Understanding lipid sorting of multicomponent cell membranes associated with tubular deformation is of essential importance to many cell activities such as filopodial growth and protein-mediated vesiculation. Here, we conduct theoretical analysis to investigate how the membrane tubulation induced by an external pulling force over a finite region is regulated by the coupling between the lipid composition and the membrane bending rigidity and tension. It is shown that the presence of the lipid-disordered phase facilitates the nanotube formation by reducing the force barrier. As the pulling region size and the membrane tension increase, the membrane tubulation becomes discontinuous regardless of the coupling effect. The direct proportional relationships between the maximum pulling force and size of pulling region at different coupling scenarios are identified. Analytical solutions for the linear force-extraction relation and the membrane configurations in the early stage of the membrane extraction are obtained. Our results indicate that in the case of a relatively small pulling region, the coupling between the membrane composition and mechanical properties plays an important role in regulating the membrane extraction, and such an effect due to the phase separation diminishes gradually as the pulling region enlarges and the force barrier becomes dominated by a large pulling region.

Most soft materials resist volumetric changes much more than shape distortions. This experimental observation led to the introduction of the incompressibility constraint in the constitutive description of soft materials. The incompressibility constraint provides analytical solutions for problems which, otherwise, could be solved numerically only. However, in the present work, we show that the enforcement of the incompressibility constraint in the analysis of the failure of soft materials can lead to somewhat nonphysical results. We use hyperelasticity with energy limiters to describe the material failure, which starts via the violation of the condition of strong ellipticity. This mathematical condition physically means inability of the material to propagate superimposed waves because cracks nucleate perpendicular to the direction of a possible wave propagation. By enforcing the incompressibility constraint, we sort out longitudinal waves, and consequently, we can miss cracks perpendicular to longitudinal waves. In the present work, we show that such scenario, indeed, occurs in the problems of uniaxial tension and pure shear of natural rubber. We also find that the suppression of longitudinal waves via the incompressibility constraint does not affect the consideration of the material failure in equibiaxial tension and the practically relevant problem of the failure of rubber bearings under combined shear and compression.

Staggered architectures widely seen in load-bearing biological materials provide not only excellent supporting functions resisting static loading but also brilliant protecting functions attenuating the dynamic impact. However, there are very few efforts to unveil the relationship between staggered architectures and damping properties within load-bearing biological and bioinspired materials, while its static counterpart has been intensively studied over the past decades. Here, based on the Floquet theory, we developed a new generic method to evaluate the dynamic modulus of the composites with various staggered architectures. Comparisons with the finite element method results showed that the new method can give more accurate predictions than previous methods based on the tension-shear chain model. Moreover, the new method is more generic and applicable for two- and three-dimensional arbitrarily staggered architectures. This method provides a useful tool to understand the relationship between micro-architecture and damping property in natural load-bearing biological materials and to facilitate the architectural design of high-damping bioinspired composites.

Recent studies have shown that steady and unsteady operation of a belt drive may exhibit regimes absent of sliding at the belt–pulley interface, where instead detachment waves serve to relax stress in the so-called “slip” arc. To explore this finding further, herein we present an experimental and theoretical investigation into frictional mechanics in a simple belt drive system. To estimate friction experimentally, we perform a stress analysis based on spatio-temporal measurements of the belt tension, traction, and contact area evolution. Subsequently, we develop a model taking into account both bulk and surface hysteretic losses to explain the experimental observations. Our results show that the shear strain at the belt–pulley interface differs significantly between the driver and the driven pulleys, resulting in much larger mechanical losses in the driver case. The shear strain drops at the transition from the adhesion to the slip arc, and, in contrast to accepted theories, the slip arc contributes little to nothing to the power transmission. Our model reveals that the contact area evolution correlates to the shear traction changes and that viscoelastic shear and stretching dominate in the belt rolling friction. A significant contribution of detachment waves to the energy dissipation explains the higher mechanical losses observed in the driver case.

Porous bulk metallic glasses (BMGs) exhibit an excellent combination of superior mechanical properties such as high strength, high resilience, large malleability, and energy absorption capacity. However, a mechanistic understanding of their response under diverse states of stress encountered in practical load-bearing applications is lacking in the literature. In this work, this gap is addressed by performing three-dimensional finite element simulations of porous BMGs subjected to a wide range of tensile and compressive states of stress. A unit cell approach is adopted to investigate the mechanical behavior of a porous BMG having 3% porosity. A parametric study of the effect of stress triaxialities T = 0, ±1/3, ±1, ±2, ±3, and ±∞, which correspond to stress states ranging from pure deviatoric stress to pure hydrostatic stress under tension and compression, is conducted. Apart from the influence of T, the effects of friction parameter, strain-softening parameter and Poisson’s ratio on the mechanics of deformation of porous BMGs are also elucidated. The results are discussed in terms of the simulated stress-strain curves, pore volume fraction evolution, strain to failure, and development of plastic deformation near the pore. The present results have important implications for the design of porous BMG structures.

The recently developed theory for isotropic material failure is briefly outlined. Many steps and stages of the verification process for the theory are fully documented so that it can be used with assurance in a wide variety of directions. Then, the failure theory is used to develop a new measure or index for the degree of ductility of material failure in any state of stress. This new failure property is named the ductility number, Nd. It is rigorously derived, intuitively compatible, and very easy to use. Applications and interpretations of Nd are given.

The modeling of the different mechanical behaviors of brittle and quasi-brittle materials in tension and compression leads to partitioning of the strain (or stress) tensor into a positive part and a negative part. In this study, applying a recently proposed general method to the two-dimensional (2D) strain and stress tensors, closed-form coordinate-free expressions are obtained for their decompositions which are orthogonal in the sense of an inner product where the forth-order elastic stiffness or compliance acts as a metric. The orthogonal decompositions are given analytically and explicitly for all possible 2D elastic symmetries, i.e., isotropic, orthotropic, square, and totally anisotropic elastic materials. These results can be directly used, for example, in developing phase field methods for modeling and simulating the fracture of isotropic and anisotropic brittle and quasi-brittle materials.

Predeformation simultaneously changes the effective material stiffness as well as the geometric configuration and therefore may be utilized to tune wave propagation in soft phononic crystals (PCs). Moreover, the band gaps of soft PCs, as compared with those of the hard ones, are more sensitive to the external mechanical stimuli. A one-dimensional tunable soft acoustic diode based on soft functionally graded (FG) PCs is proposed. The two-way asymmetric propagation behavior is studied at the resonant frequency within the band gap. Numerical results show that the operating frequency (i.e., the resonant peak) of the soft graded acoustic diode can be altered by adjusting the mechanical biasing fields (including the longitudinal prestress and the lateral equibiaxial tension). The adjustment becomes significant when the strain-stiffening effect of the Gent hyperelastic material is properly harnessed. Furthermore, the prestress or equibiaxial tension can affect the two-way filtering of the soft FG PC in a separate and different manner. In addition, it is much easier to realize the tunable acoustic diode by exploiting soft FG materials with stronger compressibility. It is shown that the introduction of acoustic impedance is beneficial for predicting the tunable effects. The simulations and conclusions should provide a solid guidance for the design of tunable two-way unidirectional acoustic diodes made from soft hyperelastic materials.

We experimentally study the dynamic behavior of a belt-drive system to explore the effect of loading conditions, driving speed, and system inertia on both the frequency and amplitude of the observed frictional and rotational instabilities. A self-excited oscillation is reported whereby local detachment events in the belt–pulley interface serve as harmonic forcing of the pulley, leading to angular velocity oscillations that grow in time. Both the frictional instabilities and the pulley oscillations depend strongly on operating conditions and system inertia, and differ between the driver and driven pulleys. A larger net torque applied to the pulley generally intensifies Schallamach waves of detachment in the driver case but has little influence on other measured response quantities. Higher driving speeds accelerate the occurrence of frictional instabilities as well as pulley oscillations in both cases. Increasing the system's inertia does not affect the behavior of contact instabilities, but does lead to a steadier rotation of the pulley and more pronounced fluctuations in the belt tension. A simple dynamic model of the belt-drive system demonstrates good agreement with the experimental results and provides strong evidence that frictional instabilities are the primary source of the system's self-oscillation.

A six-node incompatible graded finite element is developed and studied. Such element is recommended for use since it is more accurate than four-node compatible element and more efficient than eight-node compatible element in two-dimensional plane elasticity. This paper presents comparison between six-node incompatible (QM6) and four-node compatible (Q4) graded elements. Numerical solution is obtained from abaqus using UMAT capability of the software and exact solution is provided as reference for comparison. A graded plate with exponential and linear gradation subjected to traction and bending load is considered. Additionally, three-node triangular (T3) and six-node triangular (T6) graded elements are compared to QM6 element. Incompatible graded element is shown to give better performance in terms of accuracy and computation time over other element formulations for functionally graded materials (FGMs).

We consider the plane deformations of an infinite elastic solid containing an arbitrarily shaped compressible liquid inhomogeneity in the presence of uniform remote in-plane loading. The effects of residual interface tension and interface elasticity are incorporated into the model of deformation via the complete Gurtin–Murdoch (G–M) interface model. The corresponding boundary value problem is reformulated and analyzed in the complex plane. A concise analytical solution describing the entire stress field in the surrounding solid is found in the particular case involving a circular inhomogeneity. Numerical examples are presented to illustrate the analytic solution when the uniform remote loading takes the form of a uniaxial compression. It is shown that using the simplified G–M interface model instead of the complete version may lead to significant errors in predicting the external loading-induced stress concentration in gel-like soft solids containing submicro- (or smaller) liquid inhomogeneities.

This paper presents a detailed study on the fracture behaviors of soft materials with hard inclusion. Stress concentrations on the interfaces of hard and soft materials are considered as the key factor for structure fracture. Based on linear fracture theory, the fracture behaviors of soft materials with elliptical hard inclusion are investigated. Stress concentrations, consisting of tensile, hoop, and compressive stress, are observed with changes of inclusion geometries and the modulus ratio of hard and soft materials. And their influences on the categories of principal stress concentration are shown in a phase diagram in the current paper. Finite element analysis is carried out with consideration of the large deformation of soft material, which demonstrates the effectiveness of the theoretical predictions in a great scope of applied loading. Finally, the predictions based on theoretical and simulation results are validated by experiments. This work points out that the hard line inclusion is the source of danger in soft materials just like the crack in brittle materials.

Fiber-based materials are prevalent around us. While microscopically these systems resemble a discrete assembly of randomly interconnected fibers, the network architecture varies from one system to another. To identify the role of the network architecture, we study here cellular and fibrous random networks in tension and compression, and in the context of large strain elasticity. We observe that, compared to cellular networks of same global parameter set, fibrous networks exhibit in tension reduced strain stiffening, reduced fiber alignment, and reduced Poisson's contraction in uniaxial tension. These effects are due to the larger number of kinematic constraints in the form of cross-links per fiber in the fibrous case. The dependence of the small strain modulus on network density is cubic in the fibrous case and quadratic in the cellular case. This difference persists when the number of cross-links per fiber in the fibrous case is rendered equal to that of the cellular case, which indicates that the different scaling is due to the higher structural disorder of the fibrous networks. The behavior of the two network types in compression is similar, although softening induced by fiber buckling and strain localization is less pronounced in the fibrous case. The contribution of transient interfiber contacts is weak in tension and important in compression.

The application of explicit dynamics to simulate quasi-static events often becomes impractical in terms of computational cost. Different solutions have been investigated in the literature to decrease the simulation time and a family of interesting, increasingly adopted approaches are the ones based on the proper orthogonal decomposition (POD) as a model reduction technique. In this study, the algorithmic framework for the integration of the equation of motions through POD is proposed for discrete linear and nonlinear systems: a low dimensional approximation of the full order system is generated by the so-called proper orthogonal modes (POMs), computed with snapshots from the full order simulation. Aiming to a predictive tool, the POMs are updated in itinere alternating the integration in the complete system, for the snapshots collection, with the integration in the reduced system. The paper discusses details of the transition between the two systems and issues related to the application of essential and natural boundary conditions (BCs). Results show that, for one-dimensional (1D) cases, just few modes are capable of excellent approximation of the solution, even in the case of stress–strain softening behavior, allowing to conveniently increase the critical time-step of the simulation without significant loss in accuracy. For more general three-dimensional (3D) situations, the paper discusses the application of the developed algorithm to a discrete model called lattice discrete particle model (LDPM) formulated to simulate quasi-brittle materials characterized by a softening response. Efficiency and accuracy of the reduced order LDPM response are discussed with reference to both tensile and compressive loading conditions.

The dynamic tensile response of additively manufactured (AM) dense and porous Ti6Al4V specimens was investigated under quasi-static and dynamic tension. The porous specimens contained single embedded spherical pores of different diameters. Such artificial spherical pores can mimic the behavior of realistic flaws in the material. It was found that beyond a certain pore diameter (Ø600 μ m), the failure is determined according to the pore location, characterized by an abrupt failure and a significant decrease of ductility, while below that diameter, necking and fracture do not occur at the pore. The dynamic tensile mechanical behavior of the additively manufactured dense material was found to be similar to that of the conventional equivalent material, but the ductility to failure of the latter is observed to be higher.

Guided by the experimental observations in the literature, this paper discusses two possible modes of defect growth in soft solids for which the size-dependent fracture mechanics is not always applicable. One is omni-directional growth, in which the cavity expands irreversibly in all directions; and the other is localized cracking along a plane. A characteristic material length is introduced, which may shed light on the dominant growth mode for defects of different sizes. To help determine the associated material properties from experimental measurement, the driving force of defect growth as a function of the remote load is calculated for both modes accordingly. Consequently, one may relate the measured critical load to the critical driving force and eventually to the associated material parameters. For comprehensiveness, the calculations here cover a class of hyperelastic materials. As an application of the proposed hypothesis, the experimental results (Cristiano et al., 2010, “An Experimental Investigation of Fracture by Cavitation of Model Elastomeric Networks,” J. Polym. Sci. Part B: Polym. Phys., 48 (13), pp. 1409–1422) from two polymers with long and short chain elastomeric network are examined. The two polymers seem to be susceptible to either of the two dominating modes, respectively. The results are interpreted, and the material characteristic length and other growth parameters are determined.

We proposed an eccentric ellipse criterion to describe the failure of amorphous materials under a combination of normal stress σ and shear stress τ . This criterion can reflect a tension–compression strength asymmetry, and unify four previous failure criteria in the σ–τ stress space, including von Mises criterion, Drucker–Prager criterion, Christensen criterion, and ellipse criterion. We examined the validity of the eccentric ellipse criterion in the tensile-shear failure regimes using the results from our atomistic simulations for two typical amorphous CuZr and LiSi, and recent tension–torsion experiments on metallic glasses. The predictions from the eccentric ellipse criterion agree well with these results from atomistic simulations and experiments. It indicates that this eccentric ellipse criterion is essential for the tensile-shear failure of amorphous materials.

The conventional contact mechanics does not account for surface tension; however, it is important for micro- or nanosized contacts. In the present paper, the influences of surface tension on the indentations of an elastic half-space by a rigid sphere, cone, and flat-ended cylinder are investigated, and the corresponding singular integral equations are formulated. Due to the complicated structure of the integral kernel, it is difficult to obtain their analytical solutions. By using the Gauss–Chebyshev quadrature formula, the integral equations are solved numerically first. Then, for each indenter, the analytical solutions of two limit cases considering only the bulk elasticity or surface tension are presented. It is interesting to find that, through a simple combination of the solutions of two limit cases and fitting the direct numerical results, the dependence of load on contact radius or indent depth for general case can be given explicitly. The results incorporate the contribution of surface tension in contact mechanics and are helpful to understand contact phenomena at micro- and nanoscale.

In this paper, a three-dimensional (3D) finite-element (FE) contact model of a 6 + 1 wire rope strand bent over a simplified traction sheave is developed to investigate the traction behavior at the interface. The stress as well as the tension distribution within the 6 + 1 wire rope are discussed first. The FE analysis indicates that ascending preload at rope-ends leads to the incensement of the real contact wrap angle, which is critical in the calculation of traction capability. Meanwhile, the influences of groove angle on the contact pressure distribution and traction capability are demonstrated as well.

In this paper, a recently developed higher-order microplane (HOM) model for softening and localization is implemented within a isogeometric finite-element framework. The HOM model was derived directly from a three-dimensional discrete particle model, and it was shown to be associated with a high-order continuum characterized by independent rotation and displacement fields. Furthermore, the HOM model possesses two characteristic lengths: the first associated with the spacing of flaws in the material internal structure and related to the gradient character of the continuum; the second associated with the size of these flaws and related to the micropolar character of the continuum. The displacement-based finite element implementation of this type of continua requires C 1 continuity both within the elements and at the element boundaries. This motivated the implementation of the concept of isogeometric analysis which ensures a higher degree of smoothness and continuity. Nonuniform rational B-splines (NURBS) based isogeometric elements are implemented in a 3D setting, with both displacement and rotational degrees-of-freedom at each control point. The performed numerical analyses demonstrate the effectiveness of the proposed HOM model implementation to ensure optimal convergence in both elastic and softening regime. Furthermore, the proposed approach allows the natural formulation of a localization limiter able to prevent strain localization and spurious mesh sensitivity known to be pathological issues for typical local strain-softening constitutive equations.