The process of charging and discharging of lithium-ion batteries results in the intercalation and ejection of lithium ions in the anode material. The ensuing electro-chemo-mechanical stresses and accompanying microstructural changes lead to a complex state of inelastic deformation and damage in the silicon electrode that cause a significant capacity loss within just a few cycles. In this study, we attempt to understand, from an atomistic viewpoint, the mechanisms underlying the plasticity behavior of Si-anode as a function of lithiation. Conventional molecular dynamics simulations are of limited use since they are restricted to loading rates in the order of 10 8 s −1 . Practical charging-discharging rates are several orders of magni- tude slower, thus precluding a realistic atomistic assessment of the highly rate-dependent mechanical behavior of lithiated silicon anodes via conventional molecular dynamics. In this work, we use a time-scaling approach that is predicated on a combination of a potential energy surface sampling method, minimum energy pathway, kinetic Monte Carlo, and transition state theory, to achieve applied strain rates as low as 1 s −1 . We assess and compare the atomistic mechanisms of plastic deformation in three different lithium concentration structures: LiSi 2 , LiSi, and Li 15 Si 4 for various strain-rates. We find that the strain rate plays a significant role in the alteration of the deformation and damage mechanisms including the evolution of the plastic deformation, nucleation of shear transformation zone, and void nucleation. Somewhat anomalously, LiSi appears to demonstrate (comparatively) the least strain rate sensitivity.

The goal of this paper is to derive closed form expressions for the energy release rate and mode partitioning of face/core debonds in sandwich composites, which include loading in shear. This is achieved by treating a finite length sandwich beam as having a “debonded” section where the debonded top face and the substrate (core and bottom face) are free and a “joined” section where a series of springs (elastic foundation) exists between the face and the substrate. The elastic foundation analysis is comprehensive and includes the deformation of the substrate part (unlike other elastic foundation studies in the literature) and is done for a general asymmetric sandwich construction. A J-integral approach is subsequently used to derive a closed form expression for the energy release rate. In the context of this elastic foundation model, a mode partitioning approach based on the transverse and axial displacements at the beginning of the elastic foundation (“debond tip”) is proposed. The results are compared with finite element results and show very good agreement.

Two-dimensional hexachiral lattices belong to the family of honeycomb-like mechanical metamaterials such as triangular, hexagonal, and kagome lattices. The common feature of this family of beam-based metamaterials is their six-fold rotational symmetry which guarantees their (transversely-) isotropic elastic response. In the case of hexachiral lattices, a single geometric parameter may be introduced to control the degree of chirality such that the elastic Poisson's ratio can be adjusted between 0.33 and −0.8. Detailed finite element simulations are performed to establish the structure–property relationships for hexachiral lattices for relative densities ranging from 1% to 45%. It is shown that both the Young's and shear moduli are always lower for hexachiral structures than for optimal lattices (triangular and kagome). This result is in line with the general understanding that stretching-dominated architectures outperform bending-dominated architectures. The same conclusions may be drawn from the comparison of the tensile yield strength. However, hexachiral structures provide a lower degree of plastic anisotropy than stretching-dominated lattices. Furthermore, special hexachiral configurations have been identified that exhibit a slightly higher shear yield strength than triangular and kagome lattices, thereby presenting an example of bending-dominated architectures outperforming stretching-dominated architectures of equal mass. Tensile specimens have been additively manufactured from a tough PLA polymer and tested to partially validate the simulation results.

The mechanics of mode-III defect initiation and quasi-static growth is examined by analyzing a torqued cylindrical bar separated at its midsection by a nonuniform, nonlinear cohesive interface. The exact analysis is based on the elasticity solution to the problem of a cylinder subjected to nonuniform shear traction at one end and an equilibrating torque at the other. The formulation leads to a pair of interfacial integral equations governing the relative rigid body rotation and the interfacial separation field. The cohesive interface is assumed to be modeled by three Needleman-type traction–separation relations characterized by a shear strength, a characteristic force length and, depending on the specific law, other parameters. Axisymmetric penny, edge, and annular interface defects are modeled by a strength function which varies with radial interface coordinate. Infinitesimal strain equilibrium solutions are sought by eigenfunction approximation of the solution of the governing interfacial integral equations. Results show that for increasing remote torque, at small values of force length, brittle behavior occurs that corresponds to sharp crack growth. At larger values of force length, ductile response occurs similar to a linear “spring” interface. Both behaviors ultimately give rise to the failure of the interface. Results for the stiff, strong interface under a small applied torque show excellent agreement with the static fracture mechanics solution of Benthem and Koiter (1973, “Asymptotic Approximations to Crack Problems,” Mechanics of Fracture, Vol. 1, G.C. Sih, ed., Noordhoff, Leyden, pp. 131–178) for the edge cracked, torsionally loaded cylindrical bar. Extensions of the theory are carried out for (i) the bi-cylinder problem and (ii) the decohesive, frictional interface problem.

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.

We consider the maximum value of the magnitude of transformation strain for an Eshelby inclusion set by the requirement of non-negative dissipation. The general formulation for a linear elastic solid shows that the dissipation associated with a strain transformation can be calculated as an integral over the transformed inclusion. Closed-form expressions are given for the maximum transformation strain magnitude in an isotropic linear elastic solid for both cylindrical and spherical inclusions that have undergone transformations corresponding to either a pure volume (or area) change or a pure shear. Most results presented are for transformations in an infinite solid and presume uniform material properties. Examples of the effect of a finite boundary and of differing material properties inside and outside the transformed inclusion are also given. The analytical results indicate that non-negative dissipation typically limits the transformation strain to being a constant of order unity times the critical stress at transformation divided by a relevant elastic modulus.

Modeling the interface between two adherents in a co-cured composite joint for a delamination analysis is always a challenge since properties and thickness of the material forming the interface are not clearly defined or well characterized. In a conventional finite element (FE) analysis using virtual crack closure technique (VCCT) based on a linear elastic fracture mechanics (LEFM) theory, adherents are assigned to share the same common nodes along their intact interface. On the other hand, an FE analysis using cohesive elements or analytical methods based on an adhesive joint model for a delamination analysis of a co-cured joint will require modeling of the interface as well as the appropriate selection of its thickness and properties. The purpose of this paper is to establish the applicability and limitation of the adhesive joint model for a delamination analysis of a co-cured composite joint. In particular, it will show that when certain requirements are met, the strain energy release rates (SERR) become independent or nearly independent of the adhesive stiffness and thickness, and thus, SERR of an adhesive joint will be the same as that for a co-cured joint. These requirements are determined from a theoretical consideration, and they can be expressed explicitly in terms of joint characteristic (or load transfer) lengths and joint physical lengths. The established requirements are further validated by numerical results for various cracked joint geometries. Finally, implication of a mode ratio obtained by the proposed adhesive joint model for a corresponding delamination crack is discussed.

The electrospinning process enables the fabrication of randomly distributed nonwoven polymer fiber networks with high surface area and high porosity, making them ideal candidates for multifunctional materials. The mechanics of nonwoven networks has been well established for elastic deformations. However, the mechanical properties of the polymer fibrous networks with large deformation are largely unexplored, while understanding their elastic and plastic mechanical properties at different fiber volume fractions, fiber aspect ratio, and constituent material properties is essential in the design of various polymer fibrous networks. In this paper, a representative volume element (RVE) based finite element model with long fibers is developed to emulate the randomly distributed nonwoven fibrous network microstructure, enabling us to systematically investigate the mechanics and large deformation behavior of random nonwoven networks. The results show that the network volume fraction, the fiber aspect ratio, and the fiber curliness have significant influences on the effective stiffness, effective yield strength, and the postyield behavior of the resulting fiber mats under both tension and shear loads. This study reveals the relation between the macroscopic mechanical behavior and the local randomly distributed network microstructure deformation mechanism of the nonwoven fiber network. The model presented here can also be applied to capture the mechanical behavior of other complex nonwoven network systems, like carbon nanotube networks, biological tissues, and artificial engineering networks.

The shear stress–strain response of an aluminum alloy is measured to a shear strain of the order of one using a pure torsion experiment on a thin-walled tube. The material exhibits plastic anisotropy that is established through a separate set of biaxial experiments on the same tube stock. The results are used to calibrate Hill's quadratic anisotropic yield function. It is shown that because in simple shear the material axes rotate during deformation, this anisotropy progressively reduces the material tangent modulus. A parametric study demonstrates that the stress–strain response extracted from a simple shear test can be influenced significantly by the anisotropy parameters. It is thus concluded that the material axes rotation inherent to simple shear tests must be included in the analysis of such experiments when the material exhibits anisotropy.

Many natural materials, such as shell and bone, exhibit extraordinary damping properties under dynamic outside excitations. To explore the underlying mechanism of these excellent performances, we carry out the shear-lag analysis on the unit cell in staggered composites. Accordingly, the viscoelastic properties of the composites, including the loss modulus, storage modulus, and loss factor, are derived. The damping properties (particularly, the loss modulus and loss factor) show an optimization with respect to the constituents' properties and morphology. The optimal scheme demands a proper selection of four key factors: the modulus ratio, the characteristic frequency of matrix, aspect ratios of tablets, and matrix. The optimal loss modulus is pointed out to saturate to an upper bound that is proportional to the elastic modulus of tablets when the viscosity of matrix increases. Furthermore, a loss factor even greater than one is achievable through microstructure design. Without the assumption of a uniform shear stress distribution in the matrix, the analysis and formulae reported herein are applicable for a wide range of reinforcement aspect ratios. Further, for low-frequency loading, we give practical formulae of the three indexes of damping properties. The model is verified by finite element analysis (FEA) and gives novel ideas for manufacturing high damping composites.

Rubber bearings, used for seismic isolation of structures, undergo large shear deformations during earthquakes as a result of the horizontal motion of the ground. However, the bearings are also compressed by the weight of the structure and possible traffic on it. Hence, failure analysis of rubber bearings should combine compression and shear. Such combination is considered in the present communication. In order to analyze failure, the strain energy density is enhanced with a limiter, which describes rubber damage. The inception of material instability and the onset of damage are marked by the violation of the condition of strong ellipticity, which is studied in the present work. Results of the studies suggest that horizontal cracks should appear because of the dominant shear deformation in accordance with the experimental observations. It is remarkable that compression delays failure in terms of the critical stretches.

Analytical displacement and stress fields with stress concentration factors (SCFs) are derived for linearly elastic annular regions subject to inhomogeneous boundary conditions: an infinite class of the mth order polynomial antiplane tractions or displacements. The solution of the Laplace equation governing the out-of-plane problem covers both rigid and void circular inclusions forming the core of the annulus. The results show first that the SCF and the loading order are inversely proportional. In particular, the SCF approaches value 2 when either the outer boundary of the annulus tends to infinity or the order of the polynomial loading increases. Second, the number of peculiar points on the inner contour having null stress increases with the increasing loading order. The analytical solution is confirmed and extended to noncircular enclosures via finite element analysis by exploiting the heat-stress analogy. The results show that the closed-form solution for a circular annulus can be used as an accurate approximation for noncircular enclosures. Altogether, the results shown can be exploited for analyzing complex loading conditions and/or multiple rigid or void inclusions for enhancing the design of hollow and reinforced composites materials.

Thermal inclusion in an elastic half-space is a classical micromechanical model for describing localized heating near a surface. This paper presents explicit analytical solutions for the complete elastic fields, including displacements, strains, and stresses, produced by an ellipsoidal thermal inclusion in a three-dimensional semi-infinite space. Unlike the famous Eshelby solution corresponding to the infinite space case, the present work demonstrates that the interior strain and stress components are no longer uniform and appear to be much more complex. Nevertheless, the results can be represented in a more compact and geometrically meaningful form by constructing auxiliary confocal ellipsoids. The derived explicit solution indicates that the shear components of the stress and strain may be represented in closed-form. The jump conditions are examined and proven to be exactly identical to the infinite space case. A purposely selected benchmark example is studied to illustrate the free boundary surface effects. The degenerate case of a spherical thermal inclusion may be derived in a closed form, and is verified by the well-known Mindlin solution.

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 idealized inverse-opal lattice is a network of slender struts that has cubic symmetry. We analytically investigate the elastoplastic properties of the idealized inverse-opal lattice. The analysis reveals that the inverse-opal lattice is bending-dominated under all loadings, except under pure hydrostatic compression or tension. Under hydrostatic loading, the lattice exhibits a stretching dominated behavior. Interestingly, for this lattice, Young's modulus and shear modulus are equal in magnitude. The analytical estimates for the elastic constants and yield behavior are validated by performing unit-cell finite element (FE) simulations. The hydrostatic buckling response of the idealized inverse-opal lattice is also investigated using the Floquet–Bloch wave method.

Knowledge of the ideal shear strength of solid single crystals is of fundamental importance. However, it is very hard to determine this quantity at finite temperatures. In this work, a theoretical model for the temperature-dependent ideal shear strength of solid single crystals is established in the view of energy. To test the drawn model, the ideal shear properties of Al, Cu, and Ni single crystals are calculated and compared with that existing in the literature. The study shows that the ideal shear strength first remains approximately constant and then decreases almost linearly as temperature changes from absolute zero to melting point. As an example of application, the “brittleness parameter” of solids at elevated temperatures is quantitatively characterized for the first time.