Journal of The Mechanics and Physics of Solids最新文献

{"title":"ENNStressNet - An unsupervised equilibrium-based neural network for end-to-end stress mapping in elastoplastic solids","authors":"Lingfeng Li ,&nbsp;Shun Li ,&nbsp;Huajian Gao ,&nbsp;Chang Qing Chen","doi":"10.1016/j.jmps.2025.106117","DOIUrl":"10.1016/j.jmps.2025.106117","url":null,"abstract":"<div><div>Determining internal stress and strain fields in solid structures under external loads has been a central focus of continuum mechanics, playing a critical role in characterizing the mechanical behaviors and properties of both engineering and biological systems. With advancements in modern optical and electron microscopy techniques, strain fields can now be directly measured using sophisticated methods such as digital image correlation and digital volume correlation. However, direct measurement of stress fields remains limited to simple cases, such as photoelastic tests and standard uniaxial or shear tests. For elastoplastic solids, which exhibit complex irreversible and history-dependent deformations, stress fields are typically inferred through numerical calculations based on empirical constitutive models that are not always reliable or even available. Here, we introduce an unsupervised equilibrium-based neural network (ENN) that is trained using readily measurable strain fields and forces from a single specimen to directly predict the internal stress field. The ENN's structure aligns with the general framework of the incremental theory of elastoplasticity, without requiring prior knowledge of its detailed mathematical form. Once trained, the ENN, referred to as ENNStressNet, serves as an end-to-end stress mapper, enabling the direct determination of stress fields from measured strain fields in elastoplastic solids with arbitrary geometries and under various external loads. This approach thus bypasses the need for constitutive modeling and numerical simulations in conventional engineering analysis.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"200 ","pages":"Article 106117"},"PeriodicalIF":5.0,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143675595","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":"Convex neural networks learn generalized standard material models","authors":"Moritz Flaschel ,&nbsp;Paul Steinmann ,&nbsp;Laura De Lorenzis ,&nbsp;Ellen Kuhl","doi":"10.1016/j.jmps.2025.106103","DOIUrl":"10.1016/j.jmps.2025.106103","url":null,"abstract":"<div><div>We propose Generalized Standard Material Networks, a machine learning framework based on convex neural networks for learning the mechanical behavior of generalized standard materials. The theory of these materials postulates the existence of two thermodynamic potentials, the Helmholtz free energy density and the dissipation rate density potential, which alone determine the constitutive material response with guaranteed thermodynamic consistency. We parameterize the two potentials with two artificial neural networks and, due to a specifically designed network architecture, we satisfy by construction all the needed properties of the two potentials. Using automatic differentiation, an implicit time integration scheme and the Newton-Raphson method, we can thus describe a multitude of different material behaviors within a single unified overarching framework, including elastic, viscoelastic, plastic, and viscoplastic material responses with hardening. By probing our framework on the synthetic data generated by five benchmark material models, we demonstrate satisfactory prediction accuracy to unseen data and a high robustness to noise. In this context, we observe a non-uniqueness of thermodynamic potentials and discuss how this affects the results of the training process. Finally, we show that a carefully chosen number of internal variables strikes a balance between fitting accuracy and model complexity.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"200 ","pages":"Article 106103"},"PeriodicalIF":5.0,"publicationDate":"2025-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143611337","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Ultra-fast physics-based modeling of the elephant trunk","authors":"Bartosz Kaczmarski ,&nbsp;Derek E. Moulton ,&nbsp;Zéphyr Goriely ,&nbsp;Alain Goriely ,&nbsp;Ellen Kuhl","doi":"10.1016/j.jmps.2025.106102","DOIUrl":"10.1016/j.jmps.2025.106102","url":null,"abstract":"<div><div>With more than 90,000 muscle fascicles, the elephant trunk is a complex biological structure and the largest known muscular hydrostat. It achieves unprecedented control through intricately orchestrated contractions of a wide variety of muscle architectures. Fascinated by the elephant trunk’s unique performance, scientists of all disciplines are studying its anatomy, function, and mechanics, and use it as an inspiration for biomimetic soft robots. Yet, to date, there is no precise mapping between microstructural muscular activity and macrostructural trunk motion, and our understanding of the elephant trunk remains incomplete. Specifically, no model of the elephant trunk employs formal physics-based arguments that account for its complex muscular architecture, while preserving low computational cost to enable fast screening of its configuration space. Here we create a reduced-order model of the elephant trunk that can – within a fraction of a second – predict the trunk’s motion as a result of its muscular activity. To ensure reliable results in the finite deformation regime, we integrate first principles of continuum mechanics and the theory of morphoelasticity for fibrillar activation. We employ dimensional reduction to represent the trunk as an active slender structure, which results in closed-form expressions for its curvatures and extension as functions of muscle activation and anatomy. We create a high-resolution digital representation of the trunk from magnetic resonance images to quantify the effects of different muscle groups. We propose a general solution method for the inverse motion problem and apply it to extract the muscular activations in three representative trunk motions: picking a fruit; lifting a log; and lifting a log asymmetrically. For each task, we identify key features in the muscle activation profiles. Our results suggest that the elephant trunk either autonomously reorganizes muscle activation upon reaching the maximum contraction or chooses the inverse problem branches that avoid reaching the contraction constraints throughout the motion. Our study provides a complete quantitative characterization of the fundamental science behind elephant trunk biomechanics, with potential applications in the material science of flexible structures, the design of soft robots, and the creation of flexible prosthesis and assist devices.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"200 ","pages":"Article 106102"},"PeriodicalIF":5.0,"publicationDate":"2025-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143628913","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Theoretical modeling of phase boundary mediated extra tensile strength and plasticity in high entropy alloys","authors":"Zhenghao Zhang,&nbsp;Yao Tang,&nbsp;Qingkun Zhao,&nbsp;Qishan Huang,&nbsp;Haofei Zhou","doi":"10.1016/j.jmps.2025.106106","DOIUrl":"10.1016/j.jmps.2025.106106","url":null,"abstract":"<div><div>High-entropy alloys (HEAs) have garnered increasing attention for their remarkable mechanical properties. However, due to the highly complex deformation mechanisms of HEAs, the current understanding of the underlying strengthening mechanisms is not yet fully developed, thereby limiting further microstructure optimization and processing. In this study, we have focused on the mechanics and theoretical modeling of Al_0.7CoCrFeNi eutectic HEAs processed by high pressure high temperature (HPHT) treatment. Our experimental results show the HPHT treatment can lead to the formation of hexagonal-like dual-phase microstructures and coherent phase boundaries with approximately doubled tensile strength and ductility. The deformation process of HPHT-treated HEAs encompasses multiple strengthening effects, including dislocation-based Taylor hardening (resulting from both statistically stored dislocations and geometrically necessary dislocations), Hall-Petch hardening, back-stress strengthening, and twinning effect. To comprehensively understand the origins of enhanced strength and ductility in HPHT-treated HEAs, we have established a constitutive theoretical model considering the multiple deformation mechanisms in the HEA samples, especially those mediated by phase boundaries, followed by crystal plasticity finite element simulations of their contributions to the mechanical properties. To ensure compatibility at large deformation, we have also proposed an algorithm for the calculation of geometrically necessary dislocations within reduced integration elements. The simulation results reveal that the enhanced coherence of phase boundaries induced by HPHT treatment is key to the activation of Taylor hardening, back-stress strengthening, and deformation twinning in the face-centered cubic (FCC) phase. Besides, due to the effective suppression of localized interface cracking, the plastic deformability of B2 phases is also enhanced, thus enabling the synergy of strength and ductility in the dual-phase system. These findings promote the understanding of strengthening mechanisms in HPHT-treated eutectic HEAs. More importantly, the constitutive model provided in this study can help theoretical investigation and quantitative analysis of metallic materials with notable interfacial effects on deformation mechanisms and mechanical properties.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"200 ","pages":"Article 106106"},"PeriodicalIF":5.0,"publicationDate":"2025-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143629066","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 continuum, computational study of morphogenesis in lithium intermetallic interfaces in solid state batteries","authors":"Mostafa Faghih Shojaei,&nbsp;Rahul Gulati,&nbsp;Krishna Garikipati","doi":"10.1016/j.jmps.2025.106073","DOIUrl":"10.1016/j.jmps.2025.106073","url":null,"abstract":"<div><div>The design of solid state batteries with lithium anodes is attracting attention for the prospect of high capacity and improved safety over liquid electrolyte systems. The nature of transport with lithium as the current carrier has as a consequence the accretion or stripping away of the anode with every charge–discharge cycle. While this poses challenges from the growth of protrusions (dendrites) to loss of contact, there lurks an opportunity: Morphogenesis at the anode–electrolyte interface layer can be studied, and may ultimately be controlled as a factor in solid state battery design. The accessible interface morphologies, the dynamic paths to them, and mechanisms to control them expand considerably if lithium alloys are introduced in the anode. The thermodynamics and kinetics of lithium intermetallics present principled approaches for morphogenic interface design. In this communication we adopt a computational approach to such an exploration. With phase field models that are parameterized by a combination of first principles atomistic calculations and experiments, we present phenomenological studies of two lithium intermetallics: Li–Mg and Li–Zn. An array of parametric investigations follows on the influence of kinetics, charge–discharge rate, cycling, transport mechanisms and grain structure. The emphasis across these computations is on the dynamic morphogenesis of the intermetallic interface. Specifically, the plating, segregation and smooth distribution of Li, Mg and Zn, the growth and disappearance of voids, evolution of solid electrolyte–anode contact area, and grain boundary structure are investigated. The computational platform is a framework for future studies of morphogenic electrolyte–anode interfaces with more extensive inputs from first principles atomistics and experiments.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"200 ","pages":"Article 106073"},"PeriodicalIF":5.0,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143593467","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 strain gradient phase field model for heterogeneous materials based on two-scale asymptotic homogenization","authors":"Heliang You ,&nbsp;Meizhen Xiang ,&nbsp;Yuhang Jing ,&nbsp;Licheng Guo ,&nbsp;Zhiqiang Yang","doi":"10.1016/j.jmps.2025.106104","DOIUrl":"10.1016/j.jmps.2025.106104","url":null,"abstract":"<div><div>Due to the inherent microstructural heterogeneity of heterogeneous materials, their macroscopic fracture behavior differs significantly from that of homogeneous materials, exhibiting phenomena such as anisotropic fracture energy and strain gradient effects. To investigate the effect of microstructure on macroscopic fracture behavior, this study proposes a novel multiscale phase field model. Based on the theory of two-scale asymptotic expansion, the model constructs an equivalent multi-field coupled boundary value framework, which includes both a strain gradient elasticity submodel and a homogenized phase field submodel. Through rigorous mathematical derivation, homogenized tensors that characterize the elastic constitutive relations and fracture properties are obtained without relying on any additional assumptions. Moreover, to distinguish the contributions of load components to crack propagation, energy decomposition strategies based on orthogonal projection are introduced for stress and higher-order stress. Compared to full-scale simulations, the proposed model significantly reduces computational cost while maintaining accuracy. Numerical simulations show that the model accurately captures the influence on crack propagation direction induced by microstructure. Additionally, the model effectively demonstrates the hindering effect of strain gradients on crack propagation, offering new insights into the size effect in the fracture of heterogeneous materials. This work provides a new framework for studying the multiscale fracture behavior of heterogeneous materials.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"200 ","pages":"Article 106104"},"PeriodicalIF":5.0,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143593468","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 magneto-mechanical growth in hyperelastic materials: Surface patterns modulation and shape control in bio-inspired structures","authors":"Zhanfeng Li ,&nbsp;Yafei Wang ,&nbsp;Zuodong Wang ,&nbsp;Chennakesava Kadapa ,&nbsp;Mokarram Hossain ,&nbsp;Xiaohu Yao ,&nbsp;Jiong Wang","doi":"10.1016/j.jmps.2025.106089","DOIUrl":"10.1016/j.jmps.2025.106089","url":null,"abstract":"<div><div>Magneto-mechanical coupling in the growth of soft materials presents challenges due to the complex interactions between magnetic fields, mechanical forces, and growth-induced deformations. While growth modeling has been extensively studied, integrating magnetic stimuli into growth processes remains underexplored. In this work, we develop a 3D governing system for capturing the coupled magneto-mechanical growth behaviors of soft materials. Based on the governing system, we propose a finite element framework, where the robustness and accuracy of the proposed framework are demonstrated through numerical simulations, including the uniaxial loading of a circular tube, a mesh convergence study, and surface pattern evolution. We also conduct experiments on surface pattern modulation in magneto-active soft materials. Specifically, we fabricate film–substrate samples and apply growth-induced instabilities combined with external magnetic fields to generate tunable surface patterns. To demonstrate the capabilities of our method, we apply our numerical framework to mimic the biological morphogenesis, such as the inversion process of the algal genus <em>Volvox</em>. Our study shows that integrating magneto-mechanical coupling with growth effects allows for flexible control over surface patterns, significantly enhancing the adaptability and responsiveness of soft materials. This work paves the way for innovative designs of adaptive and programmable soft materials, with potential applications in soft robotics, biomimetic structures, and tissue engineering.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"200 ","pages":"Article 106089"},"PeriodicalIF":5.0,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143551409","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":"Thermo-chemo-mechanical model and variational multiscale framework for material and geometric evolution in frontal polymerization","authors":"Ignasius P.A. Wijaya ,&nbsp;Philippe Geubelle ,&nbsp;Arif Masud","doi":"10.1016/j.jmps.2025.106078","DOIUrl":"10.1016/j.jmps.2025.106078","url":null,"abstract":"<div><div>This paper presents a thermodynamically consistent model for thermo-chemo-mechanical processes in frontal polymerization (FP). The model consists of cure kinetics, heat transfer, and finite strain kinematics of nonlinear inelastic solid undergoing finite deformation. The constitutive relations are derived by enforcing non-negative entropy production which implies the existence of cure induced inelastic processes during material property evolution. Rapid curing triggered by thermo-chemical processes results in traveling reaction fronts that traverse the domain, and material properties evolve across these fronts on short time scales, accompanied with chemical expansion/contraction of the constituents. Complexity of the process increases with increased rate of chemical reaction, increased rate of mass transport, and large mechanical deformations. Evolving nonlinearities and coupled thermo-chemo-mechanical effects give rise to spatially localized phenomena that exhibit shear bands, steep gradients, and boundary and/or internal layers. The presence of interfacial effects can also trigger jumps in the fields, leading to further classification as mathematically non-smooth mixed-field problems. These modeling issues require mathematical formulations that can handle rapidly evolving material nonlinearity as well as steep traveling gradients. A stabilized finite element method that is based on the Variational Multiscale (VMS) framework is employed. A unique attribute of the VMS framework is the derivation of the residual-based fine-scale models that represent subgrid scale physics. These models enhance the stability of the numerical method as well as the accuracy of the computed physics. Several test cases are presented that investigate the mathematical attributes of the constitutive model for FP, and the role of enhanced stability and higher spatial accuracy of the proposed stabilized method in free-form printing with evolving polymerization front.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"200 ","pages":"Article 106078"},"PeriodicalIF":5.0,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143562685","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":"Strength and stiffness of network materials with preferentially oriented fibers","authors":"S.N. Amjad,&nbsp;R.C. Picu","doi":"10.1016/j.jmps.2025.106101","DOIUrl":"10.1016/j.jmps.2025.106101","url":null,"abstract":"<div><div>Materials made from fibers, referred to here as Network materials, are ubiquitous in biology and engineering. In most practical situations, fibers have preferential orientation in one spatial direction or in a plane. Here we use discrete network models to derive the relationship between the stiffness and strength of networks with pre-aligned fibers and network parameters, including the degree of alignment. Both stiffness and strength can be represented by the product of two functions, one accounting for the effect of alignment and the other representing the effect of network parameters, such as the network density and fiber properties. Failure under multiaxial loading is also considered and it is concluded that failure surfaces in stress space can be collapsed by normalizing the axes with the respective (pre-alignment-dependent) uniaxial strength. This generalizes the structure-properties relation established based on uniaxial tests to the multiaxial case. The inferred scaling laws are compared with a collection of experimental data from the literature obtained with diverse network materials.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"200 ","pages":"Article 106101"},"PeriodicalIF":5.0,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143580781","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":"Multiple scales homogenisation of a porous viscoelastic material with rigid inclusions: Application to lithium-ion battery electrodes","authors":"J.M. Foster ,&nbsp;A.F. Galvis ,&nbsp;B. Protas ,&nbsp;S.J. Chapman","doi":"10.1016/j.jmps.2025.106072","DOIUrl":"10.1016/j.jmps.2025.106072","url":null,"abstract":"<div><div>This paper explores the mechanical behaviour of the composite materials used in modern lithium-ion battery electrodes. These contain relatively high modulus active particle inclusions within a two-component matrix of liquid electrolyte which penetrates the pore space within a viscoelastic polymer binder. Deformations are driven by a combination of (i) swelling/contraction of the electrode particles in response to lithium insertion/extraction, (ii) swelling of the binder as it absorbs electrolyte, (iii) external loading and (iv) flow of the electrolyte within the pores. We derive the macroscale response of the composite using systematic multiple scales homogenisation by exploiting the disparity in lengthscales associated with the size of an electrode particle and the electrode as a whole. The resulting effective model accurately replicates the behaviour of the original model (as is demonstrated by a series of relevant case studies) but, crucially, is markedly simpler and hence cheaper to solve. This has significant practical value because it facilitates low-cost, realistic computations of the mechanical states of battery electrodes, thereby allowing model-assisted development of battery designs that are better able to withstand the mechanical abuse encountered in practice and ultimately paving the way for longer-lasting batteries.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"199 ","pages":"Article 106072"},"PeriodicalIF":5.0,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143548387","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}