Journal of The Mechanics and Physics of Solids最新文献

{"title":"Dynamic crushing of metal lattice metamaterials: Shock mode diagrams and transition to topology-independent compaction regime","authors":"Brandon K. Zimmerman,&nbsp;Eric B. Herbold,&nbsp;Mukul Kumar,&nbsp;Jonathan Lind","doi":"10.1016/j.jmps.2026.106515","DOIUrl":"10.1016/j.jmps.2026.106515","url":null,"abstract":"<div><div>Additively manufactured lattice metamaterials offer design versatility in strength and energy absorption and provide an additional degree of freedom through the selection of the lattice topology. Under quasistatic loading, the unit cell structure can strongly affect the stiffness, yield, and post-yield behavior, but whether and to what degree the effect of lattice topology persists into dynamic loading scenarios, up to the compaction shock regime, has not been established. LLNL’ s ALE3D hydrocode was used to perform a computational investigation of dynamic loading in multiple lattice types, including the gyroid, octet, Schwarz D, and rhombic dodecahedron, under impact velocities from 0.25 to 2.25 km/s. Shock Hugoniots for each lattice topology are generated and compared, suggesting that above a critical velocity, distinctions between architectures may not persevere and compacted lattices behave similarly. To investigate the transition between topology-dependent quasistatic compression and the topology-independent regime above the critical velocity, a one-dimensional elastic-linear hardening plasticity-densified solid (E-LHP-DS) shock model for lattice materials was developed that relies upon confined compression to link the quasistatic and shock mechanics. Unlike similar works, the model does not assume rigid behavior prior to yield or locking behavior at densification, allowing a richer exploration of lattice mechanics. With only six parameters, the analytical model simultaneously fit quasistatic confined compression simulations for relative densities <span><math><mrow><mn>0.1</mn><mo>≤</mo><mover><mi>ρ</mi><mo>¯</mo></mover><mo>≤</mo><mn>0.9</mn></mrow></math></span> and predicted dynamic compaction behavior to traverse several distinct shock modes, each defined by a critical impact speed (equivalently, critical stresses). Comparing the numerical results to the one-dimensional E-LHP-DS shock model predictions suggests that the topology-independence under strong shocks is linked to the onset of densification, which can be predicted based on quasistatic confined compression results.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"210 ","pages":"Article 106515"},"PeriodicalIF":6.0,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146033264","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Contact in strain gradient elasticity: The rigid flat punch problem","authors":"P.A. Gourgiotis ,&nbsp;Th. Zisis ,&nbsp;A.E. Giannakopoulos ,&nbsp;H.G. Georgiadis","doi":"10.1016/j.jmps.2026.106527","DOIUrl":"10.1016/j.jmps.2026.106527","url":null,"abstract":"<div><div>This work revisits the classical flat-punch indentation problem within the framework of Mindlin’s form-II strain-gradient elasticity, uncovering new phenomena driven by the interplay between contact geometry and material length scale. The analysis is carried out under plane strain conditions, and the corresponding mixed boundary value problem is solved using integral equation techniques. Two distinct contact regimes are examined. In the first, assuming full contact beneath the rigid indenter, the pressure distribution exhibits hypersingular behavior with tensile (adhesive-like) tractions near the contact edges. These arise purely from kinematic constraints, without invoking any cohesive law or surface energy. The second regime emerges by relaxing the flatness assumption, allowing for partial separation beneath the punch. In this case, contact is sustained only within a central region, flanked by separation gaps near the edges and balanced by concentrated edge reactions. The resulting pressure is entirely positive and exhibits a classical square-root singularity. Both the contact width and edge forces are shown to depend sensitively on Poisson’s ratio and the material length scale. Beyond a critical length, the contact region collapses, and the problem reduces to the superposition of two Flamant-type concentrated contact solutions. These findings reveal a rich class of indentation responses naturally captured by strain gradient elasticity-phenomena inaccessible to classical continuum models. They may have important implications for nano/micro-indentation experiments on materials with pronounced internal length scales, such as polymers, ceramics, composites, cellular solids, masonry, and biological tissues.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"210 ","pages":"Article 106527"},"PeriodicalIF":6.0,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146033263","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Generalized configurational force for thermoelasticity with application to isogeometric analysis of thermoelastic crack propagation","authors":"Chung-Shuo Lee,&nbsp;Pei-En Chou,&nbsp;Ganesh Subbarayan","doi":"10.1016/j.jmps.2026.106541","DOIUrl":"10.1016/j.jmps.2026.106541","url":null,"abstract":"<div><div>Accurately predicting the forces driving crack propagation is critical for engineering applications where fracture is an important failure criterion. An easy to apply configurational force theory for estimating crack driving force in thermoelastic solids is derived in this study. The derivation relies on the notion of a configurational optimization problem for heterogeneities inserted into a homogeneous domain. The configurational optimization allows arbitrary objectives subject to constraints of variational principles governing the solid behavior. The optimality criteria obtained by solving an adjoint problem naturally yields a generalized Eshelby Energy-Momentum tensor, which leads to the classical <span><math><mrow><mi>J</mi><mo>−</mo></mrow></math></span>, <span><math><mrow><mi>L</mi><mo>−</mo></mrow></math></span> and <span><math><mrow><mi>M</mi><mo>−</mo></mrow></math></span> integrals of fracture mechanics when Helmholtz free energy is chosen as the objective and the problem is constrained to be isothermal. We calculate the configurational force using an isogeometric computational framework that relies on a recently developed enrichment procedure for multi-material corner singularities, of which cracks are a special case. Enriched displacement and temperature functions applied at crack tips are illustrated and demonstrated through several numerical examples on thermoelastic solids. Examples include (a) crack driving force estimation under adiabatic/isothermal conditions, (b) edge crack propagation simulation and (c) bimaterial wedge under varying mechanical and thermal loadings.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"210 ","pages":"Article 106541"},"PeriodicalIF":6.0,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146110149","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Coupled grain-pore fabric evolutions in sheared granular materials: Anisotropy lagging and geometric emergence","authors":"Amiya Prakash Das ,&nbsp;Jidong Zhao ,&nbsp;Thomas Sweijen","doi":"10.1016/j.jmps.2026.106530","DOIUrl":"10.1016/j.jmps.2026.106530","url":null,"abstract":"<div><div>The morphological evolution of pore spaces is a critical yet poorly quantified microstructural determinant of the macroscopic mechanical and hydraulic behavior of granular materials. While the anisotropy of the grain contact network (<em>F_c</em>) is known to dictate material response, the concurrent evolution of pore space anisotropy (<em>F_p</em>) and its coupling with <em>F_c</em> remains inadequately understood. This study employs Minkowski moment tensor analysis within a Discrete Element Method (DEM) framework to bridge this gap. We systematically investigate dense and loose, monodisperse and polydisperse assemblies under cyclic triaxial loading to quantify the dynamic coupling between <em>F_c</em> and <em>F_p</em>. We demonstrate a moderate to strong correlation between <em>F_c</em> and <em>F_p</em>, with a systematic lag in the response of <em>F_p</em> attributed to hierarchical geometric emergence across scales. This lag is constrained by particle-scale free-volume reorganization and its kinematic compatibility with particle motion. Additionally, key pore-scale metrics, including inverse Voronoi cell fractions <span><math><mrow><mo>(</mo><msubsup><mi>ϕ</mi><mi>v</mi><mrow><mo>−</mo><mn>1</mn></mrow></msubsup><mo>)</mo></mrow></math></span>, pore-scale porosity (<em>ϕ_p</em>), and pore shape anisotropy <span><math><mover><mi>β</mi><mo>^</mo></mover></math></span>, are well described by gamma distributions across all packing densities and strain levels. Notably, the scaled <span><math><msubsup><mi>ϕ</mi><mi>v</mi><mrow><mo>−</mo><mn>1</mn></mrow></msubsup></math></span> follows a <em>k</em>-gamma distribution, providing a statistically consistent descriptor for volume fluctuations. A strong correlation is also observed between the average pore shape factor (|<em>β</em>|_<em>avg</em>) and global porosity, suggesting that |<em>β</em>|_<em>avg</em> serves as a geometry-based descriptor linking collective pore deformation to packing density. These findings underscore the utility of the Minkowski tensor approach in capturing 3D fabric evolution and explicitly linking pore- and grain-scale interactions. The quantitative relationships and statistical descriptors presented here provide a new foundation for enhancing constitutive models in geotechnics and powder technology, offering insights relevant to future investigations into permeability evolution and shear band formation.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"210 ","pages":"Article 106530"},"PeriodicalIF":6.0,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146071614","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Toggling energy landscape to enable commutative and non-commutative responses in multistable structures","authors":"Lei Wu,&nbsp;Damiano Pasini","doi":"10.1016/j.jmps.2026.106544","DOIUrl":"10.1016/j.jmps.2026.106544","url":null,"abstract":"<div><div>The deformation of a structure may be either insensitive or sensitive to the sequence of the applied forces: the former corresponds to a commutative response, whereas the latter indicates a non-commutative response. Among diverse physical systems, an elastic multistable structure tessellated from bistable units or bits can display commutative or non-commutative responses, each dictated by the manner of interaction between the units. In this work, we elucidate the underlying physics of commutative and non-commutative responses through the lens of the energy landscape of a multistable structure, and demonstrate that initially non-commutative units can be toggled to become commutative by altering the number and distribution of local energy minima in their state space, thus enabling reprogrammable sensitivity to the loading sequence. The concept is realized and demonstrated as a multistable switch in an electrical circuit capable of offering <em>in situ</em> adjustable levels of information protection through reprogrammable sequence sensitivity.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"210 ","pages":"Article 106544"},"PeriodicalIF":6.0,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146110148","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"3D phase-field modeling of H2→H3 phase transition induced intragranular cracking in single-crystal Ni-rich layered cathodes","authors":"Zhengtao Liao ,&nbsp;Xiangbiao Liao ,&nbsp;Yuyang Lu ,&nbsp;Chengcheng Cao ,&nbsp;Linghui He ,&nbsp;Yong Ni","doi":"10.1016/j.jmps.2026.106528","DOIUrl":"10.1016/j.jmps.2026.106528","url":null,"abstract":"<div><div>Understanding the intragranular cracking mechanisms of single-crystal Ni-rich layered cathodes (SC<img>NCM) during electrochemical cycling is essential for next-generation high-energy-density and long-life Li-ion batteries. However, the complex interplay among the factors driving crack initiation and propagation remains unclear. Herein, we present a fully coupled three-dimensional phase-field model that integrates anisotropic lithium diffusion, the H2-H3 structural phase transition, stress evolution, and fracture mechanics to elucidate intragranular fracture in SC<img>NCM during deep delithiation. Simulations on representative particle geometries reveal that anisotropic diffusion and fracture energy alone can not initiate layer-parallel cracks, instead, layered delithiation pathways govern shape-dependent phase transition dynamics, while lattice mismatch from spatially heterogeneous phase transitions nucleates cracks preferentially at particle surfaces and drives their propagation along layered planes, in good agreement with experimental observations. Cubic particles with uniform layers form cracks prematurely, whereas spherical and octahedral particles—with shorter surface layers—delay crack initiation by 5.3% state of charge (SoC) due to retarded phase transition in central layers, thereby expanding the safe-charging window. Elevated charging rates accelerate central-layer phase transition, amplifying misfit and triggering earlier cracking, while reduced phase-transition eigenstrain or flatter aspect ratios mitigate stress concentrations and suppress damage. These results establish a predictive link between phase transition dynamics and intragranular fracture, providing design strategies for mechanically robust high-energy-density cathodes.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"210 ","pages":"Article 106528"},"PeriodicalIF":6.0,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146033262","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A generalized higher-order phase-field model for brittle fracture in anisotropic rocks","authors":"Sijia Liu ,&nbsp;Yunteng Wang ,&nbsp;Xueyu Geng ,&nbsp;Wei Wu","doi":"10.1016/j.jmps.2026.106526","DOIUrl":"10.1016/j.jmps.2026.106526","url":null,"abstract":"<div><div>In this work, we formulate a generalized higher-order phase-field model within the rotated anisotropic framework for simulating brittle phenomena in anisotropic rocks. Our phase-field model accounts for both the anisotropic critical fracture energy release rate and the anisotropic degradation in stiffness. The innovative aspects of this model include (i) a fourth-order structural tensor enabling simulations of strongly anisotropic fractures with arbitrary, non-orthogonal symmetry axes for capturing the complexity of natural geological media; (ii) a volumetric–deviatoric coupling energy density for transitions from anisotropic responses in the undamaged state to isotropic responses in the damaged state; (iii) a patch-based Hessian recovery algorithm ensuring stable solutions of the higher-order PDEs to reduce the computational cost; and (iv) stochastic perturbations integrated into the anisotropic crack surface density function to capture microstructural heterogeneity. Several numerical benchmark examples are provided. The numerical results are compared with some laboratory experiments on brittle fracture in anisotropic rocks.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"210 ","pages":"Article 106526"},"PeriodicalIF":6.0,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146056280","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"In search of constitutive conditions in isotropic hyperelasticity: polyconvexity versus true-stress-true-strain monotonicity","authors":"Maximilian P. Wollner ,&nbsp;Gerhard A. Holzapfel ,&nbsp;Patrizio Neff","doi":"10.1016/j.jmps.2025.106465","DOIUrl":"10.1016/j.jmps.2025.106465","url":null,"abstract":"<div><div>The polyconvexity of a strain-energy function is nowadays increasingly presented as the ultimate material stability condition for an idealized elastic response. While the mathematical merits of polyconvexity are clearly understood, its mechanical consequences have received less attention. In this contribution we contrast polyconvexity with the recently rediscovered true-stress-true-strain monotonicity (TSTS-M⁺⁺) condition. By way of explicit examples, we show that neither condition by itself is strong enough to guarantee physically reasonable behavior for ideal isotropic elasticity. In particular, polyconvexity does not imply a monotone trajectory of the Cauchy stress in unconstrained uniaxial extension which TSTS-M⁺⁺ ensures. On the other hand, TSTS-M⁺⁺ does not impose a monotone Cauchy shear stress response in simple shear which is enforced by Legendre-Hadamard ellipticity and in turn polyconvexity. Both scenarios are proven through the construction of appropriate strain-energy functions. Consequently, a combination of polyconvexity, ensuring Legendre-Hadamard ellipticity, and TSTS-M⁺⁺ seems to be a viable solution to Truesdell’s Hauptproblem. However, so far no isotropic strain-energy function has been identified that satisfies both constraints globally at the same time. Although we are unable to deliver a valid solution here, we provide several results that could prove helpful in the construction of such an exceptional strain-energy function. <em>In memory of</em> Miroslav Šilhavý (1949–2025)</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"209 ","pages":"Article 106465"},"PeriodicalIF":6.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145689708","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Homogenization framework for rigid and non-rigid foldable origami metamaterials","authors":"Xuwen Li,&nbsp;Amin Jamalimehr,&nbsp;Mathias Legrand,&nbsp;Damiano Pasini","doi":"10.1016/j.jmps.2026.106519","DOIUrl":"10.1016/j.jmps.2026.106519","url":null,"abstract":"<div><div>Origami metamaterials typically consist of folded sheets with periodic patterns, conferring them with remarkable mechanical properties. In the context of Continuum Mechanics, the majority of existing predictive methods are mechanism analogs which favor rigid folding and panel bending. While effective in predicting primary deformation modes, existing methods fall short in capturing the full spectrum of deformation of non-rigid foldable origami, such as the emergence of curvature along straight creases, local strain at vertices and warpage in panels. To fully capture the entire deformation spectrum and enhance the accuracy of existing methods, this paper introduces a homogenization framework for origami metamaterials where the faces are modeled as plate elements. Both asymptotic and energy-based homogenization methods are formulated and implemented. As a representative crease pattern, we examine the Miura origami sheet homogenized as an equivalent Kirchhoff-Love plate. The results reveal that certain effective elastic properties are nonlinearly related to both the initial fold angle and the crease stiffness. When benchmarked with results from fully resolved simulations, our framework yields errors up to 12.9%, while existing models, including the bar-and-hinge model and the rigid-panel model, show up to 161% error. The differences in errors are associated with the complex modes of crease and panel deformation in non-rigid origami, unexplored by the existing models. This work demonstrates a precise and efficient continuum framework for origami metamaterials as an effective strategy for predicting their elastic properties, understanding their mechanics, and designing their functionalities.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"209 ","pages":"Article 106519"},"PeriodicalIF":6.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145995466","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The effect of fiber plasticity on domain formation in soft biological composites—Part I: A bifurcation analysis","authors":"Michalis Agoras ,&nbsp;Fernanda F. Fontenele ,&nbsp;Nikolaos Bouklas","doi":"10.1016/j.jmps.2025.106482","DOIUrl":"10.1016/j.jmps.2025.106482","url":null,"abstract":"<div><div>The main objective of this work is to shed light on the effect of fiber plasticity on the macroscopic response and domain formation in soft biological composites. This goal is pursued by analyzing the plane-strain response of two-phase laminates. In the context of this problem, the effect of fiber plasticity is accounted for by allowing the elastically stiffer layers (“fiber” phase) to also yield plastically and by taking the soft layers (“matrix” phase) to be purely elastic solids. The analysis is carried out at finite elastic and plastic strains, but it is restricted to unidirectional, non-monotonic loading paths, applied by initially increasing the macroscopic stretch along the direction of the layers up to a prescribed maximum value and then decreasing the same stretch down to a minimum value. A simple expression is derived for the critical conditions at which the homogenized behavior of the laminate loses strong ellipticity for the first time along the loading path. The relevance of this result stems from the fact that the loss of macroscopic ellipticity of these composites is known to coincide with the onset of bifurcations of the long-wavelength type. It follows from this result that, just like hyperelastic laminates, elastoplastic laminates may lose macroscopic ellipticity whenever their incremental strength in shear perpendicular to the layers vanishes for the first time. It is shown by means of specific numerical calculations that fiber plasticity has a softening effect on the critical shear strength of the laminate under monotonically increasing loading and a hardening effect under monotonically decreasing loading, whereas local elasticity has the opposite effects. Thus, the effects of local elasticity and fiber plasticity compete with each other at every stage of the deformation where both mechanisms are active and whether or not a specific laminate will lose its macroscopic ellipticity along a given loading path depends crucially on the relative strengths of these effects. In this regard, the influence of the relevant loading and material parameters is investigated in detail. For situations in which loss of macroscopic ellipticity does take place, a corresponding post-bifurcation solution for the homogenized behavior of the laminate is computed. The deformed state of the material described by this solution is characterized by twin lamellar domains that are formed at a length scale much larger than the width of the original, microscopic layers, but still much smaller than the overall dimensions of the macroscopic specimen under consideration. The macroscopic response of these composites is found to be much softer along the bifurcated equilibrium path than along the corresponding principal path. Nevertheless, no macroscopic unloading has been observed in the post-bifurcation regime, indicating accordingly that the macroscopic, post-bifurcation behavior of these materials is stable.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"209 ","pages":"Article 106482"},"PeriodicalIF":6.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145845102","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}