Journal of The Mechanics and Physics of Solids最新文献

{"title":"A thermodynamically consistent multiscale thermo-mechanical-temporal damage model for quasi-brittle geomaterials","authors":"Zhaomin Lv ,&nbsp;Yuanming Lai ,&nbsp;Jianying Wu ,&nbsp;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}

{"title":"Inverse elastica: A theoretical framework for inverse design of morphing slender structures","authors":"JiaHao Li ,&nbsp;Weicheng Huang ,&nbsp;YinBo Zhu ,&nbsp;Luxia Yu ,&nbsp;Xiaohao Sun ,&nbsp;Mingchao Liu ,&nbsp;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}

{"title":"Stochastic data-driven inference of mesoscale lattice discrete particle model parameters via multiscale observations","authors":"Baixi Chen,&nbsp;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}

{"title":"Multiscale modeling on evolving grain boundary network in polycrystals incorporating triple junction migration","authors":"Qishan Huang ,&nbsp;Zhenghao Zhang ,&nbsp;Haofei Zhou ,&nbsp;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}

{"title":"Do discrete fine-scale mechanical models with rotational degrees of freedom homogenize into a Cosserat or a Cauchy continuum?","authors":"Jan Eliáš ,&nbsp;Gianluca Cusatis","doi":"10.1016/j.jmps.2025.106422","DOIUrl":"10.1016/j.jmps.2025.106422","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"207 ","pages":"Article 106422"},"PeriodicalIF":6.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145492373","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":"1D linear stability analysis based on an adjusted correction factor for dynamic expansion: Application to plates and rods","authors":"U. Houire ,&nbsp;S. Mercier ,&nbsp;C. Czarnota ,&nbsp;M. Xavier ,&nbsp;S. El Maï","doi":"10.1016/j.jmps.2025.106487","DOIUrl":"10.1016/j.jmps.2025.106487","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"208 ","pages":"Article 106487"},"PeriodicalIF":6.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145845501","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":"Stress boundedness and existence of radial minimizers in constrained nonlinear elasticity","authors":"Paolo Maria Mariano ,&nbsp;Domenico Mucci","doi":"10.1016/j.jmps.2025.106449","DOIUrl":"10.1016/j.jmps.2025.106449","url":null,"abstract":"<div><div>For simple elastic bodies in small strain regime, the convexity of the energy allows one to discuss equilibrium problems under stress constraints (the specification of an admissible convex region in the stress space) in terms of the complementary energy. In the presence of large strains, the necessary lack of energy convexity does not allow one to retrace the same path. A significant concept of complementary energy in large strain regime rests on the Legendre transform of the energy with respect to the deformation gradient, its cofactor and determinant. The related minimum problem necessarily requires that constraints be assigned to the derivatives of the energy density with respect to the variables already listed (these derivatives are required to be in a convex subset of an appropriate linear space). A problem is to characterize the related stresses in terms of a constrained energy. We tackle this problem for radially symmetric simple bodies under radial deformations and show how the resulting stress is bounded. We also prove the existence of radially symmetric minimizers for the constrained elastic energy under Dirichlet boundary conditions.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"208 ","pages":"Article 106449"},"PeriodicalIF":6.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145651076","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 neural-network-enhanced micromechanical framework with evolving reference medium for nonlinear heterogeneous materials","authors":"Ce Chen ,&nbsp;Liujun Wu ,&nbsp;Chenyang Xin ,&nbsp;Wenbin Liu ,&nbsp;Xin Yi ,&nbsp;Huiling Duan","doi":"10.1016/j.jmps.2025.106426","DOIUrl":"10.1016/j.jmps.2025.106426","url":null,"abstract":"<div><div>The mechanical response of nonlinear heterogeneous materials is strongly influenced by the deformation-dependent spatial variation of properties in the matrix and inclusions. Conventional micromechanical approaches, typically based on linearization techniques and uniform moduli within each material phase, often fail to capture the effective response of such nonlinear systems, where the local tangent modulus acts as a deformation-dependent measure of stiffness rather than an intrinsic material property. Here, we present a neural-network-enhanced micromechanical framework built upon an evolving nonlinear reference medium with spatially non-uniform tangent moduli, for composites comprising an isotropic matrix and isotropic spherical inclusions with nonlinear interfacial effects. Building on a single-inclusion configuration, where an inclusion is embedded in a reference medium, we introduce two physics-guided neural networks that capture the spatial variation with local deformation states. One network models the inclusions with prescribed properties, while the other represents the reference medium, whose material properties evolve with macroscopic deformations. By enforcing the interfacial displacement–traction condition, we identify the varying properties of the reference medium and determine the effective tangent modulus of the composite. Applied to nonlinear particle-reinforced elastomers at high volume fractions, the framework significantly outperforms classical micromechanical approaches. Moreover, the trained model demonstrates remarkable generalization across diverse nonlinear behaviors of inclusions and matrix, interfacial conditions, loading modes, and volume fractions—without retraining. The framework also extends naturally to plasticity problems, yielding accurate predictions for porous plastic solids. This work establishes a new pathway for integrating neural networks into the derivation of micromechanical relations for complex nonlinear composites.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"207 ","pages":"Article 106426"},"PeriodicalIF":6.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145546298","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":"Reduced-order representations of crystallographic texture for application to surrogate modelling of austenitic stainless steel","authors":"Hugh Dorward ,&nbsp;Mahmoud Mostafavi ,&nbsp;David M. Knowles ,&nbsp;Matthew J. Peel","doi":"10.1016/j.jmps.2025.106444","DOIUrl":"10.1016/j.jmps.2025.106444","url":null,"abstract":"<div><div>Surrogate models are a useful tool in enabling efficient modelling and propagation of uncertainty through material process-structure-property linkages. One promising application is in the modelling the dependence of macroscopic material properties on the microstructure of polycrystalline materials. However, this requires parameterisation of complex microstructural features such as crystallographic texture.</div><div>This study compares two methods for parameterising texture for use in reduced-order models: a principal component analysis reduction of generalised spherical harmonics (GSH-PCA), and a simpler, scalar parameterisation using the Taylor factor. The effectiveness of each method is demonstrated by applying each to a Gaussian process (GP) regression surrogate of material deformation, trained on data from crystal plasticity simulation.</div><div>The GSH-PCA parameterisation reduces the number of variables required to capture texture to between 5–10 for cubic-orthorhombic symmetry and has the advantage of allowing reconstruction of the original texture from the GSH-PCA coefficients. In comparison, the Taylor factor offers a simpler surrogate model with a single input parameter, however this model has less overall predictive accuracy with more uncertainty in the input variable space. Despite this, the use of GP regression as the surrogate model with functional outputs allows the uncertainties from both texture parameterisations to be propagated through to the prediction of macroscopic mechanical behaviour.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"208 ","pages":"Article 106444"},"PeriodicalIF":6.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145598603","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 time and space homogenization of viscoelastic–viscoplastic composite materials under large numbers of loading cycles","authors":"I. Doghri ,&nbsp;M. Haddad ,&nbsp;G. Tsilimidos ,&nbsp;S. Haouala","doi":"10.1016/j.jmps.2025.106423","DOIUrl":"10.1016/j.jmps.2025.106423","url":null,"abstract":"<div><div>A coupled time and space homogenization formulation is proposed for heterogeneous micro-structures with viscoelastic–viscoplastic (VE–VP) constituents and subjected to large numbers of cycles. A time homogenization theory is presented in a general setting, based on two time scales and asymptotic time expansion of the fields. It leads to a macro-time VE–VP problem being fed with stress fluctuations computed from a micro-time VE problem. New theoretical results are discussed. Coupling with space homogenization is detailed for the incremental-secant mean-field homogenization (MFH) formulation. The latter takes into account per phase residual strains and stresses upon virtual VE unloading and leads to an incremental stiffness operator which is naturally isotropic for an isotropic VE–VP constituent. Coupling with time homogenization brings new terms which are not present in the original MFH method. Computational algorithms are proposed based on implicit time integration schemes, and numerical simulations illustrate the remarkable performance of the proposed formulation and algorithms.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"207 ","pages":"Article 106423"},"PeriodicalIF":6.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145515558","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}