Mechanics of Peeling Adhesives From Soft Substrates: A Review

Peeling mechanics play a crucial role in understanding the mechanisms underlying the separation of bonded surfaces. Separation, or “delamination,” events occur in everyday scenarios, such as the detachment of a sticker from a book or the removal of a medical bandage from skin. In an industrial context, the importance of peeling mechanics extends to the repair of fractured objects using adhesive tapes, detachment of labels from barrier films employed in packaging, and behavior of composite laminates utilized in the aerospace and automotive sectors. Promoting delamination is as crucial as suppressing it and both can be managed by controlling peel strength. A fundamental understanding of peeling mechanics is thus vital for the informed design and optimization of formulations with optimal peel behavior.

To comprehend the intricate phenomena of peeling, which can involve a multitude of materials, surfaces, and environments, various analytical models and finite element analysis methods have been employed. These approaches enable numerous parameters to be probed such as peeling angle [1,2], work of adhesion [1,3], peeling velocity [4,5], predeformation of the tape [6], friction [7,8], and film stiffness [9,10].

While peel performance depends on a range of material and geometric parameters directly associated with adhesive and interfacial interactions, the type of substrate to which the adhesive is bonded also plays a significant role (Fig. 1). Rigid metals and ceramics in the automotive, construction, and electronics industries usually exhibit high surface energies, facilitating superior wettability and adhesion properties, compared to the surface energy of engineering plastics, such as polyolefins and polyesters [11]. In contrast, semi-rigid engineering plastics, soft elastomers, and human skin—commonly encountered in packaging and labeling, healthcare, and surface coating applications—typically display lower surface energies on the order of 10¹ mJ/m² [11,12], impeding the wettability and adhesion of applied adhesives. Furthermore, the differences in rigidity and geometry across the varying substrates significantly influence the adhesion performance. During the peeling process, the relative stiffness of the substrate compared to the adhesive results in distinct deformation profiles through the bulk of both the adhesive and the substrate. This interplay of mechanical response and energy dissipation plays a crucial role in determining the overall peel strength, which can vary by several orders of magnitude across substrates—typically ranging from approximately 10⁰ J/m² to 10³ J/m² for pressure-sensitive adhesives (PSAs). Therefore, understanding how a single adhesive interacts with different substrates is essential for ensuring its key functionalities, as numerous applications involve more than one surface. For example, a single adhesive must interact with a release liner to protect the adhesive surface before use and facilitate effortless release prior to use, but the same adhesive must also form a strong bond on another substrate during use.

Several outstanding review papers touch upon analytical or computational (simulation) models related to adhesive and interfacial interactions. For example, Sun et al. [13] provided insights into analytical peeling models, highlighting their ability to accurately correlate peel force with the viscoelastic properties of the PSA. Park and Paulino [14], Needleman [15], and Wciślik and Pała [16] reviewed the cohesive zone model (CZM), a tool for characterizing interfacial properties in structures that experience adhesive failure. Several other review papers have also considered deformable substrates. Sauer [17], for example, provided a comprehensive overview of the computational models, especially those that are versatile, catering to diverse adhesion mechanisms and adherent geometries. Gu et al. [18] summarized the advances in analytical and computational peeling models for capturing adhesive properties on natural and artificial surfaces. The authors demonstrate, with the aid of the peeling model, that biological and biomimetic surface adhesion can be understood, and surface adhesive material can be designed by modulating the backing and substrate topography and adding interfacial linkers. More recently, Bartlett et al. [19] extensively reviewed different types of peel tests and discussed their applications in various materials, including biological systems and soft materials.

While numerous literature reviews exist, these reviews often underemphasize the specific peel mechanics associated with soft substrates. These structures are pivotal in a variety of applications, including release liners for pressure-sensitive adhesives, bio-adhesives for human skin, water-repellent coatings, and food packaging. The following review thus examines these contexts in depth, providing an overview of the theoretical methods and some industrial applications of peeling from soft substrates. In Sec. 2, we provide an overview of theoretical foundations to understand the adhesive system. Section 3 delves into the energy-based analysis of peeling, while Sec. 4 focuses on stress-based analysis for structures with a soft substrate. In Sec. 5, we show specific applications of the analytical models and conclude with remarks and future research prospects.

The process of peeling a tape from a soft substrate is shown in Fig. 2, where the width and thickness of the tape are denoted by b and h, respectively. The soft tape (pink) is peeled away from a soft substrate (blue) of thickness $hl$ at an angle $θ$ by a peel force F that induces a steady-state peel velocity V at the end of the peeling arm. The soft substrate is mounted on a rigid backing, denoted by diagonal hashed lines. Here, the peeling arm refers to the portion of tape that is not bonded to the soft substrate (see Fig. 2).

For clarity, the tape structure shown in Fig. 2 can represent different scenarios depending on the application conditions. Failure may occur at the interface between the adhesive and the substrate material (adhesive failure) or within the adhesive material itself (cohesive failure). In instances of adhesive failure, the tape shown in Fig. 2 includes both the adhesive and backing materials. Conversely, in cases of cohesive failure, the tape shown in Fig. 2 represents the adhesive backing with part of the adhesive, whereas the substrate consists of the intended substrate and the remaining adhesive material.

Evaluating each term in Eq. (1) theoretically leads to a complete description of the peel mechanics of the adhesive system. Fracture mechanics theory can be used to evaluate the stress field around the peel front, thereby determining each term in Eq. (1). The stress field in the elastic layer structure near the peel front has a singularity, which is physically impossible because irreversible deformation, such as plastic deformation, will eliminate the singularity in real materials. To consider the local details near the peel front in materials with irreversible deformation, the CZM has been employed [21–24]. However, here, the focus is on analytical models.

To understand delamination processes, two methods are commonly used: energy-based analysis and stress-based analysis. These methods differ in their failure criterion. In energy-based analyses, the peel front propagates once the external input energy is sufficient to create a new surface. On the other hand, in stress-based analysis, the peel front propagates when the stress or deformation at the peel front reaches a critical value. In this review, we will discuss these two methods in detail, with a focus on adhesive structures with a soft substrate, as shown in Fig. 2. This review covers the basics and recent advances of these two methods. Throughout this review, the soft substrate will be represented as a light blue material, while the pink color denotes the flexible tape.

As the increment of stored strain energy from the bending deformation in the tape $d(Usba+Usbp)$ is insignificant at steady state, our focus is on evaluating the following terms: $d(Usta+Ustp+Udta+Udtp+$$Udba+Udbp)$⁠. For certain special scenarios, such as peeling a thin elastic tape from a thin elastic substrate with a peeling angle close to zero (lap joint), Kendall [28] demonstrated that only $d(Usta+Ustp)$ must be considered. Under the assumption of uniform tension deformation in the linear elastic (LE) substrate and tape, stress and deformation can be determined through force equilibrium equations, enabling calculation of $d(Usta+Ustp)$⁠. However, for many other cases, simplifying assumptions are necessary to derive analytical expressions for energy contributions from the tape. For example, some researchers neglect deformation in the bonded arm since the deformation in the bonded arm is significantly smaller than that in the peeling arm [29–32]. In this case, only the energy term $d(Ustp+Udtp+Udbp)$ needs to be evaluated.

In the following discussion, the energy terms associated with the peeling arm will be discussed, specifically $Ustp+Udtp+Udbp$⁠. Let (x, y) denote the coordinate with the origin at the peel front (see Fig. 2). Any point on the peeling arm can alternatively be represented by the arc length s of the peeling arm with the corresponding tangential angle $ϕ(s)$⁠. At steady state, the peeling arm has a fixed configuration, so $ϕ(s)$ is time independent.

Typically, peeling tests are conducted at either $θ=90deg$ or $θ=180deg$ configuration. Provided that the material constitutive model of the tape is given, then the shape of the peeling arm can be determined through Eqs. (6) and (7), which enables the derivation of the stress $σ(s)$ and strain $ε(s)$⁠, respectively. Subsequently, the value of $Ustp+Udtp+Udbp$ in Eq. (5) can be evaluated. To illustrate this process, three examples of the peeling arm are presented: elastic, elastic–plastic, and viscoelastic peeling arm.

The evaluation of the third term, $Udbp$⁠, which arises from the bending deformation, is a complex task due to the elastic–plastic constitutive relations that result in complicated mathematical forms—often making an explicit expression impossible. The current literature provides methods for assessing the dissipation resulting from the bending of the peeling arm. For instance, solutions for nonwork hardening elastic-perfect plastic [20], bilinear work hardening [20], power-law work hardening [36], and general work hardening elastic–plastic [37] peeling arms have been reported. Although the process of evaluating the dissipation from the bending of the peeling arm may be challenging, free spreadsheet tools [38] have been developed, which can be used to compute this term for the aforementioned cases.

Equations (10)–(15) present a general framework for analyzing the energy contributions from a linear viscoelastic peeling arm. This framework was utilized by Chen et al. [33], who examined a viscoelastic peeling arm with one relaxation time based on an energy balance. The authors evaluated the energy dissipation arising from the bending and stretching of the peeling arm. Similarly, Ceglie et al. [8] also considered the energy dissipation resulting from a viscoelastic peeling arm with one relaxation time. However, their focus was on thin tapes, where the bending contribution can be neglected. In this case, only the first term on the right-hand side of Eq. (5) is considered.

$dUsl$ can be evaluated from Eq. (23) for given constitutive relations $τ(v)$ and $∂u(x)/∂x$⁠. Since $τ(v)$ and $∂u(x)/∂x$ can be treated differently, we will provide two specific examples.

By substituting Eqs. (28) and (27) into Eq. (26), the dissipation from slip can be evaluated.

Clearly, Eq. (33) is unable to be applied to the case when the peeling angle is close to zero. The limitation can be attributed to the oversimplified assumption that interfacial shear stress $τ$ is uniformly distributed in a local area $−α<x<0$⁠.

The normalized applied force $F/(Γb)$ is illustrated in Fig. 5. Here, three cases are considered, each represented by different curve colors: soft tape $(Eh/Γ=10−4)$ with red curves, semi-rigid tape $(Eh/Γ=1)$ with black curves, and rigid tape $(Eh/Γ=104)$ with blue curves. The linear elastic adhesive system is analyzed under two conditions: with interfacial shear stress, represented by solid curves using Eq. (33), and without interfacial shear stress, represented by dash curves using Eq. (4) from Kendall [27].

Interestingly, our analysis reveals that Eqs. (4) and (33) yield nearly identical results for a rigid tape $Eh/Γ=104$⁠, evidenced by the overlapping blue solid and dashed curves (Fig. 5). However, as the tape becomes more flexible, the disparity between the outcomes of Eqs. (4) and (33) becomes pronounced—particularly evident in the case of extremely soft tape (red curves, Fig. 5). In such scenarios, the equation that omits interfacial dissipation predicts a relatively stable, small normalized peel force (red dashed curve). In contrast, equations that account for interfacial shear stress offer distinctly different forecasts, demonstrating a significant dependence of normalized peel force on the peel angle.

For many peeling systems, the steady-state strain energy in the substrate is negligible [34,55,58,59]. Here, the primary concern is the dissipation energy $dUds$⁠. The theoretical approaches reported in the literature can be classified as either thick or thin substrate cases.

Analytical determination of the deformation field in thick substrates is quite complicated. Only a few researchers have attempted to tackle this problem, and in most cases, oversimplified assumptions are necessary to obtain analytical expressions. For instance, Pierro et al. [34] and Afferrante and Carbone [58] analytically evaluated the dissipation of the viscoelastic substrate by assuming that the stress near the peel front is uniformly distributed in a local region of the attached area. They assume that uniform traction is applied over a segment equal to the tape thickness. This assumption is oversimplified and its validity is debatable, as discussed by Ciavarella et al. [60], because the actual interaction zone between the tape and the substrate could be either smaller or larger than the tape thickness depending on many other factors such as friction shear stress. Substrates with a single relaxation time [58] and multiple relaxation times [34] have been considered. Here, the time-dependent displacement on the substrate surface is calculated, and dissipation from the substrate can be evaluated. Subsequently, the authors obtain relationships between the work of adhesion, peeling force, peeling velocity, and Young's modulus of the peeling arm and the substrate. This relation can be reduced to the classical Kendall equation [27] under extremely fast $(V→∞)$ and slow $(V→0)$ peeling rates and can be further reduced to the classic Rivlin solution [3] when the substrate is rigid.

Menga et al. [59] consider the V-shaped periodic double peeling based on the energy-based analysis. Here, the authors consider the peeling of an elastic film from an elastic substrate. For the V-shaped doubled peeling structure, the elastic energy stored in the substrate cannot be neglected. Therefore, both the strain energy of the peeling arm and the substrate are considered. To evaluate the strain energy of the substrate, they adopt the analytical solution of the displacement of the soft substrate under uniformly distributed tractions [61]. Perrin et al. [62] obtained the relation between the peeling force and the peeling velocity. They analytically calculated the dissipation of the soft substrate within the limit of the small deformation. In particular, they obtained the relations between dissipation energy and the loss modulus of the soft substrate.

Zhu et al. [55] evaluated the viscoelastic dissipation energy from the soft substrate by using the same approach as Afferrante and Carbone [58]. The authors extended Afferrante's theory to consider the rate dependence of the work of adhesion. In particular, the authors regard the interfacial debonding as the thermally activated rupture process of the polymer chains connecting the two surfaces [41,56,63], and they analytically calculated the corresponding work of adhesion.

The stress and deformation in thin substrates have been extensively studied [25,26,64–71]. Theoretically, by determining the stress and deformation fields, the energy terms associated with the substrate can be calculated, enabling the energy-based analysis. However, in practice, many researchers analyze the failure of the adhesive with thin, soft substrates from a stress-based perspective. This approach is taken because the peel front fracture criteria can be simplified: failure is assumed to occur when the stress or deformation at the peel front exceeds a critical value. In the next section, we will delve into stress-based analysis in greater detail.

In this section, we will focus on adhesives with a thin, soft substrate. Several researchers independently developed the theory to describe the peeling mechanics of the elastic tape peeling from a thin elastic substrate [66–70,72]. The basic idea of these studies is similar; the tape is considered a bending beam, the stress and deformation field in the soft substrate of the bonded area is solved, and the failure criterion is set as the stress/strain reaches a critical value. Specifically, Kaelble [66] assumed that the soft substrate undergoes in-plane shear and uniaxial deformation. Dillard [67] used a similar idea, and the author considered the bending of the plates on incompressible elastic foundations. The elastic foundations are assumed to be under a uniaxial deformation state. More recently, this theory was applied to study the peeling process of finite-length tape on incompressible elastomeric foundations [69]. Plaut et al. [68] investigated the peeling of finite-length beams on elastic foundations. The author modeled the substrate as independent springs. The beam was modeled as inextensible, and they only considered the bending of the beam. In addition, a series of works [26,70,71] theoretically calculated the deformation and stress field in thin, soft substrates by solving the 2D equilibrium equation. The detachment criterion is defined as the condition when the stress in the substrate reaches a critical value.

Two categories can be identified based on the deformation of the soft substrate: those with small (see Fig. 6(a)) and large deformations (see Fig. 6(b)). In practical applications, in the first case, the tape consists of both backing and adhesive materials. The soft substrate typically corresponds to a soft release liner, where interfacial adhesive failure usually occurs due to the small interfacial fracture energy; here, the release liner undergoes little deformation. In contrast, in the second case, the soft substrate can undergo large deformation due to the stronger interfacial fracture energy and/or low modulus of the adhesive. Here, different types of failure can occur depending on loading conditions, material, and interface properties. For example, peeling a bandage from the skin typically represents adhesive failure, where the tape shown in Fig. 6(b) is the bandage, i.e., backing and adhesive, and the substrate is the skin. Conversely, many of the cases involving highly deformable substrates detailed later in this article involve substrate failure, where failure occurs within the highly deformable substrate (light blue) as shown in Fig. 6(b).

The stress-based analysis is fundamentally grounded in a similar procedure, specifically the stress balance method. Therefore, only one seminal work, serving as a representative example for each of the two types of structures, is discussed herein. In particular, an overview of cleavage stress analysis [25,66,73,74] is provided for the first structure (Fig. 6(a)), while the second structure (Fig. 6(a)) is discussed in terms of the balance of momentum of the tape, as described in theoretical approaches by Derail et al. [75,76] and Li et al. [77].

Figure 8 illustrates the relationship between normalized shear stress (Eq. (52)) and cleavage stress (Eq. (65)) at the interface of the soft release liner and adhesive, and their distance from the peel front. It is observed that both cleavage stress and shear stress diminish to zero as the distance from the peel front increases. Specifically, cleavage and shear stresses disappear at distances corresponding to $βx$ and $αx$ values of approximately −4 and −6, respectively. A notable distinction is observed in the behavior of these stresses: the cleavage stress exhibits oscillatory behavior before dissipating, whereas the shear stress decreases monotonically as distance increases. It is important to note that the parameters $α$ and $β$ are indicative of the stiffness of the release liner, with higher values suggesting increased rigidity. Consequently, enhancing the rigidity of the liner results in a more localized concentration of both cleavage and shear stresses, which then dissipate at shorter distances from the peel front.

Here, the cross section is considered rectangular, that is, $I=bh3/12$⁠.

Equations (74) and (75) give the same dependence of peel force on the peeling angle. Note that it may seem that Eq. (75) predicts that the peel force will depend on the release liner thickness. However, Gent and Hamed [79] pointed out that $σA$ is the average stress along the thickness of the soft release liner at the peel front. Therefore, $σA$ is not a constant value, and it may be inversely proportional $hl−1/2$⁠. As a result, both equations are independent of the liner thickness. Interestingly, comparing Eqs. (74) and (75) gives the equation $Γ∼hlσA2/2El$⁠, which represents the elastic energy stored in the thickness of the soft release liner near the peel front.

The cleavage stress method was initially developed for adhesives that feature an elastic tape and release liner, but this method can be extended to characterize structures with nonelastic properties. For instance, to capture the peeling behavior of structures with a viscoelastic release liner or tape, the elastic constitutive equations such as Eqs. (44), (46), and (55) could be replaced by the corresponding constitutive equations such as viscoelastic constitutive equations. The only premise for this approach is that the deflection deformation in the bonded area of the tape and the soft release liner should remain small (see Eq. (56)). This method can also be extended to consider the finite deflection deformation in the bonded area of the tape and the soft release liner by using the general bending equation, Eq. (6). In this case, the soft substrate experiences large deformation during the peeling process, as discussed in Sec. 4.2.

Spies [64] and Bikerman [65] established the basis for the cleavage stress method through their investigation of the detachment mechanics of an adhesive consisting of a flexible peeling arm adhered to a rigid plate with linear elastic adhesive. Based on this, Kaelble [25,66] developed the cleavage stress approach, and this theory was subsequently confirmed by experiments [74]. The basics of the cleavage stress analysis are provided in Sec. 4.1.2. This theory combined with the rate–temperature superposition principle is used to describe the peel force of the adhesive structure with a viscoelastic adhesive interlayer [73,80]. Chen and Flavin [81] extended the cleavage stress by considering the elastic–plastic tape and the elastic–plastic soft substrate. The authors found that the fracture energy is the key parameter instead of the specific constitutive relations.

Moidu and Sinclair [4,5] considered the peeling process based on both the energy and cleavage analyses. Here, the deformation in the detached area is analyzed based on the general bending theory [30,82]. The deformation in the attached area is calculated based on the cleavage stress analysis. The authors considered the elastic–plastic tape peeling from the elastic soft substrate. Energy analysis was employed, and the corresponding strain energy and the dissipation energy from plasticity were calculated from the calculated deformation. Ghatak [26] investigated the elastic flexible plate peeling from the elastic substrate with varied modulus along the x direction. The author applied the stress equilibrium equation (balance of linear momentum) to the material element in the soft substrate and the bending equation to the flexible tape. It was assumed that the plate deflection was small in the attached area of the plate and the soft substrate. The peel front was then determined by the failure criterion that the adhesive breaks at a constant critical stress. Finally, Villey et al. [83] evaluated the fracture energy $(Γ)$ using a stress-based analysis. The peeling force, derived from the cleavage stress (Eq. (69)), is employed to assess the fracture energy. The authors analytically separated the angular dependence of the fracture energy from the dependence on peeling velocity, finding that the angular dependence can be explained through the stress-based analysis. Additionally, they found that accounting for large deformations is necessary to explain the high fracture energy values observed in PSAs.

The structure of the soft substrate under large deformation is shown in Fig. 6(b). As aforementioned, various types of failure can occur. This highly deformable substrate experiences the maximum stretching at the peel front and gradually decreases toward the left of the peel front. The point where the stretch is zero, denoted by $O′$⁠, serves as the origin of the Cartesian coordinate system (Fig. 9). Note that the substrate on the left of point $O′$ experiences compression, and the influence from the left side of $O′$ on point $O′$ can be represented by a force $F0$ and a moment $Mf$⁠. The soft highly deformable substrate is assumed to be under uniaxial deformation, which can be illustrated in a series of springs (see Fig. 9).

To obtain the peel force F, the value $F0$⁠, the constitutive model of the deformable substrate $σa$⁠, the length of the peeling zone l, and the shape of the bent arm $y(x)$ need to be evaluated. Assuming that the bent arm is circular, the theoretical method can be simplified (see Appendix  B). A more rigorous method is introduced to determine the shape of bent arm $y(x)$⁠.

Here are two unknown parameters $F0$ and l, which can be numerically determined by using Eqs. (79)–(81). Note that $σa$ is determined by the constitutive model of the deformable substrate material, while $δmax$ depends on the failure conditions, and an example of the failure condition is discussed in Appendix  B in Determination of the Angular Position of the Failure Locus $θM$ section.

While initially developed for elastic tape (Eq. (77)), this approach can be extended to other material systems. Elastic–plastic [20] and viscoelastic tapes [33] can also be analyzed using the corresponding constitutive models. Furthermore, if the traction–separation law is employed for the highly deformable substrate, this theoretical method is consistent with the cohesive zone model [84].

Cleavage stress analysis is valid when deformation in the bonded arm is small. Niesiolowski and Aubrey [85] extended the cleavage stress to consider the influence of filamentation by analyzing the peeling profile in the peeling zone with large deformation. Derail et al. [75,76] considered peeling mechanics that can be applied to a highly deformable, viscoelastic substrate by assuming that the peeling profile is circular and the highly deformable substrate in the peeling zone undergoes uniaxial deformation. The authors considered both cohesive and interfacial adhesive fractures by using the corresponding failure criteria (Appendix  B).

Karwoski [86] explored the mechanics of tape peeling from the skin, summarizing several models where the force and moment equilibrium equations were utilized to establish the governing equations. To streamline the analysis, the soft deformable substrate, representing skin tissue, was modeled as a single spring—a simplification from a more complex multispring system. Additionally, both the skin surface and the tape were modeled as flexible beams. Subsequently, Plaut [87] delved into similar investigations of tape peeling behavior from the skin. This model partitioned the structure into two distinct segments: segment 1, where the tape is adhered to the skin, and segment 2, where the tape is detached. In segment 1, the mechanical behavior is primarily governed by the tape backing, which is modeled as a flexible beam. Conversely, in segment 2, the skin surface is represented as a truss (exhibiting no bending), and the soft substrate is modeled as a series of springs.

Zhang and Wang [88] examined bending in the attached and detached areas of the tape. The authors considered cohesive failure within the highly deformable substrate. Here, the Maxwell solid constitutive relation is applied to the substrate, and the detached location l between the substrate and the peeling arm is determined by the failure criterion that the substrate fibril breaks at a constant critical stretch ratio.

Poulard et al. [89] theoretically investigated the deformation of a substrate with pillar patterns. The authors assumed that all strain energy in the pillars would dissipate during the peeling process, which will increase the peeling force. Here, failure criteria similar to Johnson–Kendall–Roberts and Derjaguin–Muller–Toporov theory are selected, where the tape will detach from the substrate as the force in the pillar reaches a critical value.

Li et al. [77] derived the peel force based on a balance of linear momentum. The authors use a series of springs to represent the highly deformable substrate layer and tape. Force equilibrium was utilized, and bending of the tape was ignored. They found that the critical strain/stress of the substrate when the adhesive failure occurs is not constant and depends on the peeling angle.

Finally, He et al. [84] used a soft hydrogel as the highly deformable substrate and applied the theoretical framework in Sec. 4.2.1 to capture the debonding resistance of the hydrogel, with the further assumption that $Mf=0$⁠, i.e., $y″(0)=0$⁠. In their research, cohesive failure always occurs. Thus, the authors directly measured the constitutive relation of the deformable substrate $σa$ with corresponding $δmax$⁠. In particular, they determined the traction–separation law of the deformable substrate by using the butt-joint test [90].

The theoretical model section of this review critically assesses the theoretical underpinnings of peeling mechanics, particularly within soft adhesives that interface with soft substrates, emphasizing both energy and stress analyses. Distinctive failure criteria characterize each method. In the energy-based analysis, the peel front propagates once the external energy input suffices to generate a new surface. Conversely, the stress-based analysis dictates that the peel front moves forward when the stress or deformation at the peel front reaches a critical threshold.

For the energy analysis method, different energy terms are discussed. This analysis encompasses energy terms in both the tape and substrate, kinetic energy, energy dissipated through interfacial slippage, and fracture energy at the interface. The energy terms related to the tape—often modeled as a flexible beam—are comparatively straightforward to assess. This review covers the energy terms arising from the bending and tensile deformation of the peeling arm, particularly highlighting the elastic, elastic–plastic, and linear viscoelastic tape models. The roles of the kinetic energy and the energy dissipated from interfacial slippage are discussed, with seminal works introduced in Sec. 3.3 serving as prime examples. Moreover, the intrinsic fracture and the associated energy dissipation at the interface, along with the rate and temperature dependence of the fracture energy, are reviewed. Though the energy terms connected to the substrate present challenges, these energy terms can be evaluated with certain assumptions. For instance, for soft, thick substrates, oversimplifications are utilized, and for soft, thin substrates, the analysis stays constrained to small deformations. In the case of soft, thin substrates, energy terms can be derived from their stress and deformation fields. Practically, stress analysis typically dominates the analysis for structures incorporating thin substrates.

On the flip side, stress analysis—which predominantly focuses on the stress and deformation dynamics within a structure—is mainly pertinent to structures with thin, soft substrates. This specificity arises because the assumption of a thin substrate allows for a feasible mathematical derivation; without this assumption, the mathematical approach becomes intractable. This review covers the nuances of soft substrates experiencing both minor and substantial deformations, typically corresponding to release liners and adhesives. Seminal works by Kaelble [25,66] on soft substrates with minor deformations are dissected in depth. The application of the linear Euler–Bernoulli beam theory to the bonded area of the tape is explored, resulting in the analytical derivation of cleavage and shear stress in the elastic substrate. Notably, both cleavage stress and energy analyses reveal congruent angle dependencies. As for soft substrates with substantial deformations, large deflection theory becomes indispensable, particularly for capturing tape deformation. To solve the governing equations of peeling mechanics, one must first extract and calibrate the constitutive model of the soft adhesive and the corresponding failure conditions from experiments.

This review also highlights recent advancements in the energy and stress analysis of structures with both thin and thick substrates, as summarized in Table 1. In Table 1, a summary of various models is presented, where T and S in the rows and columns represent the tape and substrate, respectively. The acronyms used within the table are as follows: LE for linear elastic, NE for nonlinear elastic, EP for elastic–plastic, and LVE for linear viscoelastic. The terms WB and SB indicate weak bonds and strong bonds, respectively, denoting the substrate's response to small deformations under weak bonds and large deformations under strong bonds. Additionally, TnS and TkS are used to differentiate between thin and thick substrates.

It is important to note that many theoretical works have been deliberately excluded from this review, as the focus is tightly bound to peeling systems with soft substrates. Consequently, adhesive structures of different types are not covered in this review. For instance, certain studies explore scenarios such as tape peeling from thin beams or trusses. Notably, Shen et al. [91] consider peeling a thin film from a soft cantilever substrate by the energy balance analysis. In this work, bending of the cantilever substrate is analytically solved to determine the peeling angle and then the model of Kendall [27] is employed to calculate the peeling force. Peeling of PSAs from the human skin, in which the human skin is modeled as a reversible truss (elastic foundation and bending have not been incorporated), has been investigated by several authors [92–94].

In addition, theoretical works pertinent to rigid substrates have also not been incorporated into Table 1. For the theoretical works related to rigid substrates, seminal contributions were made by Rivlin [3] and Kendall [27]. A selection of additional works, though not exhaustive, will be briefly mentioned here. Loukis and Aravas [95] explored linear viscoelastic tape peeling from a rigid substrate, while Christensen and McKinley [96] studied linear viscoelastic and nonlinear viscoelastic tape peeling from a rigid substrate. Similarly, exploration by Afferrante et al. [97] into the peeling of elastic thin films from a rigid substrate, investigation by Chen et al. [33] into the flat and patterned viscoelastic tape peeling from a rigid substrate (as detailed in Sec. 3.1), and the study by Peng et al. [54] on the viscoelastic thin tape peeling from the rigid substrate (discussed in Sec. 3.4) have been consciously omitted. Additional research studies such as that by Zhu et al. [98], who investigated visco-hyperelastic tape peeling from the rigid substrate at a zero-degree peeling angle, and Ceglie and Menga [8,99], who explored the peeling behavior of thin viscoelastic tape from a rigid substrate, have also been excluded. Similarly, works by He et al. [32,100], examining hyperelastic tape peeling from a flat rigid substrate, are not covered in this review.

Peeling of a soft adhesive from a soft substrate is a common phenomenon encountered in various applications. For example, when removing an adhesive label from an elastomer-coated release liner before applying it to another substrate, achieving effortless removal without compromising the adhesive strength becomes crucial. Similarly, for skin adhesives or transdermal patches, the process of painless removal from human skin is of utmost importance. Additionally, when assessing the interfacial strength of multilayer packaging films, the peeling process is a valuable tool. Consequently, it becomes essential to develop a comprehensive understanding of the underlying mechanics of this peeling process and identify the diverse fields in which this knowledge finds significant applications. These endeavors play a pivotal role in the successful material development, precise characterization techniques, and accurate interpretation of experimental data. In this section, we aim to establish a connection between the previously discussed theories of peel mechanics and practical applications commonly experienced by industrial researchers and customers. We will demonstrate how the theoretical foundations and testing methodologies can effectively guide the creation and understanding of soft materials, both within and beyond the confines of the laboratory.

Soft adhesive tapes or pressure-sensitive adhesives are extensively employed for surface bonding in various aspects of daily life, playing indispensable roles in a broad spectrum of industries, including electronics, construction, automotive, and healthcare [101,102]. However, these adhesives are often designed to exhibit high tackiness upon contact to enable rapid bonding, making them prone to accumulating contaminants on the adhesive surface. To safeguard the adhesive surface from contamination prior to application on a substrate, release liners can be utilized. These liners consist of plastic or paper sheets, which can be coated with release coatings if necessary to meet the required release performance. The adhesive and liner layer can be two separate entities, most commonly for labels. For many self-wound tapes (e.g., packing tape), the adhesive and liner layers are not separate, with one side coated with an adhesive and the other side either coated or uncoated with a release coating. In this context, two crucial performance parameters are used to evaluate the effectiveness of release coatings in relation to the PSA: release force and subsequent adhesion strength (SAS) [103–106]. The release force measures the ease with which the PSA can be peeled off from the release coating or backing or vice versa, while the SAS represents the adhesive strength of the PSA upon removal from the release coating or backing and its subsequent attachment to a target substrate. The release performance parameters can be easily measured by mechanical testing equipment. Although the numerical aspects of release performance and visual observations by an operator can offer prompt information on failure modes (e.g., cohesive, or adhesive failure) and crack dynamics (e.g., stick-slip), they often fall short in providing insights into the fundamental origins of the release performance. Understanding the fundamental factors that influence global release performance is essential for developing new adhesives or release coatings, as well as optimizing and troubleshooting existing ones.

One of the most employed mechanisms and approaches in the development of release coatings involves reducing the surface energy to enhance repellency against the PSA and enable facile release. For elastic tape, the release force can be determined by the interfacial fracture energy via Eq. (4). More generally, the correlation between release force and fracture energy can be determined through the energy-based analysis (Sec. 3). On obtaining the relationship between release force and fracture energy, the relationship between surface energy and release force can be derived via Eq. (38). Using elastic tape as an example, the release force increases with an increase in surface energy, and vice versa (combining Eqs. (4) and (38)). In practical terms, the minimum release force, corresponding to the smallest fracture energy, can be achieved by relying solely on van der Waals interactions, specifically dispersion forces. Consequently, stronger interactions such as hydrogen bonds, acid–base interactions, covalent bonds, or the interdigitation of short chains, along with interfacial entanglements of sufficiently long chains, result in the amplification of viscoelastic energy dissipation and higher release forces.

In addition, the stress-based analysis presented in Sec. 4.1 offers a framework that could be potentially adapted for analyzing the peel mechanics of the PSA-release liner system. However, this section models the tape as a homogeneous elastic entity, a simplification that diverges from more complex real-world scenarios. In practice, tape comprises two distinct materials: a backing material, which may be modeled as an elastic material, and an adhesive material, characterized by pronounced viscoelastic properties. Consequently, caution must be exercised when applying this model. Specifically, when treating the inhomogeneous tape as a singular elastic material with an equivalent modulus, the model applicability becomes restricted to peel velocities within a certain range where the adhesive loss modulus remains negligible.

Interestingly, the relationship between surface energy and release force as implied in Eq. (38) was found to break down when peeling an organic PSA from a polydimethylsiloxane (PDMS) coating. To investigate this phenomenon, peel experiments were conducted using PDMS, hydrocarbon, and fluorocarbon-grafted coatings [107]. Despite PDMS having a higher surface energy (γ = 22 mN/m) compared to fluorocarbon (γ = 10 mN/m), the release force of the organic PSA was significantly lower for PDMS than for fluorocarbon, at a given peel velocity. Furthermore, each coating exhibited distinct peel front patterns, with PDMS showing the smoothest pattern and the lowest peel force, while fluorocarbon demonstrated a highly irregular pattern with the highest peel force.

This deviation in release forces relative to surface energy can be attributed to interfacial slippage induced by the high surface flexibility and mobility of PDMS. This slippage was visually characterized by the lateral displacement of fluorescent particles at the interface during peeling [40,107]. The fluorescent particle on PDMS moved approximately 13 µm before encountering the crack, whereas the particle on fluorocarbon only moved 1 µm. These surface dynamics observed in PDMS effectively reduce interfacial shear stress, leading to minimized energy dissipation and low release force. Several researchers have incorporated the dissipation due to interfacial slippage in their models [7,8,40]. In contrast, no interfacial slippage was observed between the organic PSA and fluorocarbon coating, resulting in a high release force due to significant energy dissipation in the adhesive, despite its extremely low surface energy.

The concept of chain flexibility in controlling release forces extends beyond PDMS, as evidenced by investigations on hydrocarbon monolayers (C16) in relation to acrylic PSAs [107]. In the liquid-like state (65% surface coverage), the chains exhibit higher mobility, allowing for more slippage, which results in a reduced release force compared to the crystalline state (100% surface coverage). However, an interesting counterargument regarding the impact of chain flexibility on release force control has also been reported. In a polycarbamate-based organic release coating system with an organic PSA, a high crystalline solid-like surface state through a high density of long alkyl chains (C16) proves advantageous in reducing the release force by suppressing entanglement with the chains of the organic PSA, compared with shorter alkyl chains (C10).

While achieving a lower release force is often a primary goal in industry, avoiding excessively low release forces remains crucial to prevent potential technical issues. For example, during storage or die-cutting into desirable forms, self-delamination of the laminates may occur. Therefore, attaining appropriate release forces based on specific applications and processing requirements is imperative. An effective approach to controlling release force in release coatings such as PDMS involves modifying elastomeric architectures through adjustments in the degree of polymerization and/or branching [108]. This tuning process not only leads to a wide variation in energy dissipation and release performance but also allows for customization of curing conditions, providing a means to achieve the desired release forces, and curing profiles.

Another approach is to add methyl silicates or MQ resins into the elastomer [109,110]. Notably, the nanoscale additives can suppress interfacial slippage in PDMS release coatings, leading to an increase in the release force. The addition of methyl silicates, which serve as high release additives (HRAs), increases the loss modulus in PDMS coatings, reducing chain flexibility and creating a surface freeze effect. This, in turn, results in increased friction, elevated energy dissipation within the sheared adhesive layer, and higher release forces. The impact of HRA on weakening interfacial slippage becomes more pronounced over extended contact times due to an increase in interfacial interactions. In addition to molecular-level chain dynamics, micropatterns on the PDMS surface at a micron scale can significantly influence the release force of the acrylic PSA through elastic deformation of the patterns [89,111].

While release force is a critical parameter for release liners, SAS holds equal importance. By laminating the PSA onto a release liner featuring a surface coated with a thin layer of slippery liquid oils, the release force can be significantly reduced [112]. However, when the PSA is laminated onto a target substrate, adhesion strength may vanish due to the migration of oils onto the adhesive surface. Therefore, careful consideration and evaluation are necessary to balance the reduction of release force while maintaining sufficient SAS.

Release or adhesion performance is significantly influenced both by the materials used and by environmental factors and testing conditions. As a result, evaluating release performance typically entails conducting characterization under various lamination conditions and peeling rates for both the PSA and the release liner, tailored to meet specific application requirements.

One common condition involves adhering a PSA strip onto a prepared release liner with a rubber roller with an approximate weight of 5 kg. Subsequently, the laminate is subjected to extended periods under a heavy weight, either at a room temperature or at an elevated temperature (e.g., 70 °C). Following aging, the laminate is affixed to a release tester, and the PSA or release liner end is pulled at a 180-deg angle at a rate of 0.3 m/min. The removed PSA is then laminated onto a stainless-steel plate and peeled at the same rate to characterize the SAS (ASTM-D6862 [113], D3330 [114], and D6252 [115]). Various ASTM standards for peel tests cater to different application scopes. For instance, ASTM D6252/D6252M is employed to measure the peel adhesion of PSA label stocks. A more thorough review of these various peel tests can be found in the study by Bartlett and Case [19].

Although commonly used, the specified peeling rate above (0.3 m/min) is considered slow for many applications, particularly in cases where peeling of high-volume PSAs from release liners is conducted on an industrial scale. To assess the effectiveness of release liners and meet demanding requirements, a much higher peeling rate, such as 300 m/min, is often selected [105,116–118]. This high-speed release can reveal significant deviations in release performance compared to slower peeling rates, depending on the types of PSAs and release liners employed. In particular, at high peeling rates, there is a notable dissipative process that significantly influences the overall release performance. The dissipative behavior primarily occurs within the soft and thick PSA (≥25 µm) rather than the thin release coating (≤1 µm), mainly due to the PSA's larger dissipation factor (tan δ), which is closely linked to the adhesion strength on a target substrate. The dissipation energy from the soft adhesive can be evaluated by using the approach discussed in Sec. 3.1.3, and the specific method can be selected from Table 1.

Interestingly, the tan δ profile of acrylic PSA, obtained through rheological tests at various frequencies, can be qualitatively correlated with the release profile of PDMS coatings at the corresponding peeling rates [108]. Although the contribution of the PSA to release force is apparent, the effects of the degree of polymerization and quantities of MQ resins on the release coatings are also significant. For instance, tightly crosslinked unfilled PDMS coatings or modified PDMS coatings with low quantities of MQ resins exhibit low release forces for organic PSA at high peeling rates [108].

The geometry and mechanical stability of the release coating also significantly impact the release performance and must be extensively characterized, along with the measurement of release force and SAS. The coating thickness is carefully controlled by taking into consideration factors like performance, processing, and cost. To measure the thickness, nondestructive analytical techniques, such as X-ray fluorescence, are often employed. These methods also facilitate rapid characterization of the mechanical strength of cured coatings after they have been exposed to abrasion or solvents, which is critical for practical long-term applications. For example, the release liner is immersed in a specific solvent to characterize the presence of uncured prepolymers that may migrate to the surface of PSA, resulting in reduced SAS. The surface of the release liner is also pressed against a fabric strip under a weight and subjected to multiple rubbing cycles to evaluate the cohesive strength of the release coating.

Release coatings are micron-thick materials applied and cured onto release liners to provide weak interaction with sticky surfaces and prevent premature and permanent adhesion. Types of release coatings include polyacrylates, carbamates, polyolefins, fluorocarbons, chromium stearate complexes, and silicones. Among them, silicone- or polydialkylsiloxane-based release coatings dominate the market due to their superior performance over other types, such as extra low release force, consistent release performance, chemical and heat resistance, and environmental friendliness [119,120]. The extraordinary performance is mainly due to the unique chemical structure of silicones, resulting in extra low release force that cannot be achieved by other types of release coatings as discussed earlier [40,107,121], making them ideal for use as release coatings. Release liners coated with a release coating are widely utilized in various areas, particularly in the PSA sector where they play a critical role in protecting the sticky PSA layer during manufacture, storage, and facilitating easy delamination and label transfer from liners onto the targeted labeling objects. The typical application of release liners includes labels, tapes, hygiene products, and food/bakery products (Fig. 10). The total global release liner market size is about 56,717 million m² with steady growth in 2020 [122].

One of the crucial development trends in the release coating sector is the enhancement of sustainability in release coating systems. This includes transitioning from solvent-based coatings to emulsion and solventless alternatives, developing release coatings with a reduced carbon footprint, creating recyclable release liners, and more. However, such changes are not without consequences, as alterations in components can impact release performance. To ensure that release coatings can effectively meet these evolving trends and coating performance targets, a profound understanding of the fundamental peeling mechanism is critical. This knowledge is essential for guiding the development direction and ensuring a prompt and successful response to market trends, thereby contributing to the overall improvement of sustainability.

As discussed earlier, the release liner market holds promising prospects and significant opportunities, particularly in the context of research papers that delve into the peeling mechanics of soft adhesives from release liners. This niche area of study plays a pivotal role in enhancing the understanding of adhesion dynamics, which in turn has wide-ranging implications across industries. This review paper focusing on peeling mechanics is poised to contribute valuable insights into the fundamental interactions between soft adhesives and release liners and a fundamental understanding of the delamination mechanism, shedding light on factors influencing adhesion and release performance.

As academia and industries continue to seek efficient and reliable ways to optimize adhesive and release coating performance, this review article provides deeper insights into the peeling mechanism of soft adhesives and opens doors to novel solutions and improved products to meet further needs. For example, the viscoelastic dissipation in the adhesive tape is supposed to play a vital role in release force. Section 3.1.3 discusses the details for the evaluation of the dissipation energy term for linear viscoelastic dissipation energy. In addition, the stress and deformation of a release liner, especially the stress and deformation around the peeling front, can be evaluated by using the method introduced in Sec. 4.1. Note that Sec. 4.1 considers the both tape and release liner as linear elastic materials. However, in practice, adhesive tape is a viscoelastic material; therefore, the theory presented in Sec. 4.1. should be extended. For instance, the rate–temperature superposition principle could be adopted in this theory to describe the peel behavior of the structure with a viscoelastic adhesive tape [73,80].

Food packaging is used to provide a barrier from harmful environmental factors such as microorganisms, light, and external gases; this barrier prevents or inhibits microbial and biochemical degradation and preserves inner aromatic gases to maintain flavor and freshness for the packed product. Therefore, the packaging should remain intact or sealed until consumer use. Flexible plastic packaging, which comprises thin film laminates, is a prevalent type of packaging that constitutes approximately 30% of the global packaging market and is increasing at an annual growth rate of 4.5%. This growth is primarily driven by the conversion of rigid packaging formats (e.g., glass, metal) to flexible packaging formats. Flexible packaging has several benefits over rigid packaging, such as being more convenient to carry and lighter in weight, which implies less energy is consumed for transportation. Flexible packaging is also more economical than rigid packaging [123].

Flexible packages are typically produced from materials like polymers, paper, and aluminum foil, utilizing a thin film or layered structure that is heat sealed [124]. This layering creates a laminate that combines unique properties and functionalities from different substances. The innermost layer is engineered for sealing, which is often referred to as the sealant layer [125]. Commonly, these sealant layers comprise thermally active materials such as thermoplastics, capable of adhering to not only similar materials but also to different substrates including plastic trays, bottles, metal cans, and glass containers. The process of sealing flexible packaging films can be accomplished through various techniques, with heat sealing being the most prevalent. Film packaging seals are primarily established via conductive heat, using a range of methods like seal bar, hot wire, hot air, pneumatic, ultrasound, and laser heating.

The seal performance is essential to ensure food safety and quality. In addition to strength, the barrier property is significant to inhibit food degradation and maintain freshness. It is noteworthy that heat-sealing applications frequently entail contact between two materials that are identical. The mechanisms contributing to adhesion and peel force involve the formation of molecular entanglements and co-crystallization at the interface between two polymer layers, among other factors, different from those discussed for release liners. These mechanisms are examined in more detail in the following sections.

Heat sealing is a process that involves melting two seal sides of packaging materials at high temperatures, allowing interphase molecular chain diffusion and solidifying them at low temperatures to create a seal. It is essential to comprehend the adhesion mechanisms to devise specific strategies to enhance the adhesion strength. Based on an energy balance perspective (see Sec. 3), the adhesion mechanisms during the heat-sealing process can be classified into two main types: those related to the interface, characterized by the interfacial fracture energy $(Γ)$⁠, and those concerning bulk materials, for which the quantity $dUd$ represents the energy dissipated within the bulk of the structure.

The main theoretical principles of forming a strong interface are to ensure close contact and robust interfacial bridging connections. The degree of contact depends largely on wettability, viscosity of sealant materials, surface contaminants, and so forth. Specifically, the wettability of the molten materials is the crucial parameter since it determines the ability to bond by filling gaps between two surfaces. The wetting behavior of a material is strongly related to its surface free energy (thermodynamic work of adhesion), and Dupre's equation is commonly used to estimate surface free energy (Eq. (36)).

In practice, some pressure is applied during heat sealing to improve adequate contact and wetting at the interface. Moreover, materials with lower viscosity at heating temperatures are preferable because they can fill gaps more easily in pouches or flow around contamination, thus achieving close contact and preventing leaks [126]. However, low-viscosity species may also reduce the overall bonding strength due to reduced entanglement. Therefore, polymer blends—for example, different grades of polyethylene—are also used to tune the heat seal strength. A similar strategy is applied when considering chain diffusion (see below), as the viscosity is closely related to chain diffusion.

Diffusion and entanglements determine the strength and effectiveness of the interfacial connections between the polymer layers. However, depending on the specific characteristics of the polymers involved, other mechanisms may also play a significant role. For example, for semicrystalline polymers, the crystallization process affects the number and the size of the crystals that form at the interface [127]. For polar polymers such as polylactic acid (PLA) and ethylene vinyl acetate, intermolecular interactions due to hydrogen bonds, polarity, and ionic groups are also important.

Since diffusion and entanglements are universal mechanisms, the following sections provide more detailed discussions of each. The investigation of chain diffusion requires a thorough understanding of the molecular level mobility of the material, which is intrinsically linked to its thermal attributes. For example, thermoplastics must be heated to enable diffusion and seal. Therefore, the thermal properties of sealant materials are of high importance. For amorphous polymers, the glass transition temperature (T_g) is most important as molecular segments transition from a glassy to a rubbery state with significant chain movement. For crystalline or semicrystalline materials, the melting temperature (T_m) is important as the crystalline phases begin to melt, and the material starts to flow. For instance, the seal initiation of semicrystalline low-density polyethylene (LDPE) or linear low-density polyethylene (LLDPE) occurs when the amorphous fraction increases by heating as crystalline regions melt and polymer chains become more mobile.

It is noteworthy that process parameters, such as interfacial temperature and seal time, are critical for sufficient diffusion and entanglements [128]. With increasing temperature, diffusion and entanglement are enhanced. The temperature at the interface should ensure the melted state of the sealant materials since melted sealant materials can facilitate better interface chain diffusion. A rapid increase in the seal strength is observed with increasing temperature until a plateau value is reached around T_m. Moreover, the sealing temperature needs to be controlled to be lower than the decomposition temperature (T_d).

The diffusion rates (chain mobility) of molecule chains depend primarily on the compatibility of the two sealant materials, molecular weight, chain branching, and so forth. For example, polymer chains with lower molecular weight tend to diffuse more rapidly. However, to obtain superior bonding strength, chains of higher molecular weight polymers are required to increase the potential for entanglements [129]—a characteristic that enhances the interfacial fracture energy and thus has a crucial effect on the final seal strength. The process of forming entanglements begins from the initial stages of sealing and continues through the cooling process. A more comprehensive discussion on fracture energy can be found in Sec. 3.4. In addition, there is a viscosity trade-off for sealant materials: slower diffusion of longer chains implies that it takes longer for these chains to form entanglements. Therefore, exploring the interplay between molecular weight, diffusion time, and fracture energy could be a compelling avenue for future research. In practice, the use of a combination of various molecular weight materials can thus balance the rate of the sealing process and the adhesion strength.

The theoretical mechanisms that underlie the behavior of bulk materials involve modifying the energy terms that originate from the bulk materials. For example, the incorporation of additives can significantly alter the properties of bulk materials, thereby affecting the energy dissipation from bulk materials. Furthermore, additives and processing aids are organic or inorganic molecules that are introduced in small quantities to the polymer matrix to adjust the properties of packaging films and/or enhance processing. According to Ref. [130], some common examples of stabilizers, modifiers, and other additives are pigments, slip agents, antiblocking, antistatic, process aids, nucleating agents, tackifiers, tougheners, and fillers.

Several ASTM standards are used to assess seal performance. Among them, ASTM F88/F88M-09 is widely used [131]. Seal strength is a measurement of the forces required to separate two sealed films. In this method, film samples are cut into strips of a specified size (e.g., 1 × 6 in.) using a die cutter of this dimension. A T-peel test is then conducted on the strips using an Instron Universal Testing Machine. T-peel tests are performed with an appropriate load cell (e.g., 5-kg load cell) at a predetermined separation rate (e.g., 10 cm/min). The maximum and average peel forces are recorded as the seal/peel strength.

Note that seal separation may also involve potential deformation or elongation of the seal films during the test. The influence of the elongation of the tape can be evaluated through energy-based and stress-based analyses. Specifically, for the elastic tape, the influence of elongation deformation can be calculated by Eq. (4).

To minimize the impact of the film material deformation, a piece of masking tape is often applied on the back of the test film strip to prevent stretching of the film. This masking tape allows for testing of adhesion between two sealed layers rather than the strength of the film itself. There are also various types of nondestructive testing and evaluation techniques that can potentially be used for the inspection of heat-sealing regions [132].

Polyolefins, especially LDPE or LLDPE, constitute the most prevalent sealing materials. Other thermoplastics such as ethylene vinyl acetate and ionomers, polyesters, including poly(ethylene terephthalate), and poly(butylene succinate) are also employed. In response to the growing demand for more environmentally friendly packaging solutions in the food packaging industry, changes encompass innovations in structure designs that facilitate better recyclability as well as bio-based and/or biodegradable alternatives such as cellulose-, starch-, PLA-based films. Further research is anticipated to design the material properties of such biodegradable alternatives and optimize their seal performance.

The selection and optimization of new materials for flexible packaging can be greatly facilitated and differentiated by applying a predictive engineering approach. Some studies have presented models of the influence of heat-sealing process parameters, such as temperature, dwell time, and pressure, on the peel strength [133,134]. However, there is a lack of research on the evaluation and modeling of peel phenomena during the peeling process. Therefore, there are opportunities to model the behavior of flexible packaging in a more comprehensive way. For instance, a parametric finite element model could be developed to simulate the progressive failure of the heat seal interface in a typical T-peel test. The seal interface could be modeled with a cohesive zone method.

To conclude, the seal strength is influenced by various factors such as the materials used, process conditions, and packaging designs. Peel modeling can facilitate a deeper understanding of peel failure modes and enable peel strength optimization. Predictive modeling for flexible packaging may contribute to the improvement and optimization of the material selection of new sustainable polymers to achieve seals with the required barrier and bonding strength.

A final commonly used application of soft adhesives on soft substrates encompasses medical adhesives, specifically those used on skin for securing wound dressings or for securing equipment like monitoring and life support devices, such as surgical drapes, steric-strips, electrodes, antimicrobial drape, wound dressings, and bandages. Adhesives for use in general biomedical applications are a rapidly growing industry with a market share of nearly $9 billion in 2021 [135]. By 2026, this industry is expected to reach nearly $12 billion, exhibiting double-digit annual growth rates [135–137]. This rapid growth is attributed to several factors, including their increased use in medical devices, implants, dental applications, and as replacements for surgical sutures or stapling to improve patient outcomes [135,137,138].

There are numerous published reviews specifically on skin adhesives, which can be largely divided into two categories: those focused on technical and materials approaches to control adhesion [139–142] and those focused on clinical cases by physicians [143–145]. To avoid repeating information already contained in these works and others, in this section, we provide only a brief overview of these works, general design criteria for skin adhesives, and unique approaches for characterizing their release performance. Several types of adhesives are used in applications for skin contact. Major categories include acrylic adhesives, silicone adhesives, polyurethane adhesives, and rubber-based adhesives, among others. Each type of adhesive has advantages and disadvantages, summarized in Table 2. Other categories for medical tapes and adhesives include polyolefins, hydrocolloids, and bio-based materials and hydrogels [140,145–147]. In particular, bio-based adhesives for such biomedical applications are a rapidly growing industry, comprising an over $2 billion market in the United States in 2021 that is expected to have a compound annual growth rate of 14% between 2022 and 2027 [147,148].

Compared with other PSA applications, the skin presents a unique and challenging adherend, distinct from other substrates due to its distinctive properties. The skin is a soft substrate with a low modulus, relatively low surface energy and a textured surface [146,150]. Additionally, the skin is a dynamic substrate undergoing rapid regeneration; as such, skin adhesives must adhere to a substrate that is constantly being shed. The skin is also susceptible to contamination from substances such as sweat and grease, which alter the surface energy and serves as a weak boundary layer, leading to poor long-term performance. Finally, the skin is prone to allergies caused by many chemicals, all of which contribute to the complexity of developing new adhesives.

Despite the challenges associated with the skin, the development of new adhesives with enhanced performance, such as controlled adhesion, hypoallergenic properties, and gentle removal, along with improved sustainability, is crucial to meet robust market demands, especially in medical and wearable electronics applications. Similar to other PSA applications, adhesives designed for skin applications prioritize three key performance factors: peel adhesion strength (resistance to removal by peeling), cohesion strength (resistance to shearing forces), and tack strength (speed of adherence to the adherent). However, skin adhesives must also have good water resistance and must pass strict quality control standards. Additional performance metrics are critical for designing these systems, including biocompatibility, skin permeability, skin trauma control, drug delivery, and others [137,139,141,145]. For example, traditional acrylic adhesives have low to moderate costs and medium to high adhesion strengths (Table 2), but cause more deformation and trauma to the skin upon removal [142,145,146,149,151]. Thus, to develop a successful product, a fundamental understanding of the peeling mechanism of the adhesive from the skin is crucial.

Beyond assessing performance via standard tests of peel adhesion strength, cohesion strength, and tack strength, several other tests have been used to evaluate clinical outcomes associated with the use of skin adhesives. Due to the wide range of skin adhesive functions and properties, the appropriate in vitro or in vivo tests to evaluate performance are application specific. For example, clinical studies on skin adhesive tapes have performed peel tests on human patients and evaluated transepidermal water loss, erythema (skin redness), and hydration following adhesive removal [145,152]. Additionally, several studies have evaluated skin adhesives in vitro using perspiration simulators to better understand the adhesive performance during sweating [153–155]. Clinical works have also measured alterations in skin barrier function, skin tearing and stripping, and skin dermatitis following adhesive removal [145,151,152]. In vivo tests of topical skin adhesive (TSA) performance also include measures of wound bursting strength and TSA flexibility [145,156–158]. As this wide range of application-specific testing protocols demonstrates, newly developed skin and tissue adhesives require additional performance testing versus standard PSAs to account for biological damage, prior to their adoption by the medical industry.

This review critically examines the theoretical foundations of peeling mechanics, with a special focus on peeling from soft substrates. It emphasizes the dual perspectives of energy and stress analysis. Additionally, the article discusses three potential industrial applications of peel mechanics. This work highlights the critical roles of viscoelastic dissipation and deformation behaviors in influencing peeling mechanics, particularly within the context of PSA-release liner systems and flexible packaging heat seal systems.

For the PSA-release liner system, the application of the stress-based analysis from Sec. 4.1 illuminates potential pathways for a more nuanced understanding of peel mechanics. This framework, albeit simplified to treat the tape as a homogeneous elastic material, hints at the complex interplay between material properties and peel behavior. In real-world scenarios, the distinct viscoelastic nature of the adhesive material emerges as a pivotal factor influencing peel behavior. The insights from Sec. 3.1.3 on evaluating viscoelastic dissipation energy further enrich our understanding of these systems and suggest a need to extend the theoretical models to encapsulate the viscoelastic characteristics of adhesive tapes. Such adaptations could leverage the rate–temperature superposition principle to yield a more accurate depiction of peel behavior under diverse conditions.

For the flexible packaging heat seal system, the theoretical concepts discussed in Sec. 3 offer a foundational understanding of the adhesion mechanisms pivotal during the heat-sealing process. The delineation of adhesion mechanisms into interface-related and bulk material-related categories provides a framework for assessing seal strength. Furthermore, the discussion on polymer chain characteristics and their diffusion rates underscores the nuanced balance between molecular weight and bonding strength, highlighting the essential role of polymer entanglement in augmenting interfacial fracture energy and, by extension, the durability of the seal.

This review also highlights several potential research avenues that remain untapped, evidenced by the unoccupied cells in Table 1. For instance, adhesive structures with both linear viscoelastic tape and linear viscoelastic substrates have yet to be extensively examined. Further exploration into these topics is not only academically stimulating but also holds substantial practical implications. For example, considering that both soft tissues and adhesives exhibit energy dissipation characteristics, developing a model that accounts for the viscoelastic properties of both the tape and the substrate could significantly advance bioadhesive applications. These gaps in research may stem from numerous factors such as the complexity of the problems, which renders mathematical models challenging to develop or apply. Often, to achieve a qualitative understanding of the peeling process, many mathematical theories may simplify the scenario by focusing on linear elastic materials, thereby neglecting more intricate physical phenomena like viscoelastic dissipation. Although these simplifications enable easier mathematical handling, they can omit critical physical insights. Nevertheless, these uncharted territories can present promising avenues for future research, holding the potential to further expand and deepen our understanding in this domain.

Y. X., C. J. E., L. F. F., and M. A. C. thank The Dow Chemical Company for supporting this collaborative research. The authors thank Tim Mitchell and Michaeleen Pacholski for useful discussions.

There are no conflicts of interest.

The authors attest that all data for this study are included in the paper.

Derail et al. [75,76] developed a theoretical method based on the balance of angular momentum to capture the peeling process of the adhesive structure with an elastic/elastic–plastic tape and viscoelastic adhesive.