
Nominal Stress [37]
(10)
σh: nominal stress
r: radius of an equivalent circular cross section
R: hook radius of curvature
Hook/asperity contact strength [11]
(11)
r: radius at tip of hooking element
Fhook/asperity: load per hook/asperity contact

Note: While load sharing can involve intense modelling and mathematics [3136], there are also simple expressions which can intuitively guide the examination of stress and strength in fastener elements. Equations (6) and (8)(11) describe how fastener element strength and stress are influenced by the radius of the hooking element. Equation (7) relates how force carried by multiple hooking elements compares to the force carried by a single hooking element.

From the specific perspective of spine and asperity contacts, release of a connection can result in two ways: (1) the loading force can overload the attachment force and break the connection, or (2) the hook can be pulled at an angle which stretches the hook until its tip slips off the asperity [11]. While these factors were developed based on the study of compliantly supported, rigid spines [11], the principles can be applied to compliant elements with more considerations.

As many hooking elements in biology often have more compliant behaviors then those used in engineering technologies [4,22,2426,29], we discuss some of the considerations and differences for compliant versus rigid hook behavior during the approach, surface contact, encounter, and release phases of attachment. Compliant structures undergo greater deflections then rigid structures from an identical external load [39,40] as their flexible structures are more capable at absorbing and storing energy [41,42]. Furthermore, compliant hooks have been found to experience higher deflection under dynamic loading then under static force [40]. According to the magnitude and static/dynamic behavior of the loading force, the geometry of the compliant hook will deflect and adapt as it approaches the mating surface.

Once the compliant hook meets the mating surface, its structure will displace under loads from the external force and mating surface. As a result, the compliant hook experiences reduced friction on the mating surface, and therefore less wear, compared to rigid hooks [41]. The deflections of the compliant hook can be highly complex, and the underlying material properties may not be known [41]. One way to better understand the material properties, and therefore behavior of a compliant hook, is to determine the Young's modulus by creating Force versus Displacement curves [39,40] or performing a cantilever test [24]. Further analysis of compliant hook behavior can be undertaken through modelling [4144].

A challenge that compliant hooks are more likely to experience than rigid hooks upon encountering an asperity or other mating element is the collision of multiple compliant hooks [41]. This collision prevents an attachment from being made with the mating surface. Collision of compliant hooks is due to their highly deflective structures which can interfere with the performance of the fastener. When designing compliant fasteners, care should be taken to consider the spacing between the hooking elements. Finally, at the release of an attachment, compliant hooks do not exhibit the backlash seen in rigid structures [41]. Being aware of the factors which influence a secure connection for an attachment with random mating surfaces can aid in designing fasteners which are more likely to attach.

2.3 Focus on Biological Probabilistic Mechanical Fasteners.

Probabilistic fasteners evolved in nature under natural selection of the species featuring them. For example, parasitic worms have large numbers of hooks to ensure attachment to a host organism [17,22]. Eggs of some fish have hooks which keep the eggs joined in strong river currents, and insects such as fleas, bat flies, and beaver beetles have tiny hooks which entangle in the fur of host animals [22]. Along with hooks of fruits [4,29], some plants have hooks on their leaves which aid in attachment and orientation towards sunlight [14,24]. Certain flowers and leaves also have surfaces that promote attachment with hooks on insect feet to aid pollination [45,46]. Most of the probabilistic fasteners in nature have one specialized fastener surface which evolved to interact during chance encounters with a wide range of surfaces in the environment (see Fig. 2 for a reference of the different types of mating surfaces). However, there are several examples of probabilistic fasteners in nature with a patterned, predetermined surface such as wing interlocking devices of beetles [4750], head arresters in dragonflies [18,21] (see Fig. 1), and bird flight feathers. A bird feather is made of a central shaft called a rachis, from which angled projections called barbs branch [22,25,26]. Branching from the barbs are even smaller angled projections called barbules. Barbules from adjacent barbs interlock via small hooks, or hooklets [22,25,26]. Together, the many hooked barbules zip up the feather to form a uniform surface [22,25,26]. The interactions between microstructures of a single feather hooking to form a uniform surface has been studied since the 1930s [51] and is now well understood [5254].

Recently, a new class of probabilistic mechanical fasteners has been discovered between overlapping flight feathers in many species of birds (apart from silent fliers such as owls) [25]. Whereas the function and performance of the hooklet-based fastening mechanism between the barbs in a single feather vane are generally known and understood [25,5458], there also exists a fastening mechanism between overlapping flight feathers, as seen in Fig. 5 [25]. Engagement of this feather-feather fastener takes place between hooked structures protruding down from the overlapping feather surface and protruding up from the underlying feather surface [25], see Fig. 5. This fastener is uniquely directional—only when the feathers are pulled away in tension, as when a bird extends its wings, do the microstructures engage to impede feather separation and ensure a continuous aerodynamic surface without gaps. As this fastener engagement is dependent upon direction, we term this mechanism a directional probabilistic fastener [25]. Directionality between significantly fewer hooking elements connecting front and hind wings is also observed during wing extension in some insects [4750]. The directional mechanical fasteners described here, are analogues to anisotropic adhesion observed in setae (small hair projections on gecko feet [3]). Depending on the angle of pull, the setae's adhesion strength is either maximized or dramatically decreased [59]. This ease of switching between strong and weak adhesion can be ideal for creating a robust, releasable adhesion [59].

Fig. 5
Unique directional mechanical probabilistic fastener between bird flight feathers based on two differently patterned mating surfaces [25]. (a) X-ray microscope micro-CT reconstruction of the directional micromechanical fastening mechanism between primary flight feathers P6 and P5 of a rock pigeon (Columbia livia). These microstructures are directional and engage when loaded under tension as when the bird extends its wings. This mechanism has been found between the primary, secondary and tail flight feathers of a large number of bird species except silent fliers such as barn owls (Tyto alba) [25]. The scale bar for the macroscopic view of P5 and P6 feathers is 1 cm. The scale bar for the microstructure CT view is 100 μm. (b) SEM images of the mating surfaces of the overlapping (P9) and underlapping (P10) side of two primary feathers that can fasten directionally in a pigeon wing. P10 images reveal the hooked rami ridges which interact with a field of lobate cilia that stick up and out of the underlying P9 feather's dorsal plane. This fastener is hierarchical, meaning that the interacting fastener elements are different scales: the hooked rami sit at the underside of barbs, whereas the hooked lobate cilia stick out on the upper side of specialized fastening barbules. (c) Beamline nano-CT reconstruction of the hooked quasi-2D rami and hooked 3D lobate cilia. The downward hooked rami tip is circled and so is the lobate cilia extending up and out of the dorsal feather surface. Note these cross section do not show the actual hooking engagement orientation. The scale bar is 10 μm. (d) 3D reconstruction of the in vivo fastening between two secondary flight feathers (S5, S6) drawn to scale based on nano-CT scans. The reconstruction shows the classical interbarb fastener that connects the distal and proximal barbule via hooklets and sticks all the barbs together in a feather vane. Remarkably, the same distal barbule featuring the hooklets can also feature the 3D hooked locate cilia that fastens the hooked rami of an overlapping feather directionally. The two fasteners are oriented approximately perpendicular, decoupling their functions. The interfeather fastener is only found between the trailing vane of the overlapping and the leading vane of the overlapping flight feathers. (e, f, g) Zoomed in (cross-sectional) nano-CT reconstruction of the directional fastening mechanism between a single hooked rami and lobate cilium. The slanted tip of the lobate cilium helps ensure the two feather surfaces mate. Scale bar 10 μm. Images adapted from Ref. [25].
Fig. 5
Unique directional mechanical probabilistic fastener between bird flight feathers based on two differently patterned mating surfaces [25]. (a) X-ray microscope micro-CT reconstruction of the directional micromechanical fastening mechanism between primary flight feathers P6 and P5 of a rock pigeon (Columbia livia). These microstructures are directional and engage when loaded under tension as when the bird extends its wings. This mechanism has been found between the primary, secondary and tail flight feathers of a large number of bird species except silent fliers such as barn owls (Tyto alba) [25]. The scale bar for the macroscopic view of P5 and P6 feathers is 1 cm. The scale bar for the microstructure CT view is 100 μm. (b) SEM images of the mating surfaces of the overlapping (P9) and underlapping (P10) side of two primary feathers that can fasten directionally in a pigeon wing. P10 images reveal the hooked rami ridges which interact with a field of lobate cilia that stick up and out of the underlying P9 feather's dorsal plane. This fastener is hierarchical, meaning that the interacting fastener elements are different scales: the hooked rami sit at the underside of barbs, whereas the hooked lobate cilia stick out on the upper side of specialized fastening barbules. (c) Beamline nano-CT reconstruction of the hooked quasi-2D rami and hooked 3D lobate cilia. The downward hooked rami tip is circled and so is the lobate cilia extending up and out of the dorsal feather surface. Note these cross section do not show the actual hooking engagement orientation. The scale bar is 10 μm. (d) 3D reconstruction of the in vivo fastening between two secondary flight feathers (S5, S6) drawn to scale based on nano-CT scans. The reconstruction shows the classical interbarb fastener that connects the distal and proximal barbule via hooklets and sticks all the barbs together in a feather vane. Remarkably, the same distal barbule featuring the hooklets can also feature the 3D hooked locate cilia that fastens the hooked rami of an overlapping feather directionally. The two fasteners are oriented approximately perpendicular, decoupling their functions. The interfeather fastener is only found between the trailing vane of the overlapping and the leading vane of the overlapping flight feathers. (e, f, g) Zoomed in (cross-sectional) nano-CT reconstruction of the directional fastening mechanism between a single hooked rami and lobate cilium. The slanted tip of the lobate cilium helps ensure the two feather surfaces mate. Scale bar 10 μm. Images adapted from Ref. [25].
Close modal

What sets the feather-feather directional probabilistic fastener apart from insect wing locking and even gecko setae, is not only the orders of magnitude higher number of hooking elements, but also the hierarchical engagement of microstructures [25]. The trailing vanes (vanes projecting from one half of the rachis which encounter aerodynamic forces after the leading edge vanes [22,25,26]) of flight feathers are comprised of specialized fastening barbules that feature lobate cilia (3D hook shaped protrusions on the upper surface of the barbule that stick up and out of trailing vane surface [25]). These lobate cilia latch stochastically onto rami (quasi 2D hooks pointing down from the barbs of the overlapping feather's leading vane). See Figure 5 for a visual of engagement between lobate cilia and rami. While both the hooked rami (hierarchical level of the barb) and lobate cilia (hierarchical level of the barbule) are of the order of ten micrometers, the hooked rami are many millimeters to centimeters long; however, the number of lobate cilia (1000 s) is much higher than the number of hooked rami (10–100 s) and a sufficient number of lobate cilia is able to secure the rami hooks under tension [25]. The structure of the feather vane cross section ensures that the underlapping and overlapping feather surfaces are correctly aligned and in contact to securely fasten [25]. According to our literature review, there is no equivalent biological or technological fastener. Given the diversity of probabilistic mechanical fasteners found in nature, many with traits that have yet to be characterized or translated into artificial fasteners, there are numerous opportunities to research and develop innovative bio-inspired mechanical fasteners.

3 Design Framework for Bio-inspired Fasteners

In this section, we discuss a design framework for developing novel bio-inspired fasteners that can be applied generally, including for our specific focus on probabilistic mechanical fasteners. The design framework, Fig. 6, has been distilled and developed based on established general design diagrams as well as bio-inspired design diagrams found across literature [27,6062]. Fastener innovation generally arises from observations, such as noticing a shortcoming in current fasteners or discovering a problem that a novel fastener could solve. For bio-inspired fasteners, it is the observation of a biological mechanism that leads to new designs (e.g., the original observation of de-Mestral resulting in hook-and-loop fasteners). Bio-inspired design builds off characterizing the biological fastener's function. Performing imaging techniques [14,18,19,24,39,63,64], and mechanical testing [14,18,23,39,40] (as well as other physical characterization processes) reveal the biological fastener's underlying structure and attachment principle(s). This leads to a general understanding of the biological fastener's method of attachment. Key behaviors and traits of the biological fastener can then be understood and inform engineering design choices such as the fastener elements' geometries, material properties, and method of manufacturing [14,17]. Once a design of the bio-inspired fastener has been determined, it can be evaluated using modelling, simulations, and mechanical performance tests. Comparison between the biological fastener and bio-inspired fastener based on metrics, such as max force per hooking element, can further aid in design evaluation and optimization. Iteration of this design framework can improve the bio-inspired fastener design and lead to new understandings of probabilistic mechanical fasteners.

Fig. 6
Bio-inspired design process for inventing new high-performance mechanical fasteners. Through a review of proposed design methods [60], and bio-inspired design methods [27,61,62], we have developed a design approach for bio-inspired mechanical fasteners. (a) The approach begins with identifying an Engineering Challenge, which cannot be solved satisfactory with existing fasteners. (b) New design solutions can be engineered by drawing Inspiration from Biology. An organism suitable for the fastening challenge can be identified through a search of the literature and collaborating with a biologist who is an expert on the functional morphology of the organism of interest. (c) Once an appropriate organism is selected, the underlying physical principals is investigated by performing a rigorous scientific Analysis of the Biological Fastener. Analysis of the fastener often involves characterization through imaging techniques and mechanical testing as well as other physical characterization methods. (d) With characterization of the biological fastener complete, the next step is to develop the bioinspired design by translating the biological fastener's biological and physical principles into engineering analogs. Considerations for selecting engineering analogs involve determining fastener element structure and selecting a material and method of manufacturing. (e) An analysis of the bio-inspired fastener is then performed through mechanical testing, modelling, and simulations. Ideally, the analysis methods for the bio-inspired fastener are sufficiently similar to those of the biological fastener so that a reasonable one-to-one comparison can be made to evaluate the performance of the engineering design. The purpose of the comparison is to determine if the bio-inspired design sufficiently captures the desired performance features of the biological fastener. If the bio-inspired design captures the desired traits of the biological fastener, it can be iterated through by returning to (d) and further develop the bio-inspired design. On the other hand, if the comparison (f) reveals that the bio-inspired design fails to capture the desired mechanical fastener traits needed, a new organism and associated biological fastener can be selected by returning to getting inspiration from biology (b). The bio-inspired design is iterated until it is determined that it provides a sufficiently meets the requirements to solve the engineering challenge at which point a novel bio-inspired fastener (g) has been developed.
Fig. 6
Bio-inspired design process for inventing new high-performance mechanical fasteners. Through a review of proposed design methods [60], and bio-inspired design methods [27,61,62], we have developed a design approach for bio-inspired mechanical fasteners. (a) The approach begins with identifying an Engineering Challenge, which cannot be solved satisfactory with existing fasteners. (b) New design solutions can be engineered by drawing Inspiration from Biology. An organism suitable for the fastening challenge can be identified through a search of the literature and collaborating with a biologist who is an expert on the functional morphology of the organism of interest. (c) Once an appropriate organism is selected, the underlying physical principals is investigated by performing a rigorous scientific Analysis of the Biological Fastener. Analysis of the fastener often involves characterization through imaging techniques and mechanical testing as well as other physical characterization methods. (d) With characterization of the biological fastener complete, the next step is to develop the bioinspired design by translating the biological fastener's biological and physical principles into engineering analogs. Considerations for selecting engineering analogs involve determining fastener element structure and selecting a material and method of manufacturing. (e) An analysis of the bio-inspired fastener is then performed through mechanical testing, modelling, and simulations. Ideally, the analysis methods for the bio-inspired fastener are sufficiently similar to those of the biological fastener so that a reasonable one-to-one comparison can be made to evaluate the performance of the engineering design. The purpose of the comparison is to determine if the bio-inspired design sufficiently captures the desired performance features of the biological fastener. If the bio-inspired design captures the desired traits of the biological fastener, it can be iterated through by returning to (d) and further develop the bio-inspired design. On the other hand, if the comparison (f) reveals that the bio-inspired design fails to capture the desired mechanical fastener traits needed, a new organism and associated biological fastener can be selected by returning to getting inspiration from biology (b). The bio-inspired design is iterated until it is determined that it provides a sufficiently meets the requirements to solve the engineering challenge at which point a novel bio-inspired fastener (g) has been developed.
Close modal

3.1 Designing Fastener Element Structure.

Probabilistic mechanical fasteners are made up of many individual hooking elements whose purpose is to catch and secure element(s) on the mating surface. The basic structure of a hooking element includes a base, stem, and grip as seen in Fig. 7 panel (a). The base grounds the hook into the fastener substrate while the stem determines how the hook protrudes from the substrate surface. The grip engages the mating element(s). Different geometries of hooking elements have been proposed to improve the hook's ability to catch and secure the mating surface [72,7594]. Some examples are shown in Fig. 7 panel (b).

Fig. 7
The anatomy and geometric parameters of a fastener's hooking element. (a) Anatomy of a hooking element described in terms of a base, stem, and gripping element. The three basic hooking element shapes are stem- based [65], J-shaped [66], and capped [67]. The base secures the hooking element into the substrate, the stem determines how the hooking element rises from the substrate surface, and the gripping element is the primary component to interact with the mating elements. (b) Diversity of existing hooking element designs for hook-and-loop fasteners. Numerous designs have been claimed in patents to improve catching and holding loop elements. J-shaped hooks engage with one loop [65], (i); one J-shaped hook engages with multiple loops [64], (ii); a capped mushroom hook engages with multiple loops [68], (iii); different sized J-shaped hooks in parallel engage loops at different lengths [68], (iv); different sized J-shaped hooks in opposition engage loops at different lengths [69], (v); hook with two gripping elements engages with multiple loops [70], (vi); (c) General design parameters for hooking element geometry. The grip can be described by five parameters: width (1), length (2), span (3), angle of curvature (4), and number of gripping elements (5). The stem can be described by three parameters: width (6), length (7), angle with respect to the base (8), angle of curvature of stem transition to base (9). The base can be described by its width (10) and length (11). Overall fastener geometry has an element width (12) and length (13) and can be rotated (14) and projected (15). (d) Examples of different hook geometries obtained by applying key hook design parameters in C that morph the hook geometry: baseline J-shaped hook [66], (i); capped hook [67] results from rotating grip with parameter 14, (ii); ridge hook [71] results from out- of-plane extrusion of the basic J-shaped hook with parameter 15, (iii); J-shaped hook [72] with varied 2D parameters (1–13), (iv); hook [71] with an added gripping element (5), (v); geometrically complex hooks result from varying 2D parameters [73], rotating the grip (14), and extruding out-of- plane (15), (vi); Drawings modified after their cited patents.
Fig. 7
The anatomy and geometric parameters of a fastener's hooking element. (a) Anatomy of a hooking element described in terms of a base, stem, and gripping element. The three basic hooking element shapes are stem- based [65], J-shaped [66], and capped [67]. The base secures the hooking element into the substrate, the stem determines how the hooking element rises from the substrate surface, and the gripping element is the primary component to interact with the mating elements. (b) Diversity of existing hooking element designs for hook-and-loop fasteners. Numerous designs have been claimed in patents to improve catching and holding loop elements. J-shaped hooks engage with one loop [65], (i); one J-shaped hook engages with multiple loops [64], (ii); a capped mushroom hook engages with multiple loops [68], (iii); different sized J-shaped hooks in parallel engage loops at different lengths [68], (iv); different sized J-shaped hooks in opposition engage loops at different lengths [69], (v); hook with two gripping elements engages with multiple loops [70], (vi); (c) General design parameters for hooking element geometry. The grip can be described by five parameters: width (1), length (2), span (3), angle of curvature (4), and number of gripping elements (5). The stem can be described by three parameters: width (6), length (7), angle with respect to the base (8), angle of curvature of stem transition to base (9). The base can be described by its width (10) and length (11). Overall fastener geometry has an element width (12) and length (13) and can be rotated (14) and projected (15). (d) Examples of different hook geometries obtained by applying key hook design parameters in C that morph the hook geometry: baseline J-shaped hook [66], (i); capped hook [67] results from rotating grip with parameter 14, (ii); ridge hook [71] results from out- of-plane extrusion of the basic J-shaped hook with parameter 15, (iii); J-shaped hook [72] with varied 2D parameters (1–13), (iv); hook [71] with an added gripping element (5), (v); geometrically complex hooks result from varying 2D parameters [73], rotating the grip (14), and extruding out-of- plane (15), (vi); Drawings modified after their cited patents.
Close modal

Most variation in hooking element geometry involves the grip. There are three broad categories of fastening elements based on commonly used grips, as shown in Fig. 7 panel (a). The first category includes J-shaped grips, also known as crook grips due to a resemblance to a shepherd's crook. [13,68,7479,86, 9599]. Second, so-called mushroom, or capped grips, which can be imagined as a crook grip rotated in space [67,99110]. Third, Stem based grips which lack the curvature found in crook grips [110,111]. Finally, another category could be considered to include ridges, which are formed by projecting a hook in space [71,112]. Complexity in grip design can further be introduced by varying the number and geometries of grips on a single element. A single fastener surface can also include hooks with variable geometries [113], spacings [71], and orientations [93], see Fig. 7 panels (b) and (d).

Given the vast multitude of variations that are possible for hooking element geometry, we have identified a simplified list of parameters, see Fig. 7 panel (c), to aid in the discussion and design of hooking elements. These ten design parameters are based on geometric parameters discussed across the literature [4,18,39,72,78,79,82,86,95,96,114,115] and include: total height, width of the base, width of stem at the “neck” transition to the grip, angle of the stem with respect to the base, angle of the neck with respect to the base, and grip height, width, length, span, and angle of curvature. Understanding relationships between these parameters is also valuable in designing hooking elements. Ratios between geometric parameters of fruit hooks have been found to greatly influence separation force [4]. Before settling on a hooking element geometry however, one must first consider the mating surface with which it will engage.

The structure of the mating surface is the primary constraint on the design of the hooking elements as it limits hooking element design. In the case of a loop mating surface, the hooking elements are constrained by how far the loops protrude from the mating surface substrate, as well as by the strength, number, and organization of the loops. Loop surfaces are often knitted [116118], woven [69,119122], or laminate [123127]. While there has been progress improving the loop design to engage with hooking elements [67,72,113,117,125,129,131141], there has been greater focus on improving hook designs to secure loop elements. For example, increasing the number of grips to catch more loops [70,79,82,84,85,87,94,114,141143] adding variable heights to hooking elements to secure longer and shorter loops [69,141,144], and even combining hooks and loops onto a single fastener surface [145], are some of the strategies devised to enhance a hooking surface's ability to catch and secure connections on the loop surface.

3.2 Choosing a Material and Method of Manufacturing.

When selecting materials and methods of manufacturing, it is important to consider the purpose of the probabilistic mechanical fastener. Since these fasteners are required to maintain a secure contact after repeated use, materials that offer both sustained strength and flexibility are ideal. Common manufacturing and material combinations for probabilistic mechanical fasteners are shown in Table 3. The early probabilistic fasteners were woven from natural fibers or nylon [10,69,119,161,162] and introduced the manufacturing method of cutting woven loop elements to form hooking elements [10,69,119,121,128,161,163,164]. To achieve high strength without the risk of brittleness, hooking elements made of steel have been manufactured using die cutting [146,147], laser cutting [12], and shape deposition [11,15,38]. In fabrication processes such as extrusion, elastic polymers including thermoplastics are utilized, because they maintain their material properties after melting and can solidify into the desired fastener geometry. Thermoplastics are also popular because they are thought to reduce skin irritation of hooking elements [86,95,160], reduce fastener noise [109,165] and perform better under intense heat when made from flame-retardant polymers [104]. For performance under a broader range of extreme temperatures, smart materials have been proposed for several probabilistic fastener designs [13,98,166]. One manufacturing application which has not been utilized for probabilistic mechanical fasteners is 3D printing. Future designs could investigate using additive manufacturing technologies to create novel probabilistic mechanical fasteners from the macrodown to the nano-and submicron scales [167].

Table 3

Methods for manufacturing and materials for probabilistic mechanical fasteners

Manufacturing methodMaterial
Die cutting•  Stainless steel 1.421 [146]•  thermoplastics [147]
Photonic Professional CT system nanoscribe GmbH•  IP-S photoresist (Nanoscribe GmbH) [14]
Shape deposition manufacturing•  High speed steel [15]•  Hardened steel [11,38]
Molding•  Shape memory alloy NiTi [13,98]•  Foam [149]•  Resin [105,150152]•  Nylon 66 [114]•  Thermoplastic [91,103, 106, 108,153]
Extrusion•  Thermoplastics [88,94,97,148,189]•  Polypropylene [155]•  Polyethylene [155]•  Shape memory plastics [156]•  Resin [105,157]•  Silicones [148,149]
Weaving/knitting•  Thermoplastics [120,159,160]•  Nylon 6 [121]•  Natural fibers [106]
Casting•  Silicones [148,149]•  Polymers [158]
Lamination/embossing•  Thermoplastics [127,142,161]
Manufacturing methodMaterial
Die cutting•  Stainless steel 1.421 [146]•  thermoplastics [147]
Photonic Professional CT system nanoscribe GmbH•  IP-S photoresist (Nanoscribe GmbH) [14]
Shape deposition manufacturing•  High speed steel [15]•  Hardened steel [11,38]
Molding•  Shape memory alloy NiTi [13,98]•  Foam [149]•  Resin [105,150152]•  Nylon 66 [114]•  Thermoplastic [91,103, 106, 108,153]
Extrusion•  Thermoplastics [88,94,97,148,189]•  Polypropylene [155]•  Polyethylene [155]•  Shape memory plastics [156]•  Resin [105,157]•  Silicones [148,149]
Weaving/knitting•  Thermoplastics [120,159,160]•  Nylon 6 [121]•  Natural fibers [106]
Casting•  Silicones [148,149]•  Polymers [158]
Lamination/embossing•  Thermoplastics [127,142,161]

Note: Since the potential applications of probabilistic fasteners are influenced by material compositions and manufacturing methods, it is beneficial to spend time considering material/manufacturing combinations which result in the desired fastener behaviors. For example, probabilistic fasteners which require strong hooking elements are suited for steel materials and can be manufactured using die cutting or shape deposition. On the other hand, more flexible probabilistic fasteners can be made from a variety of polymers and manufacturing methods.

3.3 Probabilistic Fastener Traits and Design Trade-Offs.

Depending on design choices such as element geometry, material, and method of manufacturing, there are at least eight key traits that vary among probabilistic mechanical fasteners. As seen in Fig. 8, these traits vary and combine in distinct ways across artificial and biological probabilistic mechanical fasteners. For the scoring used in Fig. 8, see Table 4. Here we discuss these traits and the corresponding design trade-offs for probabilistic mechanical fasteners.

Fig. 8
Traits comparison among artificial and biological probabilistic mechanical fasteners. There is a wide variety of artificial and biological fasteners with structures and materials suited to unique functions. (a) In general, artificial fasteners (i)–(iv) are more ordered and have a higher force of detachment compared to biological fasteners. (b) Many biological fasteners (i)–(iv) are less ordered so that they can interact with a wider range of surfaces in their environment as seen in seed and fruit hooks [4,10,24,39] and parasitic worms [17]. However, biological fasteners can also be highly specialized to engage with a specific surface, such as the dragonfly head arrester system [21] and microstructures engaging between overlapping flight feathers of many birds, such as Columbia livia (Fig. 5; [25]). There are unique traits that are only found in biological fasteners, which include directionality and associated minimal sound to fasten and detach (although fastener failure can still be as noisy as classical hook-and-loop fasteners). Comparing common fastener traits such as force to release, reusability, and element complexity gives insight in trade-offs between fastener function, structure, and material. Understanding how function, structure, and material determine fastener traits is a key step towards novel designs. A table with the criteria used to score the traits can be found in Table 4.
Fig. 8
Traits comparison among artificial and biological probabilistic mechanical fasteners. There is a wide variety of artificial and biological fasteners with structures and materials suited to unique functions. (a) In general, artificial fasteners (i)–(iv) are more ordered and have a higher force of detachment compared to biological fasteners. (b) Many biological fasteners (i)–(iv) are less ordered so that they can interact with a wider range of surfaces in their environment as seen in seed and fruit hooks [4,10,24,39] and parasitic worms [17]. However, biological fasteners can also be highly specialized to engage with a specific surface, such as the dragonfly head arrester system [21] and microstructures engaging between overlapping flight feathers of many birds, such as Columbia livia (Fig. 5; [25]). There are unique traits that are only found in biological fasteners, which include directionality and associated minimal sound to fasten and detach (although fastener failure can still be as noisy as classical hook-and-loop fasteners). Comparing common fastener traits such as force to release, reusability, and element complexity gives insight in trade-offs between fastener function, structure, and material. Understanding how function, structure, and material determine fastener traits is a key step towards novel designs. A table with the criteria used to score the traits can be found in Table 4.
Close modal
Table 4

Reference for scoring traits in Fig. 8 

Trait012345
Force to ReleaseCompletely passiveOrder at or below 10 × 10−5 NOrder of 10 × 10−4 NOrder of 10 × 10−3NOrder of 10 × 10−2 NOrder of 10 N
ReusabilityOne time use before permanent damageFew uses before permanent damageAll structures prone to damage from repetitionReusable but has structures prone to damage from RepetitionMany uses with small degree of damageMany uses with very little damage
# Mating SurfacesNo mating surfacesOne Mating surfaceOne main mating surface but can interact with other surfacesSeveral main mating surfaces but can interact with other surfacesInteracts with specific randomly encountered surfacesInteracts with wide variety of randomly encountered surfaces
Element complexityStem based fastener elementsj-based fastener elementsCapped fastener elementsMultiple grips on single fastener elementMultiple grips and different orientations of fastenersHierarchical fastening elements with different geometries
# Fastener ElementsNo individual fastener elementsVery Few fastener elements totalFew fastener elements totalSeveral fastener elements totalMany fastener elements totalField of many fastener elements on each mating surface
Degree of OrderNo discernable structure or fastening elementsTwo fastening surfaces with no set orientations/geometriesOne fastening surface with set geometryOne patterned fastening surfaceTwo patterned fastening surfaces with some variabilityTwo Artificially patterned fastening surfaces
DirectionalityNo directionalityStructures engage under all directionsStructures engage under almost all directionsStructures engage in many directionsStructures engage in up to three directionsStructures designed to only engage in a certain direction
Sound to fix/detachNo detectable soundDetectable soundDetectable and somewhat audible soundClearly audible soundHigh audible soundHighest reported sound in literature for probabilistic fasteners
Trait012345
Force to ReleaseCompletely passiveOrder at or below 10 × 10−5 NOrder of 10 × 10−4 NOrder of 10 × 10−3NOrder of 10 × 10−2 NOrder of 10 N
ReusabilityOne time use before permanent damageFew uses before permanent damageAll structures prone to damage from repetitionReusable but has structures prone to damage from RepetitionMany uses with small degree of damageMany uses with very little damage
# Mating SurfacesNo mating surfacesOne Mating surfaceOne main mating surface but can interact with other surfacesSeveral main mating surfaces but can interact with other surfacesInteracts with specific randomly encountered surfacesInteracts with wide variety of randomly encountered surfaces
Element complexityStem based fastener elementsj-based fastener elementsCapped fastener elementsMultiple grips on single fastener elementMultiple grips and different orientations of fastenersHierarchical fastening elements with different geometries
# Fastener ElementsNo individual fastener elementsVery Few fastener elements totalFew fastener elements totalSeveral fastener elements totalMany fastener elements totalField of many fastener elements on each mating surface
Degree of OrderNo discernable structure or fastening elementsTwo fastening surfaces with no set orientations/geometriesOne fastening surface with set geometryOne patterned fastening surfaceTwo patterned fastening surfaces with some variabilityTwo Artificially patterned fastening surfaces
DirectionalityNo directionalityStructures engage under all directionsStructures engage under almost all directionsStructures engage in many directionsStructures engage in up to three directionsStructures designed to only engage in a certain direction
Sound to fix/detachNo detectable soundDetectable soundDetectable and somewhat audible soundClearly audible soundHigh audible soundHighest reported sound in literature for probabilistic fasteners

Note: Figure 8 compares several probabilistic fastener traits between biological and artificial designs including: force to release, reusability, # of mating surfaces, element complexity, # of fastener elements, degree of order, directionality, and sound to fix/detach. This table provides the reasoning behind the scoring for each probabilistic fastener trait on a scale of 0 to 5.

3.3.1 Fastener Release Force.

The force required to release a mated fastener determines both the strength of attachment and the ease of detachment. In general, individual hooking elements made of engineering materials are stronger than their biological counterparts. The two strongest hooking elements for fasteners reported in the literature are microspines [15] and Metaklett hooks [146] which are both made from steel, see Fig. 9. In addition to material selection, the strength of the attachment can be increased by increasing the friction between fastening elements [171], optimizing element geometry, and increasing the scale of the hooking elements. The downside to increasing the strength of the attachment is that the ease of release is lost, see Fig. 8. Higher force to release could limit applications and potential end-users. Furthermore, increasing the hooking elements' stiffness and strength also increases their potential to damage surfaces they are not designed to mate with, such as human skin and clothing.

Fig. 9
Reported force at failure for single hooking elements in artificial and biological probabilistic fasteners across seven orders of magnitude in length. This figure presents reported values on the maximal force per hooking element for seven artificial fasteners represented by blue markers and seven biological fasteners represented by green markers. The gecko setae was not included in the linear fit but is shown for reference in gray [3]. Although the Carbon Nanotubes are at a scale where van der Waals forces become a factor [168], they were included in the fit as they are the smallest scale fastener utilizing hooking found in a search of the literature. The four artificial bio-inspired designs include the hook-and-loop [169], microspine [11], and two galium aparine leaf inspired fasteners [14]. The majority of biological data comes from analysis of leaf, seed, and fruit hook fasteners. The weak power law fit is partly due to the microspine outlier which outperforms the scaling law by a significant factor for its scale. The biological avatars were hand drawn. Artificial avatars were modified after and printed with permission from Sage Publications Inc. Journals [11], Trans Tech Publications, LTD [146], with permission of Springer [169], and the American Physical Society [170].
Fig. 9
Reported force at failure for single hooking elements in artificial and biological probabilistic fasteners across seven orders of magnitude in length. This figure presents reported values on the maximal force per hooking element for seven artificial fasteners represented by blue markers and seven biological fasteners represented by green markers. The gecko setae was not included in the linear fit but is shown for reference in gray [3]. Although the Carbon Nanotubes are at a scale where van der Waals forces become a factor [168], they were included in the fit as they are the smallest scale fastener utilizing hooking found in a search of the literature. The four artificial bio-inspired designs include the hook-and-loop [169], microspine [11], and two galium aparine leaf inspired fasteners [14]. The majority of biological data comes from analysis of leaf, seed, and fruit hook fasteners. The weak power law fit is partly due to the microspine outlier which outperforms the scaling law by a significant factor for its scale. The biological avatars were hand drawn. Artificial avatars were modified after and printed with permission from Sage Publications Inc. Journals [11], Trans Tech Publications, LTD [146], with permission of Springer [169], and the American Physical Society [170].
Close modal

3.3.2 Degree of Order and Number of Mating Surfaces.

The degree of order in a fastener is described by the spatial arrangement and orientations of fastening elements relative to each other and to the engaging surface. Probabilistic mechanical fasteners in industry tend to be more ordered than those found in nature, see Fig. 8. The evolution of burdock seeds hooking to a wide range of animal furs for seed dispersal exemplifies how it is beneficial to have a fastener with a high degree of disorder to reduce the need for attachment precision and increase the likelihood of attachment [18,22,48,49]. Whereas having two patterned and predetermined surfaces limits the available interaction surfaces, it effectively guarantees successful surface mating (see Figs. 2 and 3), because each element in the array is designed to engage with the mating surface [18,22,48,49,169]. For such predetermined fasteners, self-mating surfaces tend to have the most ordered elements while hook-and-loop fasteners are more disordered, as seen in Fig. 8.

3.3.3 Directionality.

Most probabilistic mechanical fasteners engage when the hooking and mating elements are brought into close contact; attachment is regardless of the relative motion of each surface with respect to the other, provided that their surfaces are in contact. However, in the new category of directional probabilistic fasteners we review here, the attachment is dependent upon the direction of relative movement and corresponding applied contact force. This directionality is determined by the geometry and relative orientations of the fastening elements, see Fig. 5 for an example. This requires a patterned fastener geometry that repeats across the array, of which the hooking action of each element is reversable and sufficiently aligned across all elements. Directional fasteners based on few hooking elements are found in front-hind wing interlocking mechanisms in insect [47,48,50] and between thousands of hooking elements between the overlapping flight feathers of birds [26], see Fig. 5. To our knowledge, there are currently no engineered directional artificial probabilistic mechanical fasteners. These fasteners have a particularly easy release, see Fig. 8, as disengagement only requires removal of force in the loading direction, or a displacement in any direction other than the attachment direction. Difficulties in designing for directionality include the more constrained microgeometries and alignment precision required across all micro-elements.

3.3.4 Durability.

One of the main attributes of probabilistic fasteners is durability, or the ability to repeatably perform for long periods of time under a variety of conditions. However, there are conditions which can be challenging for certain probabilistic fastener designs. Hook-and-loop fasteners, for example, are notorious for failing under conditions where dirt or lint are introduced [172]. While some fastener materials lack durability under very high or low temperatures, smart materials have been shown to improve fastener performance under extreme temperatures [13,98,160]. An area where durability has yet to be thoroughly improved for probabilistic mechanical fasteners is enhancing performance in wet and or chemical environments. For repeatable fastener applications, improved durability is key to increasing fastener lifespan and broadening applications.

3.4 Modelling and Simulation of Probabilistic Mechanical Fasteners.

Modelling and simulations of probabilistic mechanical fasteners inform design choices by predicting modes of failure. Probabilistic mechanical fasteners tend to fail in strength or stiffness and can be examined analytically using small stress–strain beam equations. Figure 10 provides an overview of the different failure modes for a hooking element modeled as a curved cantilever beam. Failure in strength has been examined for both hooking and asperity mating elements: hooking elements primarily fail under tensile and shear stress and asperity elements fail when the applied pressure exceeds their ultimate strength [11]. Failures in stiffness for hooking elements include excessive tip rotations and plastic deformations [11]. Whether modelling stiffness or strength of a fastener element, there are several variables which must be identified for the modeling framework including: operating limits of key variables (angles for tip rotation, usable asperity slopes, angles of applied load, magnitude of applied load, etc.), material properties such as Young's modulus, and type of applied load (e.g., tensile, shear, bending).

Fig. 10
Determination of hooking element failure modes based on classic cantilever beam models. Cantilever beams are used to examine hooking element failures. (a) A cantilever beam model is described with a coordinate reference system, geometric parameters such as radius of curvature and thickness/diameter, and by the applied loads. There are three modes by which a hooking element contact may fail including: (b) Failure in stiffness where the hooking element displaces at a critical angle that allows the mating element to slip away. (c) Failure in strength where the applied load results in a crack or break when a max stress is reached, causing mating element detachment, and (d) failure in the strength or stiffness of a mating structure. Blue indicates loads relevant to a model for a random asperity mating surface (such as bio-inspired spines) and red indicates loads for patterned mating surfaces (such as loop or self-mating surfaces). Drawings modified after and printed with permission from Sage Publications Inc. Journals [11].
Fig. 10
Determination of hooking element failure modes based on classic cantilever beam models. Cantilever beams are used to examine hooking element failures. (a) A cantilever beam model is described with a coordinate reference system, geometric parameters such as radius of curvature and thickness/diameter, and by the applied loads. There are three modes by which a hooking element contact may fail including: (b) Failure in stiffness where the hooking element displaces at a critical angle that allows the mating element to slip away. (c) Failure in strength where the applied load results in a crack or break when a max stress is reached, causing mating element detachment, and (d) failure in the strength or stiffness of a mating structure. Blue indicates loads relevant to a model for a random asperity mating surface (such as bio-inspired spines) and red indicates loads for patterned mating surfaces (such as loop or self-mating surfaces). Drawings modified after and printed with permission from Sage Publications Inc. Journals [11].
Close modal

The most readily available tool for multiphysics structural performance simulation is the finite element method (FEM) [13,146,166,173,174]. However, before simulating a probabilistic fastener design, there are several limitations which must be considered. A key limitation is the statistical variation in the microstructure and molecular properties of a single fastener element [175,176]. For general design purposes, these variations can be ignored and bulk material properties and geometries assumed for a quantitative analysis given that the continuum assumptions hold. For smaller scale structures, the outcomes can only be considered qualitative unless validated by experimentation [177180]. Another simulation challenge for probabilistic fasteners is the long computation time. Probabilistic fasteners are made up of a vast number of elements that fall within a broad scale range from the individual microshaped elements to the macroscale array. This limitation could be resolved by course-graining the fully resolved fastener model to predict macrofastener-level behavior; however, such models have yet to be developed for fastener simulation. We thus consider commonly used analytical continuum and FEM models for (sufficiently large) hooking and mating elements that fail in strength and stiffness.

3.4.1 Modelling Failures in Strength.

For probabilistic fastener elements, failures in strength appear as fractures and cracks and can be attributed to stress concentrations exceeding ultimate strength under applied loads. Models for failures in strength of hooking elements are found in Table 5; a visual reference for failure in strength of a cantilever beam is shown in Fig. 10. Hooking elements tend to reach their ultimate strength under tensile and shear loads. Failures from tensile stress have been modelled as cantilever beams where the max stress occurs at the base of the hooking element [11]. A more complicated model which includes the nonlinear behavior of a hook modeled as a curved beam can be used to find the max attachment force [37]. While hooking elements engaging with predetermined loops, self-mating structures, and random environmental surfaces all experience tensile loads, shear loads are more prominent in hooking elements engaging with a random asperity surface. Shear stress occurs at sharp tip of a hooking element as it is pulled across an asperity surface and can cause the tip to break and become increasingly dull [16]. Failures in strength have also been studied in asperity mating elements where max pressure exceeds the ultimate strength and the asperity itself breaks from the mating surface [11].

Table 5

Expressions for failure in strength of hooking and asperity mating elements

ModelEquationVariables
Cantilever beam [11]
(12)
δmax: max stressM: momentc: distance from neutral axisI: second moment of area
Shear stress at hook tip [16]
(13)
Fr: applied load d(y): hook cross-sectional diameter at loading position y
Asperity failure [11]
(14)
Pmax: max pressuref: normal force applied to hook/asperity contactα: radius of contact patch
Compliant hook [37]
(15)
Fh: maximum attachment forceφ: friction angle between hook and substrateR: hook radius of curvatureE: Young's modulusI: second moment of area
ModelEquationVariables
Cantilever beam [11]
(12)
δmax: max stressM: momentc: distance from neutral axisI: second moment of area
Shear stress at hook tip [16]
(13)
Fr: applied load d(y): hook cross-sectional diameter at loading position y
Asperity failure [11]
(14)
Pmax: max pressuref: normal force applied to hook/asperity contactα: radius of contact patch
Compliant hook [37]
(15)
Fh: maximum attachment forceφ: friction angle between hook and substrateR: hook radius of curvatureE: Young's modulusI: second moment of area

Note: One of the failure modes for probabilistic fastener elements is failure in strength for both hooking elements and asperities for the case of a random asperity mating surface. Here we show equations for determining loads which could be used as limiting factors when examining fastener failures in strength. Equations (12), (13), and (15) examine failures in hooking elements under applied loads while Eq. (14) examines asperity failure under loading.

3.4.2 Modelling Failures in Stiffness.

When a hooking element is elongated beyond its operating limit, it fails in stiffness. Relevant stiffness failure models and equations are found in Table 6; a visual reference of examining stiffness failure in a cantilever beam is found in Fig. 10. The failure in stiffness can be plastic or elastic. For elastic failures, there have been several approaches to describe the displacement and rotation of the hook tip at the moment it loses contact with the mating element [11,37,169]. Tip rotation of a hooking element has been examined using small stress–strain equations for models of a single curved beam [11] and for two cantilever beams where the stem and base are represented by one beam and the grip is represented by the other [169]. Small stress–strain equations are also used to find the deflection at which the connection between capped mushroom hooks are released under load [169]. Hook rotation and displacement has further been modeled using nonlinear mechanics [39]. This nonlinear model has been applied to the study of fruit hooks [39]. While there are varying levels of complexity in these approaches, the general model for hooking elements is a cantilever beam in bending which is also utilized in FEM simulations for probabilistic mechanical fasteners.

Table 6

Expressions for failure in stiffness of hooking elements

ModelEquationVariables
Curved beam [11]
(16)
α: end rotationU: strain energy in the beamM: end momentE: young's modulusI: second moment of areaβ: angle from the y-axis to the tip of the hookFx: force component in x directionFy: force component in y direction
Two cantilever beams [169]
(17)
Φ1,Φ2,Φ3: rotations at root, tip, and contact pointP: applied loadE: young's modulusI: second moment of areah: length of stemw: horizontal distance from stem to point of applied loadk: rotational stiffness of hook rootφ: initial angle from tip to horizontalλ: friction angle between hook and loop surfacesψ: angle from applied load to shaft of stem
Mushroom hooks [169]
(18)
δ: displacementP: applied forceh: height of mushroom stemrc: radius of mushroom capE: young's modulusI: second moment of area
Compliant hook [37]
(19)
F: applied forceδ(F): vertical displacementu(F): displacementvc(F): contact angle
ModelEquationVariables
Curved beam [11]
(16)
α: end rotationU: strain energy in the beamM: end momentE: young's modulusI: second moment of areaβ: angle from the y-axis to the tip of the hookFx: force component in x directionFy: force component in y direction
Two cantilever beams [169]
(17)
Φ1,Φ2,Φ3: rotations at root, tip, and contact pointP: applied loadE: young's modulusI: second moment of areah: length of stemw: horizontal distance from stem to point of applied loadk: rotational stiffness of hook rootφ: initial angle from tip to horizontalλ: friction angle between hook and loop surfacesψ: angle from applied load to shaft of stem
Mushroom hooks [169]
(18)
δ: displacementP: applied forceh: height of mushroom stemrc: radius of mushroom capE: young's modulusI: second moment of area
Compliant hook [37]
(19)
F: applied forceδ(F): vertical displacementu(F): displacementvc(F): contact angle

Note: Another failure mode for probabilistic fastener elements is failure in stiffness. Understanding limits of stiffness for fastening elements can provide limits for fastener designs. Limits of stiffness are described in Eqs. (16)(19) in terms of hooking element displacements and rotations. In Eqs. (16) and (17), we reference cantilever beam equations which define rotations of the hooking elements under an applied load. Equation (18) references the special case of displacement in mushroom shaped hooks under applied loads and Eq. (19) examines displacement in a compliant hook.

3.4.3 Finite Element Method Simulations.

Simulations complement analytical models by examining stress concentrations and deformations throughout the loading process of a hooking element. To approximate the behavior of the hooking element, beam models are used in FEM simulations [13,166]. Material properties can be assumed homogeneous or composite modelling can be used if the material is more complex, as in the case of biomaterials such as cellulose [13,98,181]. Before applying the load, the boundary conditions of the model are defined with a fixed boundary condition at one end and a free end where the load is applied. Stroke, or hook elongation, is measured as the distance from the loading point to the fixed point. Applied load plotted against stress and hook stroke can reveal the points at which the hooking element begins to yield and ultimately fails under a maximum load [13,146]. FEM simulations can also be used to optimize hooking element geometry for a given load using a parameter study [146]. In most cases, the sequence of starting with a joined fastener pair and breaking the connection is sufficient, although behavior for rejoining a broken fastener has also been examined [146]. The results of a simulation or analytical models require validation via experimental testing, especially for micro-and nanoscale fastening elements

3.5 Mechanical Testing of Probabilistic Fasteners.

The success of a probabilistic fastener is generally defined by its ability to maintain static attachment under loading and dynamically for application of a load over many cycles. For fasteners and adhesives in general, these tests include peel tests, tensile detachment tests, pull out/pull off tests, single fiber fragmentation tests, torsion tests, and blister tests [182]. The appropriate test is determined by the type of adhesive, fiber orientation, and structure of the fastening elements. For probabilistic mechanical fasteners, tests to evaluate performance include peel tests, friction tests, pull off/pull out tests, noise generation tests, and stress–strain analyses. Descriptions of some of these tests are shown in Fig. 11. When comparing fastener performance test outcomes, the effect of variables such as relative size, strength, and material choice need to be corrected for.

Fig. 11
Common mechanical tests to evaluate the performance of probabilistic fasteners. (a) 90-degree peel test applies a force normal to the cross- sectional area and increases the angle of application until all fastener elements have disengaged [169]. Note the force angle starts at 0-degrees and gradually increases to 90-degrees in this test. (b) The T peel test applies force to both mating surfaces and is not constrained by a rigid substrate [13,183]. (c) Shear peel test is applicable to directional fasteners, pulling the fastener elements in shear until they reach a critical force and disengage [183]. (d) The slip off test examines the force and angle at which a loop element loses connection with the hooking element and while the pull-out test examines the force and angle at which a hooking element is pulled out of its substrate [4,13,24,49,54,58,98,146]. (e) In the friction test, the hooking element is pulled across a surface with a random asperity distribution. A rise in the loading force pulling the hook across the surface identifies the instance when that the hooking element engages with an asperity and resists the pull of the loading force [11,13,24]. Drawings modified after [183] and printed with permission from and The Royal Society of Chemistry. Drawings modified and printed with permission from Sage Publications Inc. Journals [11] and with permission of Springer [169].
Fig. 11
Common mechanical tests to evaluate the performance of probabilistic fasteners. (a) 90-degree peel test applies a force normal to the cross- sectional area and increases the angle of application until all fastener elements have disengaged [169]. Note the force angle starts at 0-degrees and gradually increases to 90-degrees in this test. (b) The T peel test applies force to both mating surfaces and is not constrained by a rigid substrate [13,183]. (c) Shear peel test is applicable to directional fasteners, pulling the fastener elements in shear until they reach a critical force and disengage [183]. (d) The slip off test examines the force and angle at which a loop element loses connection with the hooking element and while the pull-out test examines the force and angle at which a hooking element is pulled out of its substrate [4,13,24,49,54,58,98,146]. (e) In the friction test, the hooking element is pulled across a surface with a random asperity distribution. A rise in the loading force pulling the hook across the surface identifies the instance when that the hooking element engages with an asperity and resists the pull of the loading force [11,13,24]. Drawings modified after [183] and printed with permission from and The Royal Society of Chemistry. Drawings modified and printed with permission from Sage Publications Inc. Journals [11] and with permission of Springer [169].
Close modal

3.5.1 Peel Tests.

The peel test is one of the most common tests used to evaluate probabilistic fasteners, because it is their primary method of disengagement. The peel test is performed by applying a force normal to the cross-sectional area of the fastener and gradually increasing the angle at which the force is applied [169], see Fig. 11 panel (a). Measurements of interest for this test include plotting the force versus the peel angle to find the critical angle and plotting the peel strength versus the number of peeling cycles [184]. Variations of the peel test have been developed to examine fastener performance [13,169,182,183].

In the standard peel test, the fastener half with hooking elements is adhered to a piece of tape and peeled from the mating surface, which is fixed to a rigid substrate [169]. The peel force and peel angle are related using Eq. (20) [169] where P is the peel force, b is the tape width, Ga is the energy required to de-adhere a unit area of bond, and θ is the peel angle:
(20)

Another variation is the T peel test, see Fig. 11 panel (b), where both the hooking and mating surfaces flex as they are peeled apart [13]. In a shear peel test, see Fig. 11 panel (c), a shear force is applied to each mating surface and could potentially be adapted to analyze new directional fasteners [183].

3.5.2 Friction Test.

A friction test identifies the engagement of hooking elements with a mating surface. This test is performed by dragging the hooking element surface across the complementary mating surface and measuring the force versus distance [13,24], see Fig. 11 panel (e) for a reference. Sudden force peaks reveal instances where hooking elements are engaged with the mating surface and an increase of force is required to disengage the elements. The critical angle up to which friction prevents sliding of the hooked microstructures is the friction angle and can be determined experimentally [13]. This particular test has previously been used to demonstrate the ability of leaf hooks to engage loop elements [24].

3.5.3 Pull Out and Slip Off Tests.

The pull out test, see Fig. 11 panel (d), is a destructive test which applies a tensile force to individual hooking elements to determine the max force and corresponding displacement at which the elements are removed from their substrate [4,13,24,39,58,98,146]. A general distinction from a peel test is that a pullout test has a rigid substrate while a peel test has a flexible substrate [13]. The hooking elements can also be removed from their natural substrate and glued to a more rigid substrate to examine changes in pull out behavior [39]. Pull out tests have been used to compare pull out force between different species of fruit hooks [4], to confirm capacity of metal hooking elements [146], and to examine contact separation dependence on hooking element morphology [58].

Slip off tests examine the max tensile force at which a hooking element gives way and allows a loop element to be released. The slip off, or unhooking event, is monitored by pulling the fastening elements apart along a prescribed axis line while measuring the pulling force. The pulling force is stopped at the event of unhooking, which is characterized by a sharp drop in the pulling force [98]. Finally, the force at slip off is impacted by the application of tensile forces under different angles at various locations along the hooking element as well as by changes in the morphology of the hooking element [24].

3.5.4 Noise Generation Spectral Analysis.

A noise generation spectral analysis test determines the level of noise generation during fastener detachment. Creating a fastener that is quiet compared to typical hook-and-loop fasteners for everyday use has first responder, police, and military applications [185] as well as increasing auditory comfort. Design solutions to achieve a silent fastener include avoiding a peeling detachment [165] and using shape memory polymers [108]. A spectral analysis of a NiTi hook array and Klettostar Velcro© measured noise generation during a 90-deg peel test and found the NiTi hook array to be quieter [13]. A spectral analysis of an adhesive closure revealed that it was also more silent then the hook-and-loop fastener [186]. However, there remains work to be done in developing more silent probabilistic mechanical fastener. Recently, this test was performed to failure in the newly discovered directional probabilistic fasteners in bird feathers [25]. Bio-inspired design based on the flight feather fastening mechanism (Fig. 5), may facilitate silent fasteners.

3.5.5 Additional Performance Tests and Evaluations.

Additional performance tests and evaluations have been developed to examine failures for specific probabilistic mechanical fasteners. For example, damage from repeated cycles on hook-and-loop fasteners can be revealed through imaging [186]. The durability for hook-and-loop fasteners has further been examined by analyzing performance under increasing concentrations of lint [184]. For probabilistic fasteners made of smart materials, stress-strain analyses have examined performance under varying temperatures [166] and under functional fatigue [13]. Functional fatigue tests have also been used to examine probabilistic mechanical fasteners made of steel and include dynamic, quasi-static, and alternating static and dynamic loads [146]. After loading, measurements of the deformed steel hooks can be taken using a tactile contour measurement [146] and the strength of the joining connections can be measured using a cross tension test [146]. The choice of performance test will depend on the geometry, material, and application of the fastener.

3.6 Design Benchmark: Force at Failure for Hooking Elements.

To aid in the evaluation of a probabilistic mechanical fastener design, we present a trend between the scale of the hook's grip and the max force per hooking element for a spectrum of biological, artificial, and bio-inspired probabilistic mechanical fasteners. As seen in Fig. 9, the scale of the hook's grip spans from carbon nanohooks [170] at the nm range to Metaklett [146] at the mm range. The associated forces in Fig. 9 vary from nN for carbon nanohooks [170] to the order of 10 N for microspines [15] and Metaklett [146]. Between the microspines and Metaklett, the microspines could be considered higher performing based on the smaller scale of its gripping element sustaining similar magnitudes of force. The bio-inspired hooking elements shown in Fig. 9 are microspines [15], Galium aparine inspired hooks [14], and the burdock seed inspired hook-and-loop fastener [169]. When comparing a design with the scale and max force of existing probabilistic mechanical fasteners, it is important to also consider factors such as material, mode of engagement (e.g., directionality), and the structure of the mating surface. Finally, a caution for examining hooks at the nm level is that van der Waals forces play a role at this scale [168].

Another potential metric that could be used to evaluate and compare fasteners is examining the load at which fastener elements develop cracks. While the literature has focused on fastening element failure due to slip or catastrophic failure in strength, more insight into fastener design could be gained by studying the loads at which cracks first appear and propagate in fastener elements. Fracture energy has been studied in biological composites such as shells, bones, and enamel, whose elementary units, mineralized fibrils, are structured to optimize stiffness and toughness [187]. The complex hierarchy of biological composites maximizes adhesion as well as flaw tolerance in the overall composite and in the individual fibers [59,187]. However, there is a limit at which levels of hierarchy increase adhesion strength and protect from crack formation, as described in a gecko inspired model based on van der Waals forces [59]. As more hierarchical levels of fibers are added, eventually the model reaches a point where fiber fracture becomes the dominant failure mode of the system level. The limiting hierarchical level is found by determining the fibril level at which the maximum tensile stress that the cracked fibers can sustain is greater than the adhesion strength of the system as shown by the following equation [59]:
(21)

Here Ef is the Young's modulus of the fiber, Rn is the radius of the fiber at level n, a is the crack radius, g is a geometric parameter, and Γf is the fracture energy of the fiber. The limiting factor is σnmax > Sn, where Sn is the adhesion strength [59]. To our knowledge, there is currently no artificial or bio-inspired hierarchical fastener. Using the limiting factor, σnmax as described in Eq. (21), and the principle of a limiting hierarchical level, more complex hierarchical fastener designs may be developed.

4 Applications and Opportunities

4.1 Current Areas of Application and Opportunities.

Probabilistic mechanical fasteners are particularly useful for applications which benefit from secure, repeatable, flexible attachments that require little skill. These versatile traits make probabilistic mechanical fasteners appropriate for a variety of applications. However, when choosing a fastener for a specific application, it is helpful to first compare it to other attachment technologies and determine which technology best fulfills the application requirements. In Table 7, we present a comparison of different attachment technologies to clarify when a probabilistic mechanical fastener may be appropriate over other technologies [188]. As seen in Fig. 12, fields where the probabilistic mechanical fasteners particularly flourish include medicine, apparel, storage and transportation, and robotics.

Fig. 12
Applications of mechanical probabilistic fasteners and opportunities to implement underutilized characteristics. The strong, repeatable, and reconfigurable attachments of probabilistic fasteners make them relevant to a wide variety of applications. (a) The major application areas for mechanical probabilistic fasteners are the medical, apparel, storage and transportation, and robotics fields. In each of these (and other) fields there are opportunities to improve current fastener performance and to introduce underutilized characteristics to innovate the fastener design. (b) Taking the field of robotics as an example, key applications including climbing, grasping, perching, and take off/landing all utilize the traits of high probability, strong, and repeatable probabilistic mechanical fasteners that require minimal kinematic interaction precision. Adding a novel characteristic to these probabilistic mechanical fasteners, such as directionality could advance climbing and grasping performance, while designing patterned mating surfaces for perching and takeoff/landing could provide more stability. Finally, introducing silent fastening into robotics could further improve the customer experience during human- robot interactions and enhance the overall stealth of a robot's locomotion in covert operations. Images were adapted and printed with permission from ASME[189].
Fig. 12
Applications of mechanical probabilistic fasteners and opportunities to implement underutilized characteristics. The strong, repeatable, and reconfigurable attachments of probabilistic fasteners make them relevant to a wide variety of applications. (a) The major application areas for mechanical probabilistic fasteners are the medical, apparel, storage and transportation, and robotics fields. In each of these (and other) fields there are opportunities to improve current fastener performance and to introduce underutilized characteristics to innovate the fastener design. (b) Taking the field of robotics as an example, key applications including climbing, grasping, perching, and take off/landing all utilize the traits of high probability, strong, and repeatable probabilistic mechanical fasteners that require minimal kinematic interaction precision. Adding a novel characteristic to these probabilistic mechanical fasteners, such as directionality could advance climbing and grasping performance, while designing patterned mating surfaces for perching and takeoff/landing could provide more stability. Finally, introducing silent fastening into robotics could further improve the customer experience during human- robot interactions and enhance the overall stealth of a robot's locomotion in covert operations. Images were adapted and printed with permission from ASME[189].
Close modal
Table 7

Comparison of attachment technologies and suggested areas of application (adapted with minor changes from [204])

TechnologyBenefitsLimitationsSuggested applications
Suction– Strong, repeatable attachments on smooth surfaces– High level of noise during release of suction cups– Requires a smooth surface to operate efficiently– For robotics, a pump mechanism is needed to remove and engage suction cups for locomotion applications– Static attachments on smooth surfaces
Electro-adhesion– Can attach to variety of surfaces, including both smooth and rough surfaces– Requires little energy to power to release and engage the adhesion– Quiet release and attachment mechanism– Tolerates dust and cleaning– Requires a continuous power input to maintain an attachment– Robotics climbing and locomotion
Wet Adhesion– Strong attachment on variety of surfaces– Quiet release and attachment mechanism– High-energy cost to release the attachment– Needs an adequate supply of adhesive to draw from when forming a new attachment– May leave adhesive residue on the surface– Prolonged or indefinite static attachments on surfaces which allow for adhesive residue
Dry Adhesion– Little energy input needed to maintain attachments– Quiet release and attachment mechanism– Energy to release an attachment can be high– Peeling release mechanism can cause damage to individual fastening elements– Attachment is limited or impossible on surfaces which are dusty, wet, or made of certain plastics– Temporary static attachments and climbing on clean surfaces with a degree of roughness
Claws– Little energy input needed to maintain attachments– Impervious to dust or moisture on a variety of surfaces– Very high attachment strength– Unable to climb smooth surfaces– May cause puncture, scratches, or other damage to surface– High strength grasping of surfaces which allow for damage
Probabilistic mechanical fasteners– Reversible, repeatable, and durable attachments– Reliable: secure attachment achieved without a high level of precision or expert skill– Versatile: can be designed for high or low attachment forces, can attach to custom or random mating surfaces, may be quiet or loud, and can secure and release attachments through different mechanisms such as directional or peeling attachments– Surface asperities are necessary for climbing applications– Hooking elements may damage mating surface.– Release mechanism, such as a peeling detachment, may damage hooking elements– Attachment is inhibited by dust and or moisture– Consumer friendly applications– Indefinite static attachment– Repeatable and durable attachments– Directional attachments
TechnologyBenefitsLimitationsSuggested applications
Suction– Strong, repeatable attachments on smooth surfaces– High level of noise during release of suction cups– Requires a smooth surface to operate efficiently– For robotics, a pump mechanism is needed to remove and engage suction cups for locomotion applications– Static attachments on smooth surfaces
Electro-adhesion– Can attach to variety of surfaces, including both smooth and rough surfaces– Requires little energy to power to release and engage the adhesion– Quiet release and attachment mechanism– Tolerates dust and cleaning– Requires a continuous power input to maintain an attachment– Robotics climbing and locomotion
Wet Adhesion– Strong attachment on variety of surfaces– Quiet release and attachment mechanism– High-energy cost to release the attachment– Needs an adequate supply of adhesive to draw from when forming a new attachment– May leave adhesive residue on the surface– Prolonged or indefinite static attachments on surfaces which allow for adhesive residue
Dry Adhesion– Little energy input needed to maintain attachments– Quiet release and attachment mechanism– Energy to release an attachment can be high– Peeling release mechanism can cause damage to individual fastening elements– Attachment is limited or impossible on surfaces which are dusty, wet, or made of certain plastics– Temporary static attachments and climbing on clean surfaces with a degree of roughness
Claws– Little energy input needed to maintain attachments– Impervious to dust or moisture on a variety of surfaces– Very high attachment strength– Unable to climb smooth surfaces– May cause puncture, scratches, or other damage to surface– High strength grasping of surfaces which allow for damage
Probabilistic mechanical fasteners– Reversible, repeatable, and durable attachments– Reliable: secure attachment achieved without a high level of precision or expert skill– Versatile: can be designed for high or low attachment forces, can attach to custom or random mating surfaces, may be quiet or loud, and can secure and release attachments through different mechanisms such as directional or peeling attachments– Surface asperities are necessary for climbing applications– Hooking elements may damage mating surface.– Release mechanism, such as a peeling detachment, may damage hooking elements– Attachment is inhibited by dust and or moisture– Consumer friendly applications– Indefinite static attachment– Repeatable and durable attachments– Directional attachments

Note: In order to clarify the merit of probabilistic mechanical fasteners, we present a comparison between different attachment technologies. When designing a new attachment technology, it may be useful to consult this table and confirm which attachment technology is best suited for the desired application based on its benefits and limitations.

In the medical field, probabilistic fasteners are used to provide comfortable attachments for splints [164] and disposable garments [71,78,136,190192]. An additional medical application examined using an array of hooks from a hook-and-loop fastener for the bristles of a toothbrush [193]. In medical research, a biocompatible hook-and-loop type fastener was used to attach a micro-electrode array to a nerve [173]. An area with potential opportunity for new directional probabilistic fasteners includes applications for individuals who suffer from arthritis and weak grip strength, because the directionality makes them substantially easier to release.

The textile industry employs probabilistic fasteners in footwear [194] and garments [110] for their easy adjustment and release. Probabilistic fasteners can be adjusted in a variety of step sizes while typical textile fasteners like buttons are limited by “discrete adjustment steps” [22]. The concept of easy release has further been applied in combat uniform design where hook-and-loop fasteners were shown to reduce tourniquet removal time compared to buttoned fasteners [195]. Design opportunities for textiles could include reducing snag of textiles on the hooking elements [196], comfort of fastener elements on the skin [86,95,163] and ease of attachment or release.

In storage and transportation, probabilistic mechanical fasteners are utilized to secure bulky objects. Self-mating fasteners with both hooking and mating surfaces on a single strap are the most common design used in these applications [99,197201]. However, custom designed fasteners with separate fastening surfaces have been examined for securing products within the fastener system. This is done by forming fastener elements around the outline of the product so that it can be sandwiched between the fastener surfaces [202].

In robotics, probabilistic fasteners have been employed for grasping objects and random mating surfaces in their operating environment. Spines inspired by the hooks on insect feet have been used on to grasp objects [16] including ones in low gravity environments [203] as well as for latching onto stochastic surfaces in climbing applications [11,32]. A Galium aparine leaf hook inspired fastener has also been investigated in robotic grasping applications [14]. Currently, most robotics applications have one custom designed hook-based fastener that interacts with mating surfaces featuring the typical degree of randomness encountered in the environment. The design of patterned hook and mating surfaces for locking devices is one area where robotics may benefit from probabilistic mechanical fasteners. Locking devices aid robots in energy management as well as reconfiguration [204]. Some of the ideal characteristics of locking devices in robotics have been identified to include: high locking force, short switching time, light weight, compact design, low energy consumption, adjustable locking directions, capability to lock in any position, and unlocking under a load [204]. Given that many of these characteristics are found in probabilistic fasteners, we identify locking devices as an area of opportunity for these fasteners. Specific probabilistic mechanical fasteners traits which could be incorporated into robotics applications are described in Fig. 12.

Both gecko-inspired technologies based on van der Waals forces [196,197] and electro-adhesion [188,205207] have also been used for robotics applications, most notably for locomotion [207] and climbing across surfaces [188]. There are some noteworthy differences in these technologies compared to probabilistic mechanical fasteners. Gecko-inspired technologies based on dry adhesion share similar characteristics with some probabilistic mechanical fasteners: they disengage with a peel mechanism and their effectiveness is reduced by the presence of dust [188]; however, the “van der Waals forces effectively ensure that the fastener is always ‘on’ which can increase the energy required to disengage an attachment” [188]. Electro-adhesion on the other hand, has “the benefit of low energy consumption as the attachment can easily be controlled to turn on or off” [188,206]. The electro-adhesive is controlled by switching voltages on/off to secure and release an attachment. Inspired by inchworms and caterpillars, electro-adhesion has been used on actuator feet to produce omnidirectional creeping in soft robots [207]. Additional benefits are that electro-adhesion provides dust tolerance, quiet operation, fast response, and lack of dependence on surface asperities which suits this technology for robotic locomotion [188,206]. Depending on the application, electro-adhesion or van der Waals-based designs may be preferred over probabilistic mechanical fasteners. In order to capture the strengths of each of these technologies, a robot could potentially be designed with interchangeable parts which each utilize a different attachment technology. Another possibility is to combine multiple attachment technologies into a single device to gain a more robust attachment with a broader operating range. For example, combining electrostatic adhesion with a gecko inspired setae structure has been investigated for attachment applications [205]. The potential applications afforded by combining attachment technologies is an exciting possibility inspired by biological examples of organisms integrating different attachment mechanisms to more robustly adhere to a wider range of surfaces [22,208].

4.2 Multi-Attachment Strategy to Inspire Novel Fastener Designs.

Nature has developed specialized fasteners that utilize multiple attachment principles to enhance their performance. For example, some larvae found in rivers use wet adhesion combined with mechanical hooking to secure themselves against water flow [22]. We believe that drawing from nature's strategy of enhancing fastener performance with multiple attachment principles will inspire new fastener designs. To this end, we present a strategy, as seen in Fig. 13, of combining attachment principles found in both manufacturing (Applied Physics) and nature (Biological Principles, see Fig. 1). Taking a combination of two principles from the total of 20 attachment strategies and using the C(20,2) for the combination formula C(n,r) = n!/(r!(n-r)!) reveals 190 possible designs. A search of the literature revealed that of these 190 designs, there are only three multi-attachment fasteners which have been proposed. These include combining electric and magnetic fields with hooking elements [98,209211] additional mechanical hardware with hook and loop fasteners [212], and Van der Walls fasteners with interlocking elements [213]. Including these multiple attachment principles is proposed to increase strength by improving fastener alignment and to increase durability in hook/hook-and-loop fasteners by removing the need for a peeling detachment.

Fig. 13
Enhancing probabilistic mechanical fasteners with multiple attachment principles. Combining different physical and biological principles can lead to the creation of new fasteners with improved performance. (a) A wide range of applied physics attachment principles have been harnessed across artificial fasteners based on Physical, A, Chemical, B, and Mechanical, C, interaction, respectively. (b) The described biological principles for attachment include wet adhesion, I, suction, II, hooking, III, clamping, IV, dry adhesion, V, friction, VI, interlocking, VII, and spacing, VIII; based on [19]. Our literature review revealed three innovative engineering designs which combine applied physics (a) and biological (b) principles. In column c(A.1 and III), a new active probabilistic fastener combines probabilistic hooking (b(III)) with electric current (a(A.1)) to improve the alignment of mating surfaces, fastening strength, and durability. Column c(B.1 and VII) combines Van der Walls forces (a(B.1)) with interlocking (b(VII)) to improve fastener strength. Finally, column c(A.2 and III) actively combines probabilistic hooking (b(III)) with a magnetic field (a(A.2)) to improve alignment of mating surfaces, fastening strength, and durability. Improved durability is made possible by controlling the peel-off detachment via active magnetic field (or electric current) switching [98,209–211]. This integration of applied physics with biological principles expands the opportunity for fastener innovation. Drawing modified after [19] and printed with permission from the Royal Society.
Fig. 13
Enhancing probabilistic mechanical fasteners with multiple attachment principles. Combining different physical and biological principles can lead to the creation of new fasteners with improved performance. (a) A wide range of applied physics attachment principles have been harnessed across artificial fasteners based on Physical, A, Chemical, B, and Mechanical, C, interaction, respectively. (b) The described biological principles for attachment include wet adhesion, I, suction, II, hooking, III, clamping, IV, dry adhesion, V, friction, VI, interlocking, VII, and spacing, VIII; based on [19]. Our literature review revealed three innovative engineering designs which combine applied physics (a) and biological (b) principles. In column c(A.1 and III), a new active probabilistic fastener combines probabilistic hooking (b(III)) with electric current (a(A.1)) to improve the alignment of mating surfaces, fastening strength, and durability. Column c(B.1 and VII) combines Van der Walls forces (a(B.1)) with interlocking (b(VII)) to improve fastener strength. Finally, column c(A.2 and III) actively combines probabilistic hooking (b(III)) with a magnetic field (a(A.2)) to improve alignment of mating surfaces, fastening strength, and durability. Improved durability is made possible by controlling the peel-off detachment via active magnetic field (or electric current) switching [98,209–211]. This integration of applied physics with biological principles expands the opportunity for fastener innovation. Drawing modified after [19] and printed with permission from the Royal Society.
Close modal

5 Conclusion

Probabilistic mechanical fasteners are secure, reversible, and repeatable attachment devices which require little skill to operate. While examples of different mechanisms for these fasteners are found in nature, most artificial designs are variations of the hook-and-loop fastener inspired by Galium aparine seed hooks. In total, there are only four known bio-inspired mechanical probabilistic fasteners [10,11,1417,37]. However, we have shown that there is opportunity to create a wide range of new designs by drawing upon the characteristics of fasteners found in nature, such as directionality, silent fastening, and hierarchical organization. The functionality of fasteners can be further diversified and enhanced by integrating existing physical interaction principles in the design. In summary, the combination of the bio-inspired design framework and the established and new approaches help guide solving shortcomings in existing fasteners and open pathways to new applications.

Acknowledgment

We would like to acknowledge Mark Cutkosky for helpful suggestions, Laura Matloff for comments on our outline, Teresa Feo for feather morphological expertise, and William Roderick for many insights that helped layout the review.

Funding Data

  • This review was supported by AFOSR BRI Award No. FA9550-16-1-0182 with special thanks to B. L. Lee for leading the program (Funder ID: 10.13039/100000181).

  • This review was additionally supported by AFOSR DESI Award No. FA9550-18-1-0525. L. J. was supported by an NSF GRFP award and D. L. by NSF Early Faculty Career Development (CAREER) Award No. 1552419 (Funder ID: 10.13039/100000001).

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