Journal of The Mechanics and Physics of Solids最新文献

{"title":"Inverse design of anisotropic microstructures using physics-augmented neural networks","authors":"Asghar A. Jadoon ,&nbsp;Karl A. Kalina ,&nbsp;Manuel K. Rausch ,&nbsp;Reese Jones ,&nbsp;Jan Niklas Fuhg","doi":"10.1016/j.jmps.2025.106161","DOIUrl":"10.1016/j.jmps.2025.106161","url":null,"abstract":"<div><div>Composite materials often exhibit mechanical anisotropy owing to the material properties or geometrical configurations of the microstructure. This makes their inverse design a two-fold problem. First, we must learn the type and orientation of anisotropy and then find the optimal design parameters to achieve the desired mechanical response. In our work, we solve this challenge by first training a forward surrogate model based on the macroscopic stress–strain data obtained via computational homogenization for a given multiscale material. To this end, we use partially Input Convex Neural Networks (pICNNs) to obtain a representation of the strain energy in terms of the invariants of the Cauchy–Green deformation tensor which is polyconvex with respect to the deformation gradient whereas it can have an arbitrary form with respect to the design parameters. The network architecture and the strain energy function are further modified to incorporate, by construction, physics and mechanistic assumptions into the framework. While training the neural network, we find the type of anisotropy, if any, along with the preferred directions. Once the model is trained, we solve the inverse problem using an evolution strategy to obtain the design parameters that give a desired mechanical response. We test the framework against synthetic macroscale and also homogenized data. For cases where polyconvexity might be violated during the homogenization process, we present viable alternate formulations. The trained model is also integrated into a finite element framework to invert design parameters that result in a desired macroscopic response. We show that the invariant-based model is able to solve the inverse problem for a stress–strain dataset with a different preferred direction than the one it was trained on and is able to not only learn the polyconvex potentials of hyperelastic materials but also recover the correct parameters for the inverse design problem.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"203 ","pages":"Article 106161"},"PeriodicalIF":5.0,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144223543","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":"Three-dimensional micromechanical expression for the average strain tensor of granular materials","authors":"Chaofa Zhao ,&nbsp;Ge Duan ,&nbsp;Zhongxuan Yang","doi":"10.1016/j.jmps.2025.106189","DOIUrl":"10.1016/j.jmps.2025.106189","url":null,"abstract":"<div><div>In investigations of the behaviour of granular materials, the conversion of discrete contact information, specifically the force and displacement data, into macroscopic quantities such as stress and strain is a fundamental approach. The expression for the average stress tensor, a well-established formulation, involves the summation over all interparticle contacts while considering both the contact force and geometric parameters such as the branch vector. However, for the three-dimensional case, a general micromechanical expression for the average strain tensor is still missing.</div><div>In this study, a three-dimensional micromechanical expression is derived for the average strain tensor of granular materials. The new expression for the strain tensor involves only particle positions and relative displacements between particles, and does not depend on the tessellation method applied to the space occupied by the particles and interparticle voids. To validate the accuracy of the strain tensor, displacement data of granular assemblies were generated through Discrete Element Method simulations, and the strains of granular assemblies calculated by the derived strain tensor were compared with those calculated from the macroscopic deformation of granular assemblies. The results demonstrate that the proposed strain tensor is consistent with the macroscopic strain tensor, either in triaxial compression or in simple shear tests. This research conclusively addresses the fundamental question for the three-dimensional micromechanical strain tensor of granular materials and contributes to the development of accurate micromechanics-based constitutive models for granular materials.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"202 ","pages":"Article 106189"},"PeriodicalIF":5.0,"publicationDate":"2025-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144185362","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":"Fixing non-positive energies in higher-order homogenization","authors":"Manon Thbaut ,&nbsp;Basile Audoly ,&nbsp;Claire Lestringant","doi":"10.1016/j.jmps.2025.106168","DOIUrl":"10.1016/j.jmps.2025.106168","url":null,"abstract":"<div><div>Energy functionals produced by second-order homogenization of periodic elastic structures commonly feature negative gradient moduli. This undesirable property is caused by the truncation of the energy expansion in powers of the small scale separation parameter. By revisiting Cholesky’s LDLT decomposition, we propose an alternative truncation method that restores positivity while preserving the order of accuracy. We illustrate this method on a variety of periodic structures, both continuous and discrete, and derive compact analytical expressions of the homogenized energy that are positive and accurate to second order. The method can also cure the energy functionals produced by second-order <em>dimension reduction</em>, which suffer similar non-positivity issues. It extends naturally beyond second order.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"203 ","pages":"Article 106168"},"PeriodicalIF":5.0,"publicationDate":"2025-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144205431","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":"Description of void coalescence by internal necking/shearing within XFEM via a micromechanical 3D volumetric cohesive zone model (μ-VCZM)","authors":"Antonio Kaniadakis ,&nbsp;Jean-Philippe Crété ,&nbsp;Patrice Longère","doi":"10.1016/j.jmps.2025.106176","DOIUrl":"10.1016/j.jmps.2025.106176","url":null,"abstract":"<div><div>This work addresses ductile failure in engineering structures, particularly in aerospace, naval, automotive, and nuclear industries. During accidental overloading or metal forming, materials such as titanium and aluminum alloys experience plastic deformation and ductile damage (by void nucleation, growth, and coalescence) that may eventually lead to crack propagation and fracture. The present study concentrates explicitly on the void coalescence stage. Indeed, building upon a numerical methodology developed by the present authors and detailed in a companion paper, a novel micromechanics-based volumetric cohesive zone model (<span><math><mi>μ</mi></math></span>-VCZM) is incorporated within the Extended Finite Element Method (XFEM) to reproduce the process of void coalescence while overcoming the mesh objectivity issues of the numerical results during the softening regime. The Mode I (extension) and Mode II (shear) coalescence onset criteria and evolution laws are derived from micromechanical considerations. Subsequently, the yield surfaces and the integration algorithm necessary to determine the stress state within the coalescence band are established. Finally, the micromechanics-based <span><math><mi>μ</mi></math></span>-VCZM is applied within the XFEM-VCZM unified methodology. The numerical model, implemented as user element (UEL) into the computation code <span>Abaqus</span>, demonstrates efficacy in replicating the stages of ductile fracture, highlighting its potential for addressing complex finite strain three-dimensional boundary value problems. Notably, the results obtained with coarse meshes exhibit no mesh dependency below a specific mesh size, reproducing realistic Mode I and II fracture surfaces.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"202 ","pages":"Article 106176"},"PeriodicalIF":5.0,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144147118","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":"Multifidelity analysis of oxidation-driven fracture in ultra-high temperature ceramics","authors":"Daniel Pickard,&nbsp;Raul Radovitzky","doi":"10.1016/j.jmps.2025.106175","DOIUrl":"10.1016/j.jmps.2025.106175","url":null,"abstract":"<div><div>Ultra-High Temperature Ceramics (UHTCs) such as silicon carbide (SiC) typically oxidize in extreme environments, which can result in swelling deformations and internal stresses that cause fracture. In this paper, we present two approaches to computationally model this class of technical ceramic failures, and we apply them to SiC. First, a thermodynamically-consistent continuum theory of thermo-chemo-mechanics is specialized to describe thermally-activated oxidation-induced swelling in UHTCs. In transport-limited cases, the specialized model is shown to capture the molecular diffusion of oxidant through the reaction product layer using only fundamental transport properties, i.e. without the need for calibration to reaction experiments. Second, a phenomenological model is presented that can be calibrated to passive oxidation experiments or alternatively to the fundamental model. We use this second approach to analyze oxidation-induced swelling, delamination and fracture in SiC. We implement both models in a computational discontinuous Galerkin (DG) interfacial multiphysics framework, which enables the analysis of enhanced oxidation along fractured surfaces as well as oxidation-driven fracture. We conduct simulations that provide a full description of the progression of the delamination front. Among the important new insights obtained from the analyses, we infer a direct functional dependence between the temperature-dependent oxidant diffusivity and the delamination rate.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"202 ","pages":"Article 106175"},"PeriodicalIF":5.0,"publicationDate":"2025-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144147282","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":"Nonuniform crystallization of PEEK in fused filament fabrication and its influence on subsequent mechanical properties","authors":"Zhihong Han ,&nbsp;Yulin Xiong ,&nbsp;Kaijuan Chen ,&nbsp;Zeang Zhao ,&nbsp;Jinyou Xiao ,&nbsp;Lihua Wen ,&nbsp;Ming Lei ,&nbsp;Xiao Hou","doi":"10.1016/j.jmps.2025.106208","DOIUrl":"10.1016/j.jmps.2025.106208","url":null,"abstract":"<div><div>As a typical additive manufacturing process, fused filament fabrication (FFF) commonly utilizes a cooling fan to speed up cooling and solidification of thermoplastic melts, thereby preventing the melts from flowing and improving the manufacturing quality. However, the temperature gradient created by the cooling fan often induces nonuniform crystallization, and further affects the mechanical properties in subsequent service, particularly for the thermoplastics polyether ether ketone (PEEK) with a high processing temperature. Therefore, tracing the dynamic crystallization is the key issue to achieve an integrated simulation suitable for analyzing the material-process-property relationship, and ultimately to improve the manufacturing quality. In this study, we developed a continuous phase-evolution model, suitable in the process simulation of FFF manufacturing of PEEK. Compared with existing phase-evolution models, this developed model considers the potential plastic deformation of continuously formed crystals in subsequent service. Each newly formed crystal phase is modeled by one newly added elastic-plastic branch with an initial stress-free state. Therefore, both the initial configuration at the formation moment and its impacts on the subsequent plastic deformation can be traced. By introducing the effective phase concept, the continuous added phases are equivalent to one effective phase, significantly reducing the computational burden of dynamic crystallization in PEEK. Consequently, the developed model can be implemented into the user defined subroutine for the finite element analysis, and the FFF manufacturing can be modeled by the element activation technology according to the real manufacturing path. To validate the developed model, the FFF manufacturing of a quadrangular prism specimen and the subsequent nanoindentation tests were studied. Both the crystallinity evolution during manufacturing and the mechanical properties in subsequent nanoindentation tests, respectively, at the downwind side and at the upwind side can be well predicted, indicating that the developed method can be used to design the FFF manufacturing process of engineering components.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"202 ","pages":"Article 106208"},"PeriodicalIF":5.0,"publicationDate":"2025-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144147117","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":"Nonlinearity tunes crack dynamics in soft materials","authors":"Fucheng Tian ,&nbsp;Jian Ping Gong","doi":"10.1016/j.jmps.2025.106191","DOIUrl":"10.1016/j.jmps.2025.106191","url":null,"abstract":"<div><div>Cracks in soft materials exhibit diverse dynamic patterns, involving straight, oscillation, branching, and supershear fracture. Here, we successfully reproduce these crack morphologies in a two-dimensional pre-strained fracture scenario and establish crack stability phase diagrams for three distinct nonlinear materials using a fracture phase field model. The contrasting phase diagrams highlight the crucial role of nonlinearity in regulating crack dynamics. In strain-softening materials, crack branching prevails, limiting the cracks to sub-Rayleigh states. Yet strain-stiffening stabilizes crack propagation, allowing for the presence of supershear fracture. The intriguing crack oscillations are verified to be a universal instability closely tied to the local wave speed, as manifested by its onset speed scaling linearly with the characteristic shear wave speed. The wavelength of such instability is shown to be a bilinear function of the nonlinear scale and crack driving force, with a minimum length scale associated with the dissipative zone. Moreover, our findings suggest that the increase in local wave speed near the crack tip can account for the transition of cracks from sub-Rayleigh to supershear regimes in homogeneous materials.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"202 ","pages":"Article 106191"},"PeriodicalIF":5.0,"publicationDate":"2025-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144089429","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Finite element modeling of porous ductile solids with non-uniform void size distributions","authors":"Lars Edvard Blystad Dæhli,&nbsp;David Morin,&nbsp;Odd Sture Hopperstad","doi":"10.1016/j.jmps.2025.106177","DOIUrl":"10.1016/j.jmps.2025.106177","url":null,"abstract":"<div><div>In this study, we use micromechanics-based modeling to investigate the effect of a non-uniform void size distribution on the plastic flow and fracture behavior of porous ductile solids. We perform 2D plane strain finite element simulations of statistical volume elements containing between 3 × 3 and 22 × 22 uniformly-spaced voids of varying sizes, using two different modeling approaches: (i) resolving the voids spatially and (ii) using a porous plasticity model and spatially varying the initial porosity. For each sample size, thirty statistical volume elements are generated through random sampling from a log-normal void size distribution to quantify the variation for a given number of voids. The macroscopic behavior and microstructural evolution are analyzed under different imposed stress states. Our findings indicate that non-uniform void sizes have negligible effects on initial yielding and behavior before peak stress, but the strain at which maximum stress is attained varies. Beyond peak stress, there is a significant variation in the macroscopic stress–strain response and void growth between the statistical volume elements. Mean failure strain decreases and scatter diminishes as sample size increases, but even large samples retain scatter in failure strain. We achieve tremendous speed-up using models with porous plasticity while producing results comparable to models with spatially resolved voids. This suggests that a cost-effective modeling approach, where the voided subregions of the model are described using a porous plasticity model and spatially varying initial porosity, facilitates simulations of 3D volume elements with a statistically representative number of voids.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"202 ","pages":"Article 106177"},"PeriodicalIF":5.0,"publicationDate":"2025-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144170724","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 thermal-mechanical coupling-inspired inelastic constitutive law for the growth and atrophy of biological soft tissues","authors":"Jike Han ,&nbsp;Yuka Yokoyama ,&nbsp;Taiji Adachi ,&nbsp;Shinji Nishiwaki","doi":"10.1016/j.jmps.2025.106159","DOIUrl":"10.1016/j.jmps.2025.106159","url":null,"abstract":"<div><div>This study proposes a thermal-mechanical coupling-inspired inelastic constitutive law for the growth and atrophy (for the increase and decrease of volume and mass) of biological soft tissues. The thermal-mechanical coupling-inspired formulation realizes the multiphysics modeling between the mechanical field and a scalar field, say the nutrition field, that represents the transportations of the nutrition source inside of the body and the nutrition flux on the surface. Accordingly, biological soft tissues can exhibit growth and atrophy without any displacement or force loadings, which is analogous to thermal strain. On the other hand, the inelastic constitutive modeling decomposes the deformation gradient tensor into the elastic and growth components, and the evolution laws for the growth and atrophy are derived as the stationary conditions from the dissipation optimization problem, whose mathematical manipulation is the same as the standard elastoplastic material modeling. Thanks to the proposed formulation, several characteristic material responses that are seen in natural organisms are imitated. In particular, it is successfully realized that the growth and atrophy of biological soft tissues are not exclusively determined by the value of the mean stress, and can occur even under a constant compression/tension state. Also, when biological soft tissues are subjected to repeated growth and atrophy, the cellular aging-like material response occurs due to the accumulation of hardening variables, by which biological soft tissues become insensitive to external factors that encourage growth and atrophy. Two single-element level numerical examples are presented to demonstrate the basic material responses of the proposed formulation, and two structural numerical examples are prepared to show a few characteristic growth and atrophy trends that are determined by both states of the mechanical and nutrition fields.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"202 ","pages":"Article 106159"},"PeriodicalIF":5.0,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144072698","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":"Dynamic interplay of dendrite growth and cracking in lithium metal solid-state batteries","authors":"Dingchuan Xue ,&nbsp;Cole Fincher ,&nbsp;Ruyue Fang ,&nbsp;Brian W. Sheldon ,&nbsp;Long-Qing Chen ,&nbsp;Sulin Zhang","doi":"10.1016/j.jmps.2025.106197","DOIUrl":"10.1016/j.jmps.2025.106197","url":null,"abstract":"<div><div>All-solid-state batteries (ASSBs) represent a significant leap forward compared to conventional liquid-electrolyte based batteries, offering enhanced energy density, improved safety, extended cycle longevity, and reduced environmental footprint. However, the persistent challenge of uncontrollable dendrite growth within solid electrolytes (SEs) has posed substantial obstacles to the realization of Li metal ASSBs. This study develops a phase field model to unveil a dynamic interplay between Li dendrite growth and crack propagation in the polycrystalline Li₇La₃Zr₂O₁₂ (LLZO) solid electrolyte. Our modeling highlights distinct nucleation sites for Li electrodeposition, localized in proximity to the electrode/SE interface, a phenomenon sensitive to cell geometry. Li deposition initiates local stress accumulation that wedges the SE to cracking, and fracture induced stress relaxation facilitates further Li electrodeposition. Remarkably, a reciprocal relationship emerges between Li dendrite growth and crack propagation, each process reinforcing the other in an alternating manner. The dynamic interplay unveils a characteristic “wait-and-go” temporal sequence, where the progression of Li dendrites consistently trails behind the crack tip, aligning with the previous experimental observations. Drawing from the reciprocal dynamics, we identify practical stress-engineering strategies to mitigate catastrophic cell failure by simultaneously retarding Li dendrite growth and redirecting the crack propagation paths. Our findings offer electrochemo-mechanical insights in cell design and stress management, thereby opening a unique pathway towards the realization of safe and durable Li metal ASSBs.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"202 ","pages":"Article 106197"},"PeriodicalIF":5.0,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144137696","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}