Journal of The Mechanics and Physics of Solids最新文献

{"title":"Physically-based modeling of polymer foam microstructures: from realistic cellular microstructures and their variabilities to mechanical properties","authors":"T. Roland ,&nbsp;G. Ginot ,&nbsp;M.L. Dabo ,&nbsp;C. Gauthier ,&nbsp;W. Drenckhan ,&nbsp;P. Kékicheff","doi":"10.1016/j.jmps.2025.106387","DOIUrl":"10.1016/j.jmps.2025.106387","url":null,"abstract":"<div><div>It is generally agreed that an efficient model for predicting the mechanical behavior of solid foams should present microstructural features similar to real ones. However, most theoretical results in foam micro-mechanics are based on periodic space-filling unit-cell which do not reflect the inherently random nature of real foams. The Kelvin cell or the Weaire-Phelan (WP) structure are by far the most used and yet they are only found in specialised foam. The present study therefore uses a versatile approach based on a thermodynamic description of interacting bubbles growth to produce representative volume elements of closed-cell foams with a wide variety of morphologies. Using a small set of parameters, one can build morphologies with local features specific to non-equilibrium foams. The behavior of the internal gas phase during the formation process is also modelled while assuming the absence of diffusion in the continuous medium. A sequence of mechanical micro-models is developed to study the complete compressive response ranging from the initial elastic response followed by the extensive plateau stress all the way up to the densification zone. An advanced structural analysis applied to solid foams is performed. The results are discussed in view of randomness of the cellular microstructure, anisotropic cell shape effects and inner gas pressure effect. Using regression-based approaches we attempted to build a framework capable of yielding cautious but meaningful conclusions about the relationship between topological parameters and mechanical properties<strong>.</strong> This is a major improvement over previous studies which lack variability in topological arrangement for 3D representative volume elements or which use periodic boundary conditions known to influence the way macroscopic instabilities develop.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"206 ","pages":"Article 106387"},"PeriodicalIF":6.0,"publicationDate":"2025-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145268982","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":"Differential formulation and solution of a cohesive crack problem","authors":"Madura Pathirage","doi":"10.1016/j.jmps.2025.106377","DOIUrl":"10.1016/j.jmps.2025.106377","url":null,"abstract":"<div><div>Attempts at constructing a closed-form solution to the cohesive crack model have been unsuccessful. This paper develops a procedure to derive analytical solutions to a class of non-trivial cohesive crack problems within the theory of linear elastic fracture mechanics. The nonlinear integral equation describing the cohesive model for mode I crack growth is, under certain conditions, transformed into a boundary value problem for which an analytical treatment is possible. Closed-form solutions of the stress in the cohesive zone is derived for the case of a large compact tension geometry with constant and linear softening functions. The analytical expressions of load and crack mouth opening displacement are given and compared with finite element results. A closed-form expression of size-effect is also reported. In addition, a mathematical proof of Barenblatt’s third hypothesis of smooth crack face closure at the crack tip is provided. The existing solution for a built-in cantilever beam on softening foundation is recovered for a very slender geometry, and its use for <span><math><mrow><msub><mrow><mi>a</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>/</mo><mi>h</mi><mo>&lt;</mo><mn>12</mn></mrow></math></span> should be avoided because transverse deformation does not occur in simple beam theory. Finally, the governing nonlinear differential equation corresponding to an exponential softening function is derived and solved numerically.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"206 ","pages":"Article 106377"},"PeriodicalIF":6.0,"publicationDate":"2025-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145221384","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":"Microstructure-based constitutive modeling of corneal nonlinear anisotropic rheology and modulus","authors":"Yifeng Li ,&nbsp;Zhuoran Yang ,&nbsp;Ziming Yan ,&nbsp;Zhanli Liu ,&nbsp;Kaijie Wang","doi":"10.1016/j.jmps.2025.106381","DOIUrl":"10.1016/j.jmps.2025.106381","url":null,"abstract":"<div><div>The cornea, as a soft transparent fiber-reinforced composite, exhibits nonlinear anisotropic rheology affecting its optical performance, crucial for clinical refractive correction. However, there is still lacking of constitutive models that accurately predict the cornea’s time-dependent anisotropic mechanical response. Inspired by the corneal fiber-matrix microstructure, a nonlinear anisotropic rheological model is developed under the thermodynamics framework. Firstly, through multiplicative deformation gradient decomposition, the fluid-like matrix phase is described by molecular chain reptation-based nonlinear viscoplasticity, while the solid-like fiber phase is modeled with quasilinear viscoelasticity. Then based on the rheological model, the anisotropic modulus of the cornea is numerically derived for the first time. The model is validated using experimental relaxation data of the cornea from in-plane tension and out-of-plane compression tests. The calculated relaxation modulus reveals distinct anisotropic decay patterns absent in current corneal constitutive models: the transverse direction recovers to 100.01 % of baseline, while the fiber direction retains substantial residual stiffness at 375.01 % of baseline. At last, the constitutive model is applied to study the three-dimensional corneal creep under cylindrical indentation, which is related to refractive correction using contact lens. Compared to existing models, our model predicts a 19.8 % larger flattened area and a viscous deformation that accelerates from 16.7 % to 100.9 % of elastic deformation. The nonlinear fluid-like viscous deformation of the matrix enables greater and faster morphology change of cornea, which is meaningful for improving refractive correction precision.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"206 ","pages":"Article 106381"},"PeriodicalIF":6.0,"publicationDate":"2025-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145254688","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":"Microstructured tunable media with giant negative and positive thermal expansion","authors":"Ioannis Ioannou Sougleridis ,&nbsp;Michele Brun ,&nbsp;Antonio Baldi ,&nbsp;Giorgio Carta","doi":"10.1016/j.jmps.2025.106373","DOIUrl":"10.1016/j.jmps.2025.106373","url":null,"abstract":"<div><div>This work introduces a microstructured medium designed to achieve a highly tunable effective coefficient of thermal expansion (CTE), capable of being either positive or negative. Remarkably, the effective CTE can exceed that of the constituent phases by more than one order of magnitude. The proposed microstructure consists of a periodic arrangement of thin beams with different thermomechanical properties. Owing to its simplicity, the structure can be studied analytically, allowing the key parameters governing the effective response to be readily identified and tuned. In particular, an asymptotic analysis highlights the dominant role of the internal flexural deformation modes. The analytical predictions are validated by three-dimensional numerical simulations and corroborated by experimental testing, where the simplicity of the architecture facilitates specimen fabrication. With suitable tuning, the medium can not only control longitudinal thermal expansion but also exhibit a non-zero rotational coefficient of thermal expansion, enhancing its functional versatility. These results demonstrate the potential of the proposed design for applications requiring tailored thermal expansion behavior.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"206 ","pages":"Article 106373"},"PeriodicalIF":6.0,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145209817","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":"Finite strain thermoelasticity and the Third Law of thermodynamics","authors":"Javier Bonet ,&nbsp;Antonio J. Gil","doi":"10.1016/j.jmps.2025.106372","DOIUrl":"10.1016/j.jmps.2025.106372","url":null,"abstract":"<div><div>This paper shows that commonly used large strain thermoelastic models in which the specific heat coefficient is constant or, at most, changes with temperature, are incompatible with the Third Law of thermodynamics, namely, that “<em>entropy should be zero at the Kelvin state, that is, absolute zero temperature</em>”. In particular, it will be shown that the Third Law implies that the specific heat coefficient must vary with deformation for the coupling between mechanical and thermal effects to take place. In line with this result, a simple analytical constitutive model consistent with the Third Law will be proposed. The model will be based on a multiplicative decomposition of the specific heat into a deformation dependent part and a temperature dependent component. The resulting thermoelastic model complies with the Third Law and, in addition, the necessary convexity conditions that ensure the existence of real wave speeds. It can replicate existing entropic elasticity models for rubber, describe melting and softening behaviour, and converge to the classical relationships for linear thermoelasticity in the small strain regime.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"206 ","pages":"Article 106372"},"PeriodicalIF":6.0,"publicationDate":"2025-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145155523","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":"Non-proportional plastic deformation at the micron scale: Single crystal Cu cantilever beams subjected to orthogonal bending","authors":"Bin Zhang ,&nbsp;Carl F.O. Dahlberg ,&nbsp;Tim Fischer ,&nbsp;J.W. Hutchinson ,&nbsp;W.J. Meng","doi":"10.1016/j.jmps.2025.106375","DOIUrl":"10.1016/j.jmps.2025.106375","url":null,"abstract":"<div><div>Experiments involving abrupt non-collinear changes in the direction of loading in the plastic range have been performed on micron-scale, single crystal Cu cantilever beams to provide the first data of its kind on non-proportional loading. The data is used to assess whether existing strain gradient plasticity (SGP) theories are capable of reproducing complex deformation histories representative of micron-scale metal forming processes, for which non-proportional loading is common. The data is also used to explore an issue that has arisen in efforts to develop SGP that is sufficiently accurate for engineering applications and yet not overly complex. Specifically, using a combination of experimentation and computation, the paper examines the differences in predictions made by two classes of theories presently in the mainstream, termed “incremental” and “non-incremental”, when non-proportional plastic loading occurs at the micron scale. Orthogonal bend experiments are performed on Cu single crystal cantilever beams with square cross-sections that are symmetrically oriented with respect to the vertical and horizonal bending axes. In Stage 1, the force applied to the end of the cantilever is vertical, producing bending in the vertical plane. Abruptly, in Stage 2, a horizontal force is applied with either the vertical force held constant (force control) or the vertical end-displacement of the beam held constant (displacement control). Three cantilever sizes, with widths of the square cross-section of 2, 5 and 20 microns, have been tested. The strength elevation for cantilever widths decreasing from 20 to 2 microns is about a factor of three as compared to what would be expected based on conventional plasticity theory. The incremental and non-incremental SGP theories both capture the full non-proportional loading history, including the size effect. However, they differ in their predictions of behavior in the early portion of Stage 2, due to the abrupt change in the loading path. This difference will be assessed with the aid of experimental test data.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"206 ","pages":"Article 106375"},"PeriodicalIF":6.0,"publicationDate":"2025-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145209941","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 cluster and dislocation dynamics modeling of microstructure evolution in irradiated materials","authors":"Yang Li ,&nbsp;Matthew Maron ,&nbsp;Kristopher Baker ,&nbsp;Benjamin Ramirez Flores ,&nbsp;Thomas Black ,&nbsp;James Hollenbeck ,&nbsp;Inam Lalani ,&nbsp;Nasr Ghoniem ,&nbsp;Giacomo Po","doi":"10.1016/j.jmps.2025.106366","DOIUrl":"10.1016/j.jmps.2025.106366","url":null,"abstract":"<div><div>We develop here a coupled cluster and dislocation dynamics framework to study the microstructure evolution of irradiated materials. The framework not only accounts for the three dimensional diffusion of radiation-generated clusters, but also their interaction with dislocation networks and the resultant climb motion of discrete dislocations within finite crystals. The framework is solved with a superposition solution scheme, and is applied to investigate the evolution of the irradiation-induced dislocation loops in zirconium (Zr), considering the effects of various bias factors including the diffusion anisotropy difference (DAD) of interstitials and interstitial clusters, the dislocation bias of defects to discrete dislocation segments, and the production bias of defects from the radiation cascade. We find that the DAD is the most critical factor influencing the kinetics of the loop evolution in Zr, while the recombination/interaction of mobile defects can induce a strong spatial dependence of the loop evolution together with the DAD. The method is also adopted to study the evolution of interstitial <span><math><mrow><mo>〈</mo><mi>a</mi><mo>〉</mo></mrow></math></span> and vacancy <span><math><mrow><mo>〈</mo><mi>c</mi><mo>〉</mo></mrow></math></span> dislocation loop ensembles consistent with the microstructure observed during irradiation-induced growth of Zr. Our findings not only reveal the spatial dependence of the size and ellipticity of the dislocation loops, but also suggest a limit on the anisotropy factor of interstitials to reproduce the co-growth of <span><math><mrow><mo>〈</mo><mi>a</mi><mo>〉</mo></mrow></math></span> and <span><math><mrow><mo>〈</mo><mi>c</mi><mo>〉</mo></mrow></math></span> loops in zirconium, in good agreement with experimental observations and other simulation results.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"206 ","pages":"Article 106366"},"PeriodicalIF":6.0,"publicationDate":"2025-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145155519","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":"Plastic deformation as a phase transition: A combinatorial model of plastic flow in copper single crystals","authors":"Afonso D.M. Barroso,&nbsp;Elijah Borodin,&nbsp;Andrey P. Jivkov","doi":"10.1016/j.jmps.2025.106370","DOIUrl":"10.1016/j.jmps.2025.106370","url":null,"abstract":"<div><div>Continuum models of plasticity fail to capture the richness of microstructural evolution because the continuum is a homogeneous construction. The present study shows that an alternative way is available at the mesoscale in the form of truly discrete constructions and in the discrete exterior calculus. A pre-existing continuum mean-field model with two parameters is rewritten in the language of the latter to model the properties of a network of plastic slip events in a perfect copper single crystal under uniaxial tension. The behaviour of the system is simulated in a triangular 2D mesh in 3D space employing a Metropolis–Hastings algorithm. Phases of distinct character emerge and both first-order and second-order phase transitions are observed. The phases represent arrangements of the plastic slip network with different combinations of collinear, coplanar, non-collinear and non-coplanar active slip systems. Furthermore, some of these phases can be interpreted as representing crystallographic phenomena like activation of secondary slip systems, strain localisation and fracture or amorphisation. The first-order transitions mostly occur as functions of the applied stress, while the second-order transitions occur exclusively as functions of the mean-field coupling parameter. The former are reminiscent of transitions in other statistical–mechanical models, while the latter find parallels in experimental observations.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"206 ","pages":"Article 106370"},"PeriodicalIF":6.0,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145155518","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":"Microstructure-informed hyper-viscoelastic model capturing soft tissue tensile behavior across large deformations","authors":"Lei Shi ,&nbsp;Kristin M. Myers","doi":"10.1016/j.jmps.2025.106348","DOIUrl":"10.1016/j.jmps.2025.106348","url":null,"abstract":"<div><div>Soft biological tissues exhibit highly nonlinear and time-dependent mechanical behavior arising from their complex collagen network microstructure. In this study, we present a unified, microstructure-informed hyper-viscoelastic constitutive model that captures the tensile response of soft tissues across small to large deformations under monotonic tension. The model couples a continuous fiber recruitment formulation — realized through a generalized Maxwell framework — with a physically motivated flow rule representing constrained segmental mobility. This time-dependent mechanism, inspired by reptation- and Brownian-like dynamics, captures viscoelastic relaxation governed by localized fibrillar rearrangement, interfibrillar sliding, and motion in loosely crosslinked regions. The formulation is thermodynamically consistent and includes explicit expressions for the tangent moduli to ensure computational stability in finite element simulations. The model was calibrated and validated using multi-step stress-relaxation experiments performed on human cervix specimens from both pregnant and nonpregnant individuals, revealing physiologically meaningful trends in fiber recruitment and viscoelastic properties. Notably, the model is capable of predicting faster relaxation responses using parameters calibrated from slower-relaxation data, demonstrating robustness across different strain rates. To demonstrate generalizability, the model was further applied to published datasets from rat subcutaneous tissue and bovine tendon, accurately capturing their viscoelastic responses. Compared to classical viscoelastic models, the proposed framework offers improved accuracy and mechanistic interpretability by explicitly linking macroscopic behavior to underlying collagen network structure and crosslinking density. This work provides a foundation for robust, microstructure-informed modeling of soft tissue mechanics and has broad applicability in tissue characterization and digital twin development.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"206 ","pages":"Article 106348"},"PeriodicalIF":6.0,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145155521","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":"Computational optimization of director patterns in liquid crystal elastomers","authors":"Tingting Xu ,&nbsp;Thao D. Nguyen ,&nbsp;James K. Guest","doi":"10.1016/j.jmps.2025.106369","DOIUrl":"10.1016/j.jmps.2025.106369","url":null,"abstract":"<div><div>We present a computational framework for optimizing the director distributions in viscoelastic liquid crystal elastomer (LCE) structures. The framework begins with a finite element implementation of a viscoelastic finite strain model to capture the time-dependent behavior of LCEs. This model is coupled with an optimization scheme that optimizes the spatially continuous director field for targeted mechanical performance. A time-dependent adjoint sensitivity analysis is employed to enable efficient gradient-based design updates. The framework is demonstrated through numerical examples that maximize mechanical work and maximize energy dissipation. Maximizing the mechanical work produces optimized director patterns that are aligned with principal stress directions, resulting in minimal reorientation and increased stiffness. Maximizing the energy dissipation produces director patterns that depend on whether viscous director rotation or network deformation is the dominant dissipation mechanism. These results highlight opportunities for optimizing LCE structures and underscore the importance of accurately modeling the viscoelastic response when designing LCE structures for reliable, long-term functionality.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"206 ","pages":"Article 106369"},"PeriodicalIF":6.0,"publicationDate":"2025-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145155525","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}