Journal of The Mechanics and Physics of Solids最新文献

{"title":"Anomalous size effects with fixed criticality in bistable flexible mechanical metamaterials","authors":"Zehuan Tang, Tingfeng Ma, Boyue Su, Qing Xia, Pengfei Kang, Bowei Wu","doi":"10.1016/j.jmps.2025.106296","DOIUrl":"https://doi.org/10.1016/j.jmps.2025.106296","url":null,"abstract":"When the structure deformation is dominated by the low-energy deformation mode, the structure hardens with the increase in the size (number of units) at small sizes. This anomalous behavior will eventually disappear with the decay length of the finite structure converging to a size-independent characteristic quantity, but the specific critical point at which the anomalous behavior disappears still cannot be accurately and concisely described. Here, under two steady states of the bistable chain, we observed anomalous size effects with constant and oscillating criticality (the proportion of inhomogeneous deformation), two criticalities exactly separate the increasing and decreasing intervals of stiffness variation. They are interrelated due to the implied symmetries between the two steady states. On the other hand, they are distinguished because of the opposite superposition modes under the two steady states. Specifically, the constant criticality corresponds to the anomalous size effect achieved by the competition mechanism, while the oscillating criticality reveals an anomalous size effect achieved by the new mechanism (cancellation mechanism). In the anomalous size effect achieved by the cancellation mechanism, the singular characteristics generated by the completely cancelled deformation make it very robust. This robustness reflects in that the anomalous effect is no longer limited to linear small deformation, but it can still be observed stably in nonlinear large deformation. Our study reinterprets the anomalous size effect at a quantitative level, and the proposed cancellation mechanism expands the possible application range of this anomalous effect.","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"11 1","pages":""},"PeriodicalIF":5.3,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144622400","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 statistical mechanics derivation and implementation of non-conservative phase field models for front propagation in elastic media","authors":"Travis Leadbetter, Prashant K. Purohit, Celia Reina","doi":"10.1016/j.jmps.2025.106240","DOIUrl":"https://doi.org/10.1016/j.jmps.2025.106240","url":null,"abstract":"Over the past several decades, phase field modeling has been established as a standard simulation technique for mesoscopic science, allowing for seamless boundary tracking of moving interfaces and relatively easy coupling to other physical phenomena. However, despite its widespread success, phase field modeling remains largely driven by phenomenological justifications except in a handful of instances. In this work, we leverage a recently developed statistical mechanics framework for non-equilibrium phenomena, called Stochastic Thermodynamics with Internal Variables (STIV), to provide the first derivation of a non-conservative phase field model for tracking front propagation in a one dimensional elastic medium without appeal to phenomenology or fitting to experiments or simulation data. In the resulting model, the variables obey a gradient flow with respect to a non-equilibrium free energy, although notably, the dynamics of the strain and phase variables are coupled, and while the free energy functional is non-local in the phase field variable <mml:math altimg=\"si1.svg\" display=\"inline\"><mml:mi>Φ</mml:mi></mml:math>, such non-locality deviates from the traditional <mml:math altimg=\"si2.svg\" display=\"inline\"><mml:msup><mml:mrow><mml:mrow><mml:mo>|</mml:mo><mml:mo>∇</mml:mo><mml:mi>Φ</mml:mi><mml:mo>|</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math> form. Moreover, in the systems analyzed here, the model accurately captures stress induced nucleation of transition fronts without the need to incorporate additional physics. We find that the STIV phase field model compares favorably to Langevin simulations of the microscopic system and we provide two numerical implementations enabling one to simulate arbitrary interatomic potentials.","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"23 1","pages":""},"PeriodicalIF":5.3,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144622405","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":"Dislocations in the elastic fields of randomly distributed defects","authors":"Ronghai Wu, Michael Zaiser","doi":"10.1016/j.jmps.2025.106264","DOIUrl":"https://doi.org/10.1016/j.jmps.2025.106264","url":null,"abstract":"In recent years, the behavior of dislocations in random solid solutions has received renewed interest, and several models have been discussed where random alloys are treated as effective media containing random distributions of dilatation and compression centers. More generally speaking, the arrangement of defects in metals and alloys is always characterized by statistical disorder, and the same is true for the fluctuating fields that arise from the superposition of the stress and strain fields of many defects. In order to develop models for the dynamics of dislocations interacting with such fields, a statistical description of the dislocation energy landscape and the associated configurational forces is needed, as well as methods for coarse graining these forces over dislocation segments of varying length and shape. In this context the problem arises how to regularize the highly singular stress fields associated with dislocations and other defects. Here we formulate an approach which is based upon evaluating the interaction energies and interaction forces between singular dislocations and other defects including solutes, modelled as point-like dilatation centers, and other dislocations. We characterize the interactions in terms of the probability densities of interaction energies and interaction forces, and the corresponding spatial correlation functions. We also consider the effects of dislocation core regularization, either in terms of continuously distributed Burgers vectors or by using the formalism of gradient elasticity of Helmholtz type to formulate a regularized energy functional. We demonstrate that the stress fields arising from randomly distributed defects obey in general non-Gaussian statistics, and discuss implications for the motion of dislocations.","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"109 1","pages":""},"PeriodicalIF":5.3,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144622401","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":"Morphological Evolution and Instability of Microvoids Governed by Competing Surface and Bulk Diffusion","authors":"Ping Yang, Yilun Xu, Wanghui Li, Yong-Wei Zhang, Pengyang Zhao","doi":"10.1016/j.jmps.2025.106294","DOIUrl":"https://doi.org/10.1016/j.jmps.2025.106294","url":null,"abstract":"Understanding diffusion-controlled void growth at the nanoscale under extreme environments (e.g., high temperatures, irradiation) is crucial for predicting failure in metallic materials. We develop a micromechanical model that integrates surface diffusion, bulk diffusion, and heterogeneous stress fields to capture the growth, morphological evolution and coalescence of microvoids. The model is validated against well-established analytical solutions, demonstrating high reliability and accuracy. Using this model, we explore the competitive interplay between surface diffusion and bulk diffusion in governing void shape stability and transitions. Our findings reveal that surface diffusion promotes stable, circular or elliptical morphologies, whereas bulk diffusion, especially under heterogeneous stress, induces anisotropic growth and morphological instabilities. As voids grow, the influence of surface diffusion diminishes, facilitating the formation of increasingly complex void shapes. Void coalescence behavior further reflects this interplay: in the absence of inter-void vacancy sources, bulk diffusion alone is insufficient to drive coalescence due to <ce:italic>shielding effect</ce:italic> on vacancy concentration gradient at inter-void region. In contrast, surface diffusion facilitates void coalescence, with rates increasing alongside surface diffusivity. When surface diffusion is substantially weaker than bulk diffusion, void growth becomes inherently unstable, and minor surface perturbations can trigger the nucleation of micro-cracks. These findings show excellent agreement with existing experimental results. Overall, this study provides a mechanistic understanding of diffusion-controlled void evolution and offers valuable insights into damage precursors in metals subjected to extreme environments.","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"14 1","pages":""},"PeriodicalIF":5.3,"publicationDate":"2025-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144622404","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 consistent Lagrangian theory for phase separation in chemoelastic polymeric media at large deformations","authors":"A. Gomero Soria, A. Stracuzzi, A.E. Ehret","doi":"10.1016/j.jmps.2025.106256","DOIUrl":"https://doi.org/10.1016/j.jmps.2025.106256","url":null,"abstract":"Large volume and shape changes may occur in polymer solutions and gels subject to mechanical loads or solvent loss. These deformations can lead to local alterations in composition, affecting or even triggering the phase separation into polymer-rich and solvent-rich phases. Studying microstructure evolution arising under these conditions thus necessitates a large strain formulation of the classical phase-field model for phase separation. To this end, a recent chemomechanical theory for biphasic media at large strains (Stracuzzi et al. ZAMM 8, 2018:2135–2154) was amended to incorporate the energetic contribution of interfaces between phase domains. The resulting model employs the well-established Cahn-Hilliard equation for diffusion and the Flory–Huggins mixing energy for polymer-solvent systems, expressed in a Lagrangian framework. The analysis of previous work on such referential reformulations of the original equations revealed different treatments, particularly with regard to the dependence of interfacial energy on deformation. In the present contribution, a consistent Lagrangian representation of the original model is rigorously derived, which entails a highly non-linear dependence of the interfacial energy on volume changes. The governing equations of this and a common alternative model were solved by a finite element approach, and were compared with regard to their predictions of microstructure formation in boundary value problems that lead to very large deformations, either induced by solvent evaporation or mechanical loads. In addition to the fully coupled chemomechanical theory for phase separation under large strains provided herein, the present work thus specifically highlights the importance of the constitutive model that specifies the free energy density associated with the formation of interfaces in the geometrically non-linear regime.","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"138 1","pages":""},"PeriodicalIF":5.3,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144622402","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":"Surface-polyconvex models for soft elastic solids","authors":"Martin Horák ,&nbsp;Michal Šmejkal ,&nbsp;Martin Kružík","doi":"10.1016/j.jmps.2025.106250","DOIUrl":"10.1016/j.jmps.2025.106250","url":null,"abstract":"<div><div>Soft solids with surface energy exhibit complex mechanical behavior, necessitating advanced constitutive models to capture the interplay between bulk and surface mechanics. This interplay has profound implications for material design and emerging technologies. In this work, we set up variational models for bulk-surface elasticity and explore a novel class of surface-polyconvex constitutive models that account for surface energy while ensuring the existence of minimizers.</div><div>These models are implemented within a finite element framework and validated through benchmark problems and applications, including, e.g., the liquid bridge problem and the Rayleigh-Plateau instability, for which the surface energy plays the dominant role. The results demonstrate the ability of surface-polyconvex models to accurately capture surface-driven phenomena, establishing them as a powerful tool for advancing the mechanics of soft materials in both engineering and biological applications.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"204 ","pages":"Article 106250"},"PeriodicalIF":5.0,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144622403","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":"An anisotropic damage model with defect-crack interactions for heterogeneous brittle media under high-rate loading","authors":"S. Braroo, K.T. Ramesh","doi":"10.1016/j.jmps.2025.106244","DOIUrl":"https://doi.org/10.1016/j.jmps.2025.106244","url":null,"abstract":"A defect-crack interaction informed anisotropic damage modeling framework is proposed to predict the uniaxial compressive strength of heterogeneous brittle materials under high-strain-rate loading (strain rates of <mml:math altimg=\"si1.svg\" display=\"inline\"><mml:mrow><mml:mn>1</mml:mn><mml:msup><mml:mrow><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mspace width=\"0.33em\"></mml:mspace><mml:msup><mml:mrow><mml:mi mathvariant=\"normal\">s</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math> – <mml:math altimg=\"si2.svg\" display=\"inline\"><mml:mrow><mml:mn>1</mml:mn><mml:msup><mml:mrow><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup><mml:mspace width=\"0.33em\"></mml:mspace><mml:msup><mml:mrow><mml:mi mathvariant=\"normal\">s</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>). The model is capable of accounting for the effect of interaction stress fields, produced by pre-existing defects, on cracks in a brittle material, allowing for the incorporation of material microstructure. The interaction-modified stresses are computed using the superposition technique where mean stress fields from a homogenization-based approach and perturbation stress fields from spherical-harmonics-expansion-based approach are superimposed. Sliding-crack model is employed to represent crack extension under compression, and dynamic wing-crack growth is computed under the influence of the interaction stresses. The directional influence of wing-crack growth is incorporated through an anisotropic damage model where a tensorial damage metric is employed. A linear, anisotropic increment in material compliance is derived accounting for the effect of interactions on micro-cracking based damage. Model parameters can be estimated from microstructural information and/or strength, damage and volumetric strain observed in experiments. The calibrated model is used to predict uniaxial compressive strength at varying strain rates of an engineering ceramic with good experimental match. We compare this model’s effectiveness with that of some existing micromechanics models for dynamic failure of brittle materials.","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"14 1","pages":""},"PeriodicalIF":5.3,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144622408","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":"Elastic Plateau–Rayleigh instability in soft cylinders: Surface elasticity and periodic beading","authors":"F. Magni,&nbsp;D. Riccobelli","doi":"10.1016/j.jmps.2025.106258","DOIUrl":"10.1016/j.jmps.2025.106258","url":null,"abstract":"<div><div>The Plateau–Rayleigh instability shows that a cylindrical fluid flow can be destabilized by surface tension. Similarly, capillary forces can make an elastic cylinder unstable when the elastocapillary length is comparable to the cylinder’s radius. While existing models predict a single isolated bulge as the result of an instability, experiments reveal a periodic sequence of bulges spaced out by thinned regions, a phenomenon known as beading instability. Most models assume that surface tension is independent of the deformation of the solid, neglecting variations due to surface stretch.</div><div>In this work, we assume that surface tension arises from the deformation of material particles near the free surface, treating it as a pre-stretched elastic surface surrounding the body. Using the theoretical framework proposed by Gurtin and Murdoch, we show that a cylindrical solid can undergo a mechanical instability with a finite critical wavelength if the body is sufficiently soft or axially stretched. Post-buckling numerical simulations reveal a morphology in qualitative agreement with experimental observations. Period-halving secondary bifurcations are also observed. The results of this research have broad implications for soft materials, biomechanics, and microfabrication applications where surface tension plays a crucial role.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"203 ","pages":"Article 106258"},"PeriodicalIF":5.0,"publicationDate":"2025-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144579825","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":"Structure of anisotropic bi-dimensional elasticity tensors in micromorphic and related higher-order media","authors":"Michaël Peigney","doi":"10.1016/j.jmps.2025.106252","DOIUrl":"10.1016/j.jmps.2025.106252","url":null,"abstract":"<div><div>This paper addresses the classification of constitutive tensors in bi-dimensional micromorphic elasticity, a higher-order continuum theory that extends Cauchy elasticity by introducing an additional degree of freedom in the form of a microdeformation tensor. We systematically investigate the impact of material symmetries on the forms of the constitutive elasticity tensors, reducing the number of independent parameters in the micromorphic energy. The analysis includes the first-order, second-order, and coupling elastic energies, with results presented in terms of symmetry classes and explicit matrix forms. Additionally, analogous results are derived for related higher-order theories, including the microdilatation, micropolar, microstretch, and microstrain theories.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"204 ","pages":"Article 106252"},"PeriodicalIF":5.0,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144596605","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":"Variational Linear Comparison estimates for the macroscopic response and field statistics of elasto-viscoplastic composites","authors":"P. Ponte Castañeda","doi":"10.1016/j.jmps.2025.106245","DOIUrl":"10.1016/j.jmps.2025.106245","url":null,"abstract":"<div><div>This work provides a generalization of the Variational Linear Comparison method (Ponte Castañeda, 1991) for elasto-viscoplastic (EVP) composites. To this end, use is made of Rayleigh’s least dissipation variational principle, leading to the characterization of the time-incremental macroscopic response of the composites in terms of suitably defined macroscopic Rayleigh potentials. By combining this variational framework with linearization schemes based on the notion of ‘comparison’ linear viscoelastic (LVE) composites, estimates are obtained for the macroscopic constitutive relation of the EVP composite in terms of the constitutive response of the comparison LVE composite, where the viscosities of the phases correspond to the secant viscosities of the phases of the EVP composite, evaluated at the instantaneous values of the second moments of the stress or strain-rate fields in the phases of the LVE comparison composite. The methodology is illustrated for particulate microstructures by application of the estimates of Willis (1977) for the comparison LVE composite, for which the use of time-differential operators can be exploited to generate evolution equations not only for the macroscopic fields but also for the field statistics — including the covariance of the fluctuations (which are not normally available from the correspondence principle). After testing the methodology for LVE composites, results are obtained for the class of EVP composites with particulate microstructures and general compressible, isotropic behavior for the phases. The new method recovers earlier results for the incompressible case, but it is also computationally robust when the phases are compressible (where other approximate methods have significant issues, especially when the phases are not well-ordered or when cyclic loading is applied), and it is the only method to date to be able to recover exactly, by construction, the limiting cases of purely elastic, purely viscoplastic and LVE behaviors.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"204 ","pages":"Article 106245"},"PeriodicalIF":5.0,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144578243","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}