Pub Date : 2026-02-01Epub Date: 2025-12-13DOI: 10.1016/j.jmps.2025.106480
Hio Konishi , Seishiro Matsubara , So Nagashima , Dai Okumura
In this study, we refine the strain energy function of fiber-reinforced hyperelastic materials by adding a unique nonlinear term with a negative exponent on , i.e., , where is the pseudo-invariant of the right Cauchy–Green tensor, defined as the squared stretch in a fiber direction. This additional term is comprehensively tested when combined with the simple linear form or the conventional quadratic form . The conventional quadratic form causes unphysical material instability under principal stretches, where the instantaneous stiffness changes negatively in certain deformation regions. Using the negative exponent on can prevent this instability. The specific linear combination, , is unconditionally free from the instability under principal stretches. The instantaneous stiffness is linearly enhanced by fiber reinforcement, unlike the complex responses by a quadratic combination. This refinement is not incompatible with the physical interpretation of the material instability under simple shear deformation. A comprehensive understanding is achieved through the sufficient condition for derived from the strong ellipticity inequality.
{"title":"Using a negative exponent to prevent unphysical instability in fiber-reinforced hyperelastic materials","authors":"Hio Konishi , Seishiro Matsubara , So Nagashima , Dai Okumura","doi":"10.1016/j.jmps.2025.106480","DOIUrl":"10.1016/j.jmps.2025.106480","url":null,"abstract":"<div><div>In this study, we refine the strain energy function of fiber-reinforced hyperelastic materials by adding a unique nonlinear term with a negative exponent on <span><math><msub><mi>I</mi><mn>4</mn></msub></math></span>, i.e., <span><math><mrow><msubsup><mi>I</mi><mn>4</mn><mrow><mo>−</mo><mi>M</mi></mrow></msubsup><mo>−</mo><mn>1</mn><mspace></mspace><mrow><mo>(</mo><mi>M</mi><mo>></mo><mn>0</mn><mo>)</mo></mrow></mrow></math></span>, where <span><math><msub><mi>I</mi><mn>4</mn></msub></math></span> is the pseudo-invariant of the right Cauchy–Green tensor, defined as the squared stretch in a fiber direction. This additional term is comprehensively tested when combined with the simple linear form <span><math><mrow><mo>(</mo><mrow><msub><mi>I</mi><mn>4</mn></msub><mo>−</mo><mn>1</mn></mrow><mo>)</mo></mrow></math></span> or the conventional quadratic form <span><math><msup><mrow><mo>(</mo><mrow><msub><mi>I</mi><mn>4</mn></msub><mo>−</mo><mn>1</mn></mrow><mo>)</mo></mrow><mn>2</mn></msup></math></span>. The conventional quadratic form causes unphysical material instability under principal stretches, where the instantaneous stiffness changes negatively in certain deformation regions. Using the negative exponent on <span><math><msub><mi>I</mi><mn>4</mn></msub></math></span> can prevent this instability. The specific linear combination, <span><math><mrow><mrow><mo>(</mo><mrow><msub><mi>I</mi><mn>4</mn></msub><mo>−</mo><mn>1</mn></mrow><mo>)</mo></mrow><mo>+</mo><mrow><mo>(</mo><mrow><msubsup><mi>I</mi><mn>4</mn><mrow><mo>−</mo><mi>M</mi></mrow></msubsup><mo>−</mo><mn>1</mn></mrow><mo>)</mo></mrow><mo>/</mo><mi>M</mi></mrow></math></span>, is unconditionally free from the instability under principal stretches. The instantaneous stiffness is linearly enhanced by fiber reinforcement, unlike the complex responses by a quadratic combination. This refinement is not incompatible with the physical interpretation of the material instability under simple shear deformation. A comprehensive understanding is achieved through the sufficient condition for <span><math><msub><mi>I</mi><mn>4</mn></msub></math></span> derived from the strong ellipticity inequality.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"208 ","pages":"Article 106480"},"PeriodicalIF":6.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145760384","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 : 2026-02-01Epub Date: 2025-12-16DOI: 10.1016/j.jmps.2025.106479
Ye Feng , Lu Hai
This paper develops a novel class of phase-field cohesive fracture models that naturally incorporate strong displacement discontinuities within a continuum framework. We derive the nonhomogeneous analytical solutions in one dimension (1D), demonstrating for the first time the emergence of a Dirac δ-function-type strain in phase-field models from crack nucleation to complete rupture, without requiring the limit of vanishing phase-field characteristic length ℓ. This enables the direct representation of discrete crack displacement jumps. We demonstrate the instability of homogeneous solutions through a second-order stability analysis, further highlighting the significance of the derived singular nonhomogeneous solutions. The proposed approach overcomes the limitation of conventional phase-field methods in capturing strong discontinuities, while retaining their advantages-such as mesh objectivity and the ability to handle complex crack topologies-due to the retained diffusive phase-field distribution. Furthermore, the implementation of the cohesive law into the phase-field model can be achieved in a more straightforward manner. The model’s effectiveness beyond 1D is validated by 2D and 3D numerical examples. These developments may open new possibilities for: (i) multiscale fracture analysis where competing length scales coexist, and (ii) multiphysics problems requiring precise kinematics of crack opening.
{"title":"Phase-field cohesive fracture models with strong displacement discontinuities","authors":"Ye Feng , Lu Hai","doi":"10.1016/j.jmps.2025.106479","DOIUrl":"10.1016/j.jmps.2025.106479","url":null,"abstract":"<div><div>This paper develops a novel class of phase-field cohesive fracture models that naturally incorporate strong displacement discontinuities within a continuum framework. We derive the nonhomogeneous analytical solutions in one dimension (1D), demonstrating <em>for the first time</em> the emergence of a Dirac <em>δ</em>-function-type strain in phase-field models from crack nucleation to complete rupture, without requiring the limit of vanishing phase-field characteristic length ℓ. This enables the direct representation of discrete crack displacement jumps. We demonstrate the instability of homogeneous solutions through a second-order stability analysis, further highlighting the significance of the derived singular nonhomogeneous solutions. The proposed approach overcomes the limitation of conventional phase-field methods in capturing strong discontinuities, while retaining their advantages-such as mesh objectivity and the ability to handle complex crack topologies-due to the retained diffusive phase-field distribution. Furthermore, the implementation of the cohesive law into the phase-field model can be achieved in a more straightforward manner. The model’s effectiveness beyond 1D is validated by 2D and 3D numerical examples. These developments may open new possibilities for: (i) multiscale fracture analysis where competing length scales coexist, and (ii) multiphysics problems requiring precise kinematics of crack opening.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"208 ","pages":"Article 106479"},"PeriodicalIF":6.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145784919","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 : 2026-02-01Epub Date: 2025-12-20DOI: 10.1016/j.jmps.2025.106488
JiaHao Li , Weicheng Huang , YinBo Zhu , Luxia Yu , Xiaohao Sun , Mingchao Liu , HengAn Wu
Inverse design of morphing slender structures with programmable curvature has significant applications in various engineering fields. Most existing studies formulate it as an optimization problem, which requires repeatedly solving the forward equations to identify optimal designs. Such methods, however, are computationally intensive and often susceptible to local minima issues. In contrast, solving the inverse problem theoretically, which can bypass the need for extensive forward simulations, is highly efficient yet remains challenging, particularly for cases involving arbitrary boundary conditions, such as clamped-free and clamped-clamped boundary conditions. Here, we develop a systematic theoretical framework based on Kirchhoff rod model, termed inverse elastica, for the direct determination of the undeformed configuration from a target deformed shape along with prescribed BCs. Building upon the classical Kirchhoff rod model, inverse elastica is derived by supplementing the geometric equations of undeformed configurations. Compared to forward solving of Kirchhoff rod model, inverse elastica shows several features: reduced nonlinearity, inverse loading and solution multiplicity. Building upon inverse elastica, we develop a theory-assisted optimization strategy for cases in which the constrains of the undeformed configurations cannot be directly formulated as boundary conditions. Using this strategy, we achieve rational inverse design of complex spatial curves and curve-discretized surfaces with varying Gaussian curvatures. Our theoretical predictions are validated through both discrete elastic rod simulations and experiments. While grounded in theory, the engineering value of inverse elastica is demonstrated through design of a deployable and conformable hemispherical helical antenna. This work thus provides a novel strategy for inverse design of morphing slender structures, opening new avenues for applications in morphing structures, soft robotics, deployable radio-frequency systems, architectural design, and beyond.
{"title":"Inverse elastica: A theoretical framework for inverse design of morphing slender structures","authors":"JiaHao Li , Weicheng Huang , YinBo Zhu , Luxia Yu , Xiaohao Sun , Mingchao Liu , HengAn Wu","doi":"10.1016/j.jmps.2025.106488","DOIUrl":"10.1016/j.jmps.2025.106488","url":null,"abstract":"<div><div>Inverse design of morphing slender structures with programmable curvature has significant applications in various engineering fields. Most existing studies formulate it as an optimization problem, which requires repeatedly solving the forward equations to identify optimal designs. Such methods, however, are computationally intensive and often susceptible to local minima issues. In contrast, solving the inverse problem theoretically, which can bypass the need for extensive forward simulations, is highly efficient yet remains challenging, particularly for cases involving arbitrary boundary conditions, such as clamped-free and clamped-clamped boundary conditions. Here, we develop a systematic theoretical framework based on Kirchhoff rod model, termed inverse elastica, for the direct determination of the undeformed configuration from a target deformed shape along with prescribed BCs. Building upon the classical Kirchhoff rod model, inverse elastica is derived by supplementing the geometric equations of undeformed configurations. Compared to forward solving of Kirchhoff rod model, inverse elastica shows several features: reduced nonlinearity, inverse loading and solution multiplicity. Building upon inverse elastica, we develop a theory-assisted optimization strategy for cases in which the constrains of the undeformed configurations cannot be directly formulated as boundary conditions. Using this strategy, we achieve rational inverse design of complex spatial curves and curve-discretized surfaces with varying Gaussian curvatures. Our theoretical predictions are validated through both discrete elastic rod simulations and experiments. While grounded in theory, the engineering value of inverse elastica is demonstrated through design of a deployable and conformable hemispherical helical antenna. This work thus provides a novel strategy for inverse design of morphing slender structures, opening new avenues for applications in morphing structures, soft robotics, deployable radio-frequency systems, architectural design, and beyond.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"208 ","pages":"Article 106488"},"PeriodicalIF":6.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145796196","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}
Quasi-brittle geomaterials in deep geological environments exhibit complex, multiscale degradation influenced by coupled pressure-temperature-time (PTT) processes. This study presents an original thermodynamically consistent, micromechanics-based constitutive framework to capture the full evolution of thermo-mechanical-temporal (TMT) damage in these materials. The model unifies three primary dissipative mechanisms–frictional sliding, instantaneous damage, and rheological degradation–by incorporating temperature-dependent elasticity, friction, cohesion, and relaxation behavior. A generalized variational structure is formulated based on Helmholtz free energy and convex dissipation potential, naturally yielding orthogonal evolution laws for internal variables. To enable full TMT coupling, a temperature evolution equation is derived, accounting for internal heat generation and conduction. Closed-form analytical expressions for macroscopic stress-strain-damage relationships and strength criteria are derived with clear physical interpretations. For numerical implementation, a unified framework is developed, combining a semi-implicit correction scheme for instantaneous response and a fast integration algorithm for rheological evolution. The model’s predictions are validated against multistage triaxial creep experiments on Qirehatar and Beishan granites under coupled thermal-mechanical-creep loading conditions. The model successfully reproduces nonlinear deformation, strength evolution, and long-term creep failure, demonstrating robust predictive capability across different lithologies and loading regimes. Key findings reveal that short-term response is controlled by thermal softening of elastic stiffness, while long-term instability arises from synergistic effects of cohesion variation and thermally activated rheological relaxation under elevated temperatures. In summary, the proposed model provides a unified and thermodynamically consistent framework for evaluating the long-term stability of quasi-brittle geomaterials under deep engineering conditions, advancing the understanding of deep rock behavior in complex coupled PTT environments.
{"title":"A thermodynamically consistent multiscale thermo-mechanical-temporal damage model for quasi-brittle geomaterials","authors":"Zhaomin Lv , Yuanming Lai , Jianying Wu , Lunyang Zhao","doi":"10.1016/j.jmps.2025.106483","DOIUrl":"10.1016/j.jmps.2025.106483","url":null,"abstract":"<div><div>Quasi-brittle geomaterials in deep geological environments exhibit complex, multiscale degradation influenced by coupled pressure-temperature-time (PTT) processes. This study presents an original thermodynamically consistent, micromechanics-based constitutive framework to capture the full evolution of thermo-mechanical-temporal (TMT) damage in these materials. The model unifies three primary dissipative mechanisms–frictional sliding, instantaneous damage, and rheological degradation–by incorporating temperature-dependent elasticity, friction, cohesion, and relaxation behavior. A generalized variational structure is formulated based on Helmholtz free energy and convex dissipation potential, naturally yielding orthogonal evolution laws for internal variables. To enable full TMT coupling, a temperature evolution equation is derived, accounting for internal heat generation and conduction. Closed-form analytical expressions for macroscopic stress-strain-damage relationships and strength criteria are derived with clear physical interpretations. For numerical implementation, a unified framework is developed, combining a semi-implicit correction scheme for instantaneous response and a fast integration algorithm for rheological evolution. The model’s predictions are validated against multistage triaxial creep experiments on Qirehatar and Beishan granites under coupled thermal-mechanical-creep loading conditions. The model successfully reproduces nonlinear deformation, strength evolution, and long-term creep failure, demonstrating robust predictive capability across different lithologies and loading regimes. Key findings reveal that short-term response is controlled by thermal softening of elastic stiffness, while long-term instability arises from synergistic effects of cohesion variation and thermally activated rheological relaxation under elevated temperatures. In summary, the proposed model provides a unified and thermodynamically consistent framework for evaluating the long-term stability of quasi-brittle geomaterials under deep engineering conditions, advancing the understanding of deep rock behavior in complex coupled PTT environments.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"208 ","pages":"Article 106483"},"PeriodicalIF":6.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145813940","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 : 2026-02-01Epub Date: 2025-12-13DOI: 10.1016/j.jmps.2025.106481
Baixi Chen, Alessandro Fascetti
Concrete failure mechanics exhibit significant variability at the macroscopic scale, which is predominantly driven by stochasticity at the spatial scale of the coarse aggregate particles, generally referred to as mesoscopic scale. However, mesoscale material parameters are difficult to estimate, making uncertainty quantification a fundamental challenge. To address this limitation, a data-driven multiscale inverse inference framework is proposed to quantify the stochastic mesoscale behavior by integrating both mesoscale and macroscale observations. In this framework, a stochastic data-driven model using a hybrid Proper Orthogonal Decomposition–Gaussian Process Regression (POD-GPR) algorithm is first developed based on data generated by mesoscale Lattice Discrete Particle Model (LDPM) simulations. Leveraging this efficient data-driven model, a novel multiscale Bayesian inverse inference method is proposed to infer the stochastic distributions of the mesoscale features. When applied to experimental data, the proposed framework successfully captures the stochastic distributions of mesoscale material parameters, reproduces macroscale responses, and outperforms conventional single-scale Bayesian inference approaches. Additionally, SHapley Additive exPlanations (SHAP) are integrated to further interpret the effect of mesoscale stochastic material behavior on macroscale uncertainty, offering valuable insights for the accuracy improvement of LDPM simulations and future mesoscale-level optimization to achieve more robust macroscale performance.
{"title":"Stochastic data-driven inference of mesoscale lattice discrete particle model parameters via multiscale observations","authors":"Baixi Chen, Alessandro Fascetti","doi":"10.1016/j.jmps.2025.106481","DOIUrl":"10.1016/j.jmps.2025.106481","url":null,"abstract":"<div><div>Concrete failure mechanics exhibit significant variability at the macroscopic scale, which is predominantly driven by stochasticity at the spatial scale of the coarse aggregate particles, generally referred to as mesoscopic scale. However, mesoscale material parameters are difficult to estimate, making uncertainty quantification a fundamental challenge. To address this limitation, a data-driven multiscale inverse inference framework is proposed to quantify the stochastic mesoscale behavior by integrating both mesoscale and macroscale observations. In this framework, a stochastic data-driven model using a hybrid Proper Orthogonal Decomposition–Gaussian Process Regression (POD-GPR) algorithm is first developed based on data generated by mesoscale Lattice Discrete Particle Model (LDPM) simulations. Leveraging this efficient data-driven model, a novel multiscale Bayesian inverse inference method is proposed to infer the stochastic distributions of the mesoscale features. When applied to experimental data, the proposed framework successfully captures the stochastic distributions of mesoscale material parameters, reproduces macroscale responses, and outperforms conventional single-scale Bayesian inference approaches. Additionally, SHapley Additive exPlanations (SHAP) are integrated to further interpret the effect of mesoscale stochastic material behavior on macroscale uncertainty, offering valuable insights for the accuracy improvement of LDPM simulations and future mesoscale-level optimization to achieve more robust macroscale performance.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"208 ","pages":"Article 106481"},"PeriodicalIF":6.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145760442","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}
In crystals, grains with different orientations form grain boundaries (GBs), while the meeting of three neighboring GBs gives rise to triple junctions (TJs). TJs are therefore ubiquitous crystalline defects in polycrystals and bear effect to the microstructural evolution of GB network via modulating GB migration and grain growth kinetics. Since the plastic deformation of TJs depend inherently on their atomic structures and migration pathways, it is crucial to establish a direct connection between the TJ kinetics and the grain growth of polycrystals. We propose a multiscale formulation to incorporate molecular dynamics (MD), kinetic Monte Carlo (kMC) simulation, and theoretical modeling of TJ kinetics to unravel the importance of structure-dependent TJ migration mechanisms in regulating GB network evolution in polycrystals. At an atomic scale, MD simulations have demonstrated that both the TJ disclinations and asymmetry can inhibit the glide of disconnections into TJs and thus obstruct the migration of TJs. Based on the atomistic insights, a theoretical model has been developed to describe the structure-dependent TJ migration kinetics, differing from the infinite TJ mobility hypothesis frequently utilized in existing formulations. The migration of an individual TJ, which is featured by the flux and accumulation of disconnections and their interactions with disclinations, can be captured by our model using kMC simulations, furnishing a dataset of TJ structure-mobility relationship. The atomistically-informed TJ kinetics and TJ mobility dataset are incorporated into a polycrystalline kMC model, which is capable of modelling TJ-influenced grain growth kinetics and grain size distribution evolution. Our work not only provides physical insights into the TJ-mediated GB migration mechanisms, but also offers a multiscale formulation for predicting the evolution of GB network in polycrystalline metals.
{"title":"Multiscale modeling on evolving grain boundary network in polycrystals incorporating triple junction migration","authors":"Qishan Huang , Zhenghao Zhang , Haofei Zhou , Wei Yang","doi":"10.1016/j.jmps.2025.106485","DOIUrl":"10.1016/j.jmps.2025.106485","url":null,"abstract":"<div><div>In crystals, grains with different orientations form grain boundaries (GBs), while the meeting of three neighboring GBs gives rise to triple junctions (TJs). TJs are therefore ubiquitous crystalline defects in polycrystals and bear effect to the microstructural evolution of GB network via modulating GB migration and grain growth kinetics. Since the plastic deformation of TJs depend inherently on their atomic structures and migration pathways, it is crucial to establish a direct connection between the TJ kinetics and the grain growth of polycrystals. We propose a multiscale formulation to incorporate molecular dynamics (MD), kinetic Monte Carlo (kMC) simulation, and theoretical modeling of TJ kinetics to unravel the importance of structure-dependent TJ migration mechanisms in regulating GB network evolution in polycrystals. At an atomic scale, MD simulations have demonstrated that both the TJ disclinations and asymmetry can inhibit the glide of disconnections into TJs and thus obstruct the migration of TJs. Based on the atomistic insights, a theoretical model has been developed to describe the structure-dependent TJ migration kinetics, differing from the infinite TJ mobility hypothesis frequently utilized in existing formulations. The migration of an individual TJ, which is featured by the flux and accumulation of disconnections and their interactions with disclinations, can be captured by our model using kMC simulations, furnishing a dataset of TJ structure-mobility relationship. The atomistically-informed TJ kinetics and TJ mobility dataset are incorporated into a polycrystalline kMC model, which is capable of modelling TJ-influenced grain growth kinetics and grain size distribution evolution. Our work not only provides physical insights into the TJ-mediated GB migration mechanisms, but also offers a multiscale formulation for predicting the evolution of GB network in polycrystalline metals.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"208 ","pages":"Article 106485"},"PeriodicalIF":6.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145784912","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 : 2026-02-01Epub Date: 2025-12-05DOI: 10.1016/j.jmps.2025.106448
Srivatsa Bhat Kaudur, Claudio V. Di Leo
A continuum-scale thermo-chemo-mechanical modeling framework is developed to investigate the multiphysics behavior of thermochemical energy storage (TES) materials undergoing hydration and dehydration during thermal cycling. The formulation integrates species diffusion, chemical reaction kinetics, heat generation/transport, and mechanical deformation within a unified theoretical framework to resolve spatial and temporal evolution of species concentration, reaction progress, temperature, and stress across material domains. A series of non-dimensional parametric studies quantifies the influence of key material parameters, including thermal conductivity, diffusivity, and reaction kinetics, on transformation dynamics, revealing critical interdependencies among physical processes that govern TES performance. To illustrate the capabilities of the framework, simulations of representative potassium carbonate pellets are presented with constitutive models and material properties adopted from the literature. In order to isolate chemo-thermal effects and facilitate comparison with fully coupled simulations, initial case studies focus on pellet hydration/dehydration without mechanical coupling, demonstrating the predictive capability of the model in capturing chemo-thermal gradients and transient performance. Subsequently, a fully coupled simulation is presented to explicitly illustrate the influence of mechanical stresses on the progression of the reaction. Mechanical stress can alter local chemical equilibrium conditions, thereby enhancing or suppressing hydration and dehydration reactions. By systematically accounting for interactions between stress, reaction pathways, and transport phenomena, this framework enables a mechanistic understanding of the dynamic interplay of physical processes that govern energy storage efficiency and material reliability, ultimately supporting the design of more robust and high-performance TES systems.
{"title":"Coupled thermo-chemo-mechanical modeling of reactive solids: Applications to thermochemical energy storage materials","authors":"Srivatsa Bhat Kaudur, Claudio V. Di Leo","doi":"10.1016/j.jmps.2025.106448","DOIUrl":"10.1016/j.jmps.2025.106448","url":null,"abstract":"<div><div>A continuum-scale thermo-chemo-mechanical modeling framework is developed to investigate the multiphysics behavior of thermochemical energy storage (TES) materials undergoing hydration and dehydration during thermal cycling. The formulation integrates species diffusion, chemical reaction kinetics, heat generation/transport, and mechanical deformation within a unified theoretical framework to resolve spatial and temporal evolution of species concentration, reaction progress, temperature, and stress across material domains. A series of non-dimensional parametric studies quantifies the influence of key material parameters, including thermal conductivity, diffusivity, and reaction kinetics, on transformation dynamics, revealing critical interdependencies among physical processes that govern TES performance. To illustrate the capabilities of the framework, simulations of representative potassium carbonate pellets are presented with constitutive models and material properties adopted from the literature. In order to isolate chemo-thermal effects and facilitate comparison with fully coupled simulations, initial case studies focus on pellet hydration/dehydration without mechanical coupling, demonstrating the predictive capability of the model in capturing chemo-thermal gradients and transient performance. Subsequently, a fully coupled simulation is presented to explicitly illustrate the influence of mechanical stresses on the progression of the reaction. Mechanical stress can alter local chemical equilibrium conditions, thereby enhancing or suppressing hydration and dehydration reactions. By systematically accounting for interactions between stress, reaction pathways, and transport phenomena, this framework enables a mechanistic understanding of the dynamic interplay of physical processes that govern energy storage efficiency and material reliability, ultimately supporting the design of more robust and high-performance TES systems.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"208 ","pages":"Article 106448"},"PeriodicalIF":6.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145689704","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 : 2026-02-01Epub Date: 2025-12-04DOI: 10.1016/j.jmps.2025.106467
Peijie Zhang , Xueyan Chen , Penghui Yu , Kun Zhao , Hang Yin , Changguo Wang , Huifeng Tan , Muamer Kadic
Although lattice mechanical metamaterials offer low weight and tailorable properties, they face a fundamental barrier to adoption at low relative densities: optimising elastic-plastic performance usually results in reduced buckling resistance (nonlinear stability). Here, we present a novel shell-lattice metamaterial design methodology that eliminates the need to compromise between high yield strength and nonlinear stability at low relative densities. This methodology also provides high specific stiffness and high energy absorption. Our design features seamlessly integrated elliptical hollow struts and hollow spherical nodes. Leveraging a stretching-dominated mechanism augmented by contact-enhanced stabilisation, the architecture provides compensatory reinforcement under large deformations. We numerically investigate and experimentally validate the influence of key geometrical ratios on the mechanical properties. Crucially, elastic isotropy can be achieved through parameter optimisation, and broad tenability enables customised anisotropic elastic responses for diverse applications. Across relative densities ranging from 0.01 to 0.5, our proposed shell lattices demonstrate consistent superiority over conventional truss and shell lattices of equal density. At a relative density of 0.1, the designs deliver a 5 % rise in Young’s modulus, a 38 % increase in yield strength, and almost double the energy absorption capacity, significantly outperforming conventional TPMS-like shell lattices. These enhancements arise from internal contact mechanisms that stabilise post-buckling behaviour, yielding consistent or enhanced stress-strain responses. This methodology overcomes the limitations of low-density stretching-dominated lattices, paving the way for advanced, lightweight, load-bearing structures, energy absorbers, and multifunctional metamaterials.
{"title":"Shell-lattice metamaterials with intrinsic contact stabilization for exceptional mechanical performance and nonlinear stability","authors":"Peijie Zhang , Xueyan Chen , Penghui Yu , Kun Zhao , Hang Yin , Changguo Wang , Huifeng Tan , Muamer Kadic","doi":"10.1016/j.jmps.2025.106467","DOIUrl":"10.1016/j.jmps.2025.106467","url":null,"abstract":"<div><div>Although lattice mechanical metamaterials offer low weight and tailorable properties, they face a fundamental barrier to adoption at low relative densities: optimising elastic-plastic performance usually results in reduced buckling resistance (nonlinear stability). Here, we present a novel shell-lattice metamaterial design methodology that eliminates the need to compromise between high yield strength and nonlinear stability at low relative densities. This methodology also provides high specific stiffness and high energy absorption. Our design features seamlessly integrated elliptical hollow struts and hollow spherical nodes. Leveraging a stretching-dominated mechanism augmented by contact-enhanced stabilisation, the architecture provides compensatory reinforcement under large deformations. We numerically investigate and experimentally validate the influence of key geometrical ratios on the mechanical properties. Crucially, elastic isotropy can be achieved through parameter optimisation, and broad tenability enables customised anisotropic elastic responses for diverse applications. Across relative densities ranging from 0.01 to 0.5, our proposed shell lattices demonstrate consistent superiority over conventional truss and shell lattices of equal density. At a relative density of 0.1, the designs deliver a 5 % rise in Young’s modulus, a 38 % increase in yield strength, and almost double the energy absorption capacity, significantly outperforming conventional TPMS-like shell lattices. These enhancements arise from internal contact mechanisms that stabilise post-buckling behaviour, yielding consistent or enhanced stress-strain responses. This methodology overcomes the limitations of low-density stretching-dominated lattices, paving the way for advanced, lightweight, load-bearing structures, energy absorbers, and multifunctional metamaterials.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"208 ","pages":"Article 106467"},"PeriodicalIF":6.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145689710","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 : 2026-02-01Epub Date: 2025-11-11DOI: 10.1016/j.jmps.2025.106422
Jan Eliáš , Gianluca Cusatis
This article answers the question of whether homogenization of discrete fine-scale mechanical models, such as particle or lattice models, gives rise to an equivalent continuum that is of Cauchy-type or Cosserat-type. The study employs the machinery of asymptotic expansion homogenization to analyze discrete mechanical models with rotational degrees of freedom commonly used to simulate the mechanical behavior of heterogeneous solids. The proposed derivation has general validity in both stationary (steady-state) and transient conditions (assuming wavelength much larger that particle size) and for arbitrary nonlinear, inelastic fine-scale constitutive equations. The results show that the unit cell problem is always stationary, and the only inertia term appears in the linear momentum balance equation at the coarse scale. Depending on the magnitude of the local bending stiffness, mathematical homogenization rigorously identifies two limiting conditions that correspond to the Cauchy continuum and the Cosserat continuum. A heuristic combination of these two limiting conditions provides very accurate results also in the transition from one limiting case to the other. Finally, the study demonstrates that cases for which the Cosserat character of the homogenized response is significant are associated with non-physically high fine-scale bending stiffness and, as such, are of no interest in practice.
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Pub Date : 2026-02-01Epub Date: 2025-12-25DOI: 10.1016/j.jmps.2025.106487
U. Houire , S. Mercier , C. Czarnota , M. Xavier , S. El Maï
This work investigates the onset and development of plastic strain localization during the dynamic expansion of metallic shells. The multiple necking and fragmentation scenario are here viewed as originating from the development of geometrical perturbations (i.e., surface roughness), whose time evolution plays a critical role for the late free flight of fragments. Based on the extended 1DXLSA (One-Dimensional eXtended Linear Stability Analysis) model of Xavier et al. (2021), and using the 2DXLSA of Xavier et al. (2020) and FEM calculations as references, we propose an adjustment of the stress approximation in the neck section to better capture the onset of multiple necking in cylindrical (plate) and ring (round bar) geometries. A modified Bridgman correction factor is then introduced, which highlights the limitations of the previous 1DXLSA study. A good agreement in terms of time evolution of the perturbations is obtained between Finite element simulations, two-dimensional linear stability approach and the new 1D model.
本文研究了金属壳在动态膨胀过程中塑性应变局部化的发生和发展。多重颈缩和破碎情景被认为起源于几何扰动（即表面粗糙度）的发展，其时间演化对碎片的后期自由飞行起着关键作用。基于Xavier et al.（2021）的扩展1DXLSA（一维扩展线性稳定性分析）模型，并参考Xavier et al.（2020）的2DXLSA和FEM计算，我们提出了颈部截面应力近似的调整，以更好地捕捉圆柱形（板）和环形（圆杆）几何形状的多重颈部的开始。然后引入了一个修正的Bridgman校正因子，这突出了先前的1DXLSA研究的局限性。有限元模拟、二维线性稳定性方法和新的一维模型在扰动的时间演化方面有很好的一致性。
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