Pub Date : 2026-10-01DOI: 10.1016/j.jmps.2026.106877
Luis Eon,Riccardo Gatti,Benoît Appolaire
{"title":"Coupled Phase-Field Fracture and Discrete Dislocation Dynamics for Short-Crack Propagation","authors":"Luis Eon,Riccardo Gatti,Benoît Appolaire","doi":"10.1016/j.jmps.2026.106877","DOIUrl":"https://doi.org/10.1016/j.jmps.2026.106877","url":null,"abstract":"","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"84 1","pages":"106877"},"PeriodicalIF":5.3,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149209010","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}
Pub Date : 2026-10-01DOI: 10.1016/j.jmps.2026.106873
Nasser Firouzi,Timon Rabczuk
{"title":"Unified Physics-Constrained Symbolic Regression for Anisotropic Hyperelastic Materials","authors":"Nasser Firouzi,Timon Rabczuk","doi":"10.1016/j.jmps.2026.106873","DOIUrl":"https://doi.org/10.1016/j.jmps.2026.106873","url":null,"abstract":"","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"14 1","pages":"106873"},"PeriodicalIF":5.3,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149209009","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}
Pub Date : 2026-10-01DOI: 10.1016/j.jmps.2026.106875
Manas V. Upadhyay
{"title":"A probabilistic framework for irreversible kinetics","authors":"Manas V. Upadhyay","doi":"10.1016/j.jmps.2026.106875","DOIUrl":"https://doi.org/10.1016/j.jmps.2026.106875","url":null,"abstract":"","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"51 1","pages":"106875"},"PeriodicalIF":5.3,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149209011","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}
Pub Date : 2026-09-23DOI: 10.1016/j.jmps.2026.106861
Souhayl Sadik, Arash Yavari
We formulate a nonlinear geometric theory of visco-anelasticity that unifies viscoelastic and anelastic responses within a single thermodynamic framework. At each material point, the total deformation gradient is multiplicatively decomposed into elastic, viscous, and anelastic distortions, thereby generalizing the Bilby-Kröner-Lee decomposition to visco-anelasticity. The theory explicitly incorporates the material metric, which encodes the evolving natural configuration of the solid, the transformed structural tensors, and provides a consistent formulation of the constitutive equations, the balance laws, the thermodynamic potentials, and the kinetic equations. The first and second laws of thermodynamics are systematically applied to derive the constitutive and evolution equations without invoking observer invariance. Anisotropy is treated in full generality through structural tensors. As illustrative examples, we specialize the general framework to isotropic and transversely isotropic visco-anelastic solids. Two examples within the class of universal deformations, which admit closed-form or partially closed-form solutions, show how the proposed framework can be used to model the coupled viscous and anelastic response of incompressible anisotropic solids with distributed eigenstrains and the associated residual stresses. This geometric framework unifies nonlinear viscoelasticity and anelasticity by coupling time-dependent and eigenstrain-driven effects within a single, fully consistent geometric formulation. In particular, the proposed framework clarifies the geometric structure of the elastic, viscous, and anelastic distortions and resolves ambiguities associated with intermediate configurations in existing formulations of nonlinear viscoelasticity and viscoplasticity.
{"title":"Nonlinear Anisotropic Visco-Anelasticity","authors":"Souhayl Sadik, Arash Yavari","doi":"10.1016/j.jmps.2026.106861","DOIUrl":"https://doi.org/10.1016/j.jmps.2026.106861","url":null,"abstract":"We formulate a nonlinear geometric theory of visco-anelasticity that unifies viscoelastic and anelastic responses within a single thermodynamic framework. At each material point, the total deformation gradient is multiplicatively decomposed into elastic, viscous, and anelastic distortions, thereby generalizing the Bilby-Kröner-Lee decomposition to visco-anelasticity. The theory explicitly incorporates the material metric, which encodes the evolving natural configuration of the solid, the transformed structural tensors, and provides a consistent formulation of the constitutive equations, the balance laws, the thermodynamic potentials, and the kinetic equations. The first and second laws of thermodynamics are systematically applied to derive the constitutive and evolution equations without invoking observer invariance. Anisotropy is treated in full generality through structural tensors. As illustrative examples, we specialize the general framework to isotropic and transversely isotropic visco-anelastic solids. Two examples within the class of universal deformations, which admit closed-form or partially closed-form solutions, show how the proposed framework can be used to model the coupled viscous and anelastic response of incompressible anisotropic solids with distributed eigenstrains and the associated residual stresses. This geometric framework unifies nonlinear viscoelasticity and anelasticity by coupling time-dependent and eigenstrain-driven effects within a single, fully consistent geometric formulation. In particular, the proposed framework clarifies the geometric structure of the elastic, viscous, and anelastic distortions and resolves ambiguities associated with intermediate configurations in existing formulations of nonlinear viscoelasticity and viscoplasticity.","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"41 1","pages":""},"PeriodicalIF":5.3,"publicationDate":"2026-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149085496","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}
Pub Date : 2026-07-29DOI: 10.1016/j.jmps.2026.106781
Hadrien Oliveri, Ibrahim Cheddadi
Correction to “Hydromechanical field theory of plant morphogenesis” (Journal of the Mechanics and Physics of Solids 196, 10603, 10.1016/j.jmps.2025.106035).
{"title":"Correction to: “Hydromechanical field theory of plant morphogenesis”","authors":"Hadrien Oliveri, Ibrahim Cheddadi","doi":"10.1016/j.jmps.2026.106781","DOIUrl":"https://doi.org/10.1016/j.jmps.2026.106781","url":null,"abstract":"Correction to “Hydromechanical field theory of plant morphogenesis” (Journal of the Mechanics and Physics of Solids 196, 10603, <ce:inter-ref xlink:href=\"https://doi.org/10.1016/j.jmps.2025.106035\" xlink:type=\"simple\">10.1016/j.jmps.2025.106035</ce:inter-ref>).","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"72 1","pages":""},"PeriodicalIF":5.3,"publicationDate":"2026-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148690794","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}
Pub Date : 2026-07-14DOI: 10.1016/j.jmps.2026.106766
Hai Xin, Tianhong Gu, Finn Giuliani, T. Ben Britton, Mei Zhan, Yilun Xu, Zebang Zheng
{"title":"Corrigendum to “Discontinuous plasticity in Sn single crystals: A combined experiment and modelling study” [Journal of the Mechanics and Physics of Solids 215 (2026) 106714]","authors":"Hai Xin, Tianhong Gu, Finn Giuliani, T. Ben Britton, Mei Zhan, Yilun Xu, Zebang Zheng","doi":"10.1016/j.jmps.2026.106766","DOIUrl":"https://doi.org/10.1016/j.jmps.2026.106766","url":null,"abstract":"","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"232 1","pages":""},"PeriodicalIF":5.3,"publicationDate":"2026-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148462021","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}
Pub Date : 2026-06-05DOI: 10.1016/j.jmps.2026.106702
Md Rezaul Karim, Trisha Sain
{"title":"Corrigendum to “Degradation of constitutive response to mass loss: Predicting hydrolytic aging in vitrimers via reaction-modified transient network theory” [Journal of the Mechanics and Physics of Solids 213 (2026) 106605]","authors":"Md Rezaul Karim, Trisha Sain","doi":"10.1016/j.jmps.2026.106702","DOIUrl":"https://doi.org/10.1016/j.jmps.2026.106702","url":null,"abstract":"","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"11 1","pages":"106702"},"PeriodicalIF":5.3,"publicationDate":"2026-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148287349","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}
Pub Date : 2026-05-01Epub Date: 2026-02-09DOI: 10.1016/j.jmps.2026.106546
Cesar Spadea , Pedro Ponte Castañeda
Generalizing Hill’s classical formulation for purely elastic and purely viscoplastic composites, Ponte Castañeda (2025) proposed a variational framework for the time-incremental macroscopic response of elasto-viscoplastic (EVP) composites based on Rayleigh’s least dissipation principle. This framework enabled a consistent extension of the Variational Linear Comparison method (Ponte Castañeda, 1991), yielding estimates for the time-dependent macroscopic response of EVP composites in terms of the constitutive response of comparison linear viscoelastic (LVE) composites. In this approach, the viscosities of the LVE phases correspond to the secant viscosities of the EVP phases, evaluated at the instantaneous values of the second moments of the stress or strain-rate fields in the phases of the LVE comparison composite. In the present work, we leverage the estimates of Lahellec et al. (2024) for the macroscopic response and phase second moments in LVE composites — derived via the correspondence principle from the corresponding estimates of Willis (1977) for purely elastic composites — to generate predictions for EVP composites with isotropic phases and particulate microstructures. The new estimates significantly improve upon earlier results for the same class of EVP composites obtained by Ponte Castañeda (2025) using alternative LVE approximations. While the previously used estimates for the LVE composite were exact for the macroscopic response, the corresponding second moment predictions were only approximate, leading to inaccuracies for EVP composites with strong nonlinearities and large heterogeneity contrast. Numerical results for various special cases, including compressible non-well-ordered phases, ideally plastic (rate-independent) behavior and cyclic loadings, illustrate the enhanced capabilities of the new estimates.
{"title":"Variational linear comparison estimates for elasto-viscoplastic composites with isotropic phases and microstructures","authors":"Cesar Spadea , Pedro Ponte Castañeda","doi":"10.1016/j.jmps.2026.106546","DOIUrl":"10.1016/j.jmps.2026.106546","url":null,"abstract":"<div><div>Generalizing Hill’s classical formulation for purely elastic and purely viscoplastic composites, Ponte Castañeda (2025) proposed a variational framework for the time-incremental macroscopic response of elasto-viscoplastic (EVP) composites based on Rayleigh’s least dissipation principle. This framework enabled a consistent extension of the Variational Linear Comparison method (Ponte Castañeda, 1991), yielding estimates for the time-dependent macroscopic response of EVP composites in terms of the constitutive response of comparison linear viscoelastic (LVE) composites. In this approach, the viscosities of the LVE phases correspond to the secant viscosities of the EVP phases, evaluated at the instantaneous values of the second moments of the stress or strain-rate fields in the phases of the LVE comparison composite. In the present work, we leverage the estimates of Lahellec et al. (2024) for the macroscopic response and phase second moments in LVE composites — derived via the correspondence principle from the corresponding estimates of Willis (1977) for purely elastic composites — to generate predictions for EVP composites with isotropic phases and particulate microstructures. The new estimates significantly improve upon earlier results for the same class of EVP composites obtained by <span><span>Ponte Castañeda (2025)</span></span> using alternative LVE approximations. While the previously used estimates for the LVE composite were exact for the macroscopic response, the corresponding second moment predictions were only approximate, leading to inaccuracies for EVP composites with strong nonlinearities and large heterogeneity contrast. Numerical results for various special cases, including compressible non-well-ordered phases, ideally plastic (rate-independent) behavior and cyclic loadings, illustrate the enhanced capabilities of the new estimates.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"211 ","pages":"Article 106546"},"PeriodicalIF":6.0,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146152937","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}
Pub Date : 2026-05-01Epub Date: 2026-02-07DOI: 10.1016/j.jmps.2026.106543
A. Rodella , J.-J Marigo , C. Maurini , S. Vidoli
We investigate sharp-interface cohesive fracture models formulated as energy minimization problems. We argue that models with arbitrary cohesive interfaces are incompatible with linear bulk elasticity, in the sense that they cannot feature solutions in the form of a regular crack with a simple tip. To this end, we provide analytical and numerical solutions for a model problem consisting of a single straight crack under mode-III loading, where we show that the stress magnitude exceeds the cohesive yield threshold in a finite region around the crack tip. Our findings are consistent with the unavailability of existence results for such models, related to the lack of lower semicontinuity of the associated variational problem. In the mathematical literature, lower semicontinuity and existence of solutions is recovered by introducing a relaxed functional combining the cohesive surface energy on the crack set with a bulk behavior comparable to perfect plasticity, where the bulk strength is determined by the maximal allowable traction of the cohesive law. The relaxed energy provides a homogenised macroscopic model of the possible microscopic structuring of a dense distribution of cracks with vanishing displacement jumps. We report numerical simulations in antiplane shear that illustrate that the relaxed model admits an equilibrium solution in the form of straight cracks that capture both crack nucleation and propagation. Cracks emerging from pre-existing flaws and notches exhibit a smooth transition from classical crack tip plasticity solutions near the notch to a propagating cohesive crack accompanied by an elongated zone around the tip where the nonlinear bulk behavior is active and the stress is constant. We discuss how these observations can inform the development of mathematically consistent coupled models with a minimal number of constitutive parameters, highlighting the inconsistencies observed when arbitrarily combining models with different surface and bulk strengths.
{"title":"Sharp-interface cohesive fracture models with consistent bulk energies: Numerical investigations","authors":"A. Rodella , J.-J Marigo , C. Maurini , S. Vidoli","doi":"10.1016/j.jmps.2026.106543","DOIUrl":"10.1016/j.jmps.2026.106543","url":null,"abstract":"<div><div>We investigate sharp-interface cohesive fracture models formulated as energy minimization problems. We argue that models with arbitrary cohesive interfaces are incompatible with linear bulk elasticity, in the sense that they cannot feature solutions in the form of a regular crack with a simple tip. To this end, we provide analytical and numerical solutions for a model problem consisting of a single straight crack under mode-III loading, where we show that the stress magnitude exceeds the cohesive yield threshold in a finite region around the crack tip. Our findings are consistent with the unavailability of existence results for such models, related to the lack of lower semicontinuity of the associated variational problem. In the mathematical literature, lower semicontinuity and existence of solutions is recovered by introducing a relaxed functional combining the cohesive surface energy on the crack set with a bulk behavior comparable to perfect plasticity, where the bulk strength is determined by the maximal allowable traction of the cohesive law. The relaxed energy provides a homogenised macroscopic model of the possible microscopic structuring of a dense distribution of cracks with vanishing displacement jumps. We report numerical simulations in antiplane shear that illustrate that the relaxed model admits an equilibrium solution in the form of straight cracks that capture both crack nucleation and propagation. Cracks emerging from pre-existing flaws and notches exhibit a smooth transition from classical crack tip plasticity solutions near the notch to a propagating cohesive crack accompanied by an elongated zone around the tip where the nonlinear bulk behavior is active and the stress is constant. We discuss how these observations can inform the development of mathematically consistent coupled models with a minimal number of constitutive parameters, highlighting the inconsistencies observed when arbitrarily combining models with different surface and bulk strengths.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"211 ","pages":"Article 106543"},"PeriodicalIF":6.0,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146134450","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}
Pub Date : 2026-04-01Epub Date: 2026-02-06DOI: 10.1016/j.jmps.2026.106542
Haolin Li , Menglei Li , Jinshuai Bai , Zahra Sharif Khodaei , M.H. Aliabadi
Materials with designed microstructures can exhibit effective mechanical properties that are rare or non-existent in nature. Their analysis usually requires accurate and efficient homogenisation tools capable of handling complex geometries and large deformations. Unlike composites with finite phase transitions, metamaterials often feature infinite phase contrast and complex morphologies that challenge conventional numerical methods. In this work, we propose a mesh-free physics-informed neural network (PINN) framework designed specifically for homogenisation of metamaterial structures. The framework matches the efficiency of FEM and FFT-based approaches for large-scale 3D problems and hyperelastic analyses, whilst offering significantly easier implementation than those other numerical methods. The effectiveness of the proposed method is achieved through: a) a new network architecture that embeds homogenisation boundary conditions directly into the solution output, and b) an energy-based residual formulation that enables fast convergence and efficient solving for both linear elastic and hyperelastic problems. The proposed approach is validated on a range of representative 2D and 3D metamaterials, including lattices, triply periodic minimal surface structures, and stochastic architectures with complex random morphology. The PINN predictions of effective elastic tensors, directional stiffness surfaces, and local displacement and stress fields show good agreement with high-resolution FEM solutions for applications such as buckling lattices and auxetic structures operating in the finite-strain regime. In addition, the same framework is shown to handle higher-order homogenisation with strain-gradient loading and to support progressive loading strategies that efficiently resolve nonlinear, large-deformation responses. These results demonstrate that the proposed PINN-based homogenisation scheme provides an accurate and scalable alternative for the multiscale analysis and design of architected metamaterials.
{"title":"An energy-based physics-informed neural network framework for efficient mesh-free homogenisation of architected metamaterials","authors":"Haolin Li , Menglei Li , Jinshuai Bai , Zahra Sharif Khodaei , M.H. Aliabadi","doi":"10.1016/j.jmps.2026.106542","DOIUrl":"10.1016/j.jmps.2026.106542","url":null,"abstract":"<div><div>Materials with designed microstructures can exhibit effective mechanical properties that are rare or non-existent in nature. Their analysis usually requires accurate and efficient homogenisation tools capable of handling complex geometries and large deformations. Unlike composites with finite phase transitions, metamaterials often feature infinite phase contrast and complex morphologies that challenge conventional numerical methods. In this work, we propose a mesh-free physics-informed neural network (PINN) framework designed specifically for homogenisation of metamaterial structures. The framework matches the efficiency of FEM and FFT-based approaches for large-scale 3D problems and hyperelastic analyses, whilst offering significantly easier implementation than those other numerical methods. The effectiveness of the proposed method is achieved through: a) a new network architecture that embeds homogenisation boundary conditions directly into the solution output, and b) an energy-based residual formulation that enables fast convergence and efficient solving for both linear elastic and hyperelastic problems. The proposed approach is validated on a range of representative 2D and 3D metamaterials, including lattices, triply periodic minimal surface structures, and stochastic architectures with complex random morphology. The PINN predictions of effective elastic tensors, directional stiffness surfaces, and local displacement and stress fields show good agreement with high-resolution FEM solutions for applications such as buckling lattices and auxetic structures operating in the finite-strain regime. In addition, the same framework is shown to handle higher-order homogenisation with strain-gradient loading and to support progressive loading strategies that efficiently resolve nonlinear, large-deformation responses. These results demonstrate that the proposed PINN-based homogenisation scheme provides an accurate and scalable alternative for the multiscale analysis and design of architected metamaterials.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"210 ","pages":"Article 106542"},"PeriodicalIF":6.0,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146134448","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}
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