Journal of The Mechanics and Physics of Solids最新文献

{"title":"Grain-size dependence of plastic-brittle transgranular fracture","authors":"Jean-Michel Scherer ,&nbsp;Mythreyi Ramesh ,&nbsp;Blaise Bourdin ,&nbsp;Kaushik Bhattacharya","doi":"10.1016/j.jmps.2025.106116","DOIUrl":"10.1016/j.jmps.2025.106116","url":null,"abstract":"<div><div>The role of grain size in determining fracture toughness in metals is incompletely understood with apparently contradictory experimental observations. We study this grain-size dependence computationally by building a model that combines the phase-field formulation of fracture mechanics with dislocation density-based crystal plasticity. We apply the model to cleavage fracture of body-centered cubic materials in plane strain conditions, and find non-monotonic grain-size dependence of plastic-brittle transgranular fracture. We find two mechanisms at play. The first is the nucleation of failure due to cross-slip in critically located grains within transgranular band of localized deformation, and this follows the classical Hall–Petch law that predicts a higher failure stress for smaller grains. The second is the resistance to the propagation of a mode I crack, where grain boundaries can potentially pin a crack, and this follows an inverse Hall–Petch law with higher toughness for larger grains. The result of the competition between the two mechanisms gives rise to non-monotonic behavior and reconciles the apparently contradictory experimental observations.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"200 ","pages":"Article 106116"},"PeriodicalIF":5.0,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143725422","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":"Interlayer Shear Behaviors of Bilayer Graphene with A Moiré Pattern","authors":"Qiancheng Ren ,&nbsp;Jinglan Liu ,&nbsp;Qi Yang ,&nbsp;Pei Zhao","doi":"10.1016/j.jmps.2025.106123","DOIUrl":"10.1016/j.jmps.2025.106123","url":null,"abstract":"<div><div>The mechanical behavior of van der Waals (vdW) interfaces under shear is important for micro-nano mechanics. However, due to the diverse structures of vdW interfaces, there is still a lack of systematic and quantitative research. Here we focus on the simplest vdW interface formed by flat carbon rings, construct twisted bilayer graphene (tBLG) with different moiré patterns through the twist angle design between lattices, and analyze the interfacial behavior under shear from three aspects of experiment, theory, and molecular dynamics simulations. The interfacial shear strength and stiffness for tBLG with different twist angles are obtained, and more results reveal that although the change in twist angle has little effect on the average interlayer distance, the interlayer interaction changed significantly, and with the evolution of the moiré pattern the interlayer damage is still strongly related to the dislocations. This study provides important insights into understanding the interlayer mechanical behavior of vdW interfaces and low-dimensional layered materials.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"200 ","pages":"Article 106123"},"PeriodicalIF":5.0,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143687075","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":"Distinguish the calibration of conventional and data-driven constitutive model: the role of state boundary surfaces","authors":"Zhihui Wang,&nbsp;Roberto Cudmani,&nbsp;Andrés Alfonso Peña Olarte","doi":"10.1016/j.jmps.2025.106122","DOIUrl":"10.1016/j.jmps.2025.106122","url":null,"abstract":"<div><div>In conventional constitutive models for granular materials, calibration involves estimating a few parameters within known mathematical expressions. In contrast, data-driven constitutive models couple the model structure and parameters. Addressing this fundamental difference, the development of constitutive models based on Physics-encoded Neural Networks (PeNN) is guided from the perspective of conventional model development, highlighting similarities and differences. The crucial physical information that influences PeNN is explained, and the incorporation of three key state boundary surfaces in pressure–porosity space—critical state, loosest state, and densest state—via physics-informed deep learning is detailed. Physics-informed calibration is performed using the augmented Lagrangian method; then, the calibrated models undergo extensive drained and undrained simulations. Results indicate that using only physical information from state boundary surfaces, without data within these boundaries, fails to calibrate data-driven models; thus, boundary surface information represents partial physical information. While combining partial physical information with reasonably distributed data can improve model development under limited experimental data, adding more partial physical information and data does not necessarily enhance the results. The finding aims to bridge the gap between conventional and data-driven constitutive models, hopefully increasing the reliability and interpretability of data-driven models.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"200 ","pages":"Article 106122"},"PeriodicalIF":5.0,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143792827","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":"Modeling the crack propagation of ductile fibril reinforced polymer membrane with the consideration of drawing fibrils","authors":"Xiangyang Zhou,&nbsp;Diankai Qiu,&nbsp;Zhutian Xu,&nbsp;Linfa Peng","doi":"10.1016/j.jmps.2025.106118","DOIUrl":"10.1016/j.jmps.2025.106118","url":null,"abstract":"<div><div>Microfibril reinforced polymer composites (MFCs) are polymer-polymer composites with ductile fibrils embedded, usually increasing the tenacity of the polymer matrix. One of the successful applications is the expanded polytetrafluoroethylene (ePTFE) reinforced perfluorinated sulfonic acid (PFSA) membrane, in which the embedded ePTFE fibrils evolve into drawing fibril connecting crack surfaces, significantly increasing the fracture toughness of the membrane. Among the fracture modeling techniques, the virtual crack closure technique (VCCT) provides a thermodynamics-consistent explanation of crack propagation of the material, while the effect of drawing fibrils in the case is hard to be considered. The cohesive zone model (CZM) considers the gradual damage progress of the material at the crack tip through the traction-separation law, which is suitable for describing the evolution of drawing fibrils but the applicability of the empirical traction-separation laws to drawing fibrils remains uncertain. This paper establishes the constitutive and fracture models of the ePTFE reinforced PFSA membrane, and numerically realizes the fracture propagation of the microfibril reinforced material through the user subroutine of ABAQUS. For the constitutive modeling, an extended eight-chain model with the consideration of the fibril orientation is established to describe the deformation resistance of the fibril reinforcement. For the fracture modeling, a fracture criterion with the consideration of the negative work of the drawing fibrils at the crack tip is established, and numerically implemented through the extended VCCT. Uniaxial tensile tests and fracture tests of pure and various composite membranes are conducted, which verified the accuracy of the present model in describing the higher mechanical property and fracture tenacity of the composite materials. The model reveals the enhancement mechanism of the ductile fibril network and providing a new perspective of fracture modeling for ductile fibril reinforced polymer membranes.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"200 ","pages":"Article 106118"},"PeriodicalIF":5.0,"publicationDate":"2025-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143675642","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 nonlinear model of shearable elastic rod from an origami-like microstructure displaying folding and faulting","authors":"M. Paradiso,&nbsp;F. Dal Corso,&nbsp;D. Bigoni","doi":"10.1016/j.jmps.2025.106100","DOIUrl":"10.1016/j.jmps.2025.106100","url":null,"abstract":"<div><div>A new continuous model of <em>shearable</em> rod, subject to large elastic deformation, is derived from nonlinear homogenization of a one-dimensional periodic microstructured chain. As particular cases, the governing equations reduce to the Euler elastica and to the shearable elastica known as ‘Engesser’, that has been scarcely analysed so far. The microstructure that is homogenized is made up of elastic hinges and four-bar linkages, which may be realized in practice using origami joints. The equivalent continuous rod is governed by a Differential–Algebraic system of nonlinear Equations (DAE), containing an internal length ratio, and showing a surprisingly rich mechanical landscape, which involves a twin sequence of bifurcation loads, separated by a ‘transition’ mode. The latter occurs, for simply supported and cantilever rods in a ‘bookshelf-like’ mode and in a mode involving faulting (formation of a step in displacement), respectively. The postcritical response of the simply supported rod exhibits the emergence of folding, an infinite curvature occurring at a point of the rod axis, developing into a curvature jump at increasing load. Faulting and folding, excluded for both Euler and Reissner models and so far unknown in the rod theory, represent ‘signatures’ revealing the origami design of the microstructure. These two features are shown to be associated with bifurcations and, in particular folding, with a secondary bifurcation of the corresponding discrete chain when the number of elements is odd. Beside the intrinsic theoretical relevance to the field of structural mechanics, our results can be applied to various technological contexts involving highly compliant mechanisms, such as the achievement of objective trajectories with soft robot arms through folding and localized displacement of origami-inspired or multi-material mechanisms.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"200 ","pages":"Article 106100"},"PeriodicalIF":5.0,"publicationDate":"2025-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143675592","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":"A multiscale-multiphysics framework for modeling organ-scale liver regrowth","authors":"Adnan Ebrahem,&nbsp;Jannes Hohl,&nbsp;Etienne Jessen,&nbsp;Marco F.P. ten Eikelder,&nbsp;Dominik Schillinger","doi":"10.1016/j.jmps.2025.106113","DOIUrl":"10.1016/j.jmps.2025.106113","url":null,"abstract":"<div><div>We present a framework for modeling liver regrowth on the organ scale that is based on three components: (1) a multiscale perfusion model that combines synthetic vascular tree generation with a multi-compartment homogenized flow model, including a homogenization procedure to obtain effective parameters; (2) a poroelastic finite growth model that acts on all compartments and the synthetic vascular tree structure; (3) an evolution equation for the local volumetric growth factor, driven by the homogenized flow rate into the microcirculation as a measure of local hyperperfusion and well-suited for calibration with available data. We apply our modeling framework to a prototypical benchmark and a full-scale patient-specific liver, for which we assume a common surgical cut. Our simulation results demonstrate that our model represents hyperperfusion as a consequence of partial resection and accounts for its reduction towards a homeostatic perfusion state, exhibiting overall regrowth dynamics that correspond well with clinical observations. In addition, our results show that our model also captures local hypoperfusion in the vicinity of orphan vessels, a key requirement for the prediction of ischemia or the preoperative identification of suitable cut patterns.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"200 ","pages":"Article 106113"},"PeriodicalIF":5.0,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143644334","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":"Minimizing finite viscosity enhances relative kinetic energy absorption in bistable mechanical metamaterials but only with sufficiently fine discretization: A nonlinear dynamical size effect","authors":"Haning Xiu ,&nbsp;Ryan Fancher ,&nbsp;Ian Frankel ,&nbsp;Patrick Ziemke ,&nbsp;Müge Fermen-Coker ,&nbsp;Matthew Begley ,&nbsp;Nicholas Boechler","doi":"10.1016/j.jmps.2025.106105","DOIUrl":"10.1016/j.jmps.2025.106105","url":null,"abstract":"<div><div>Bistable mechanical metamaterials have shown promise for mitigating the harmful consequences of impact by converting kinetic energy into stored strain energy, offering an alternative and potentially synergistic approach to conventional methods of attenuating energy transmission. In this work, we numerically study the dynamic response of a one-dimensional bistable metamaterial struck by a high speed impactor where the impactor velocity is commensurate with the sound speed, using the peak kinetic energy experienced at midpoint of the metamaterial compared to that in an otherwise identical linear system as our performance metric. We make five key findings: (1) The bistable material can counter-intuitively perform better (to nearly <span><math><mrow><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mn>3</mn></mrow></msup><mo>×</mo></mrow></math></span> better than the linear system) as the viscosity <em>decreases</em> but remains finite, however this only occurs when sufficiently fine discretization has been reached (<em>i.e.</em> the system approaches sufficiently close to the continuum limit); (2) This discretization threshold is sharp, and depends on the viscosity present; (3) The bistable materials can also perform significantly worse than linear systems (for low discretization and viscosity or zero viscosity); (4) The dependence on discretization stems from the partition of energy into trains of solitary waves that have pulse lengths proportional to the unit cell size, where, with intersite viscosity, the solitary wave trains induce high velocity gradients and thus enhanced damping compared to linear, and low-unit-cell-number bistable, materials; and (5) When sufficiently fine discretization has been reached at low viscosities, the bistable system consistently outperforms the linear one for a wide range of impactor conditions, without impact condition regions of underperformance. The first point is particularly important, as it shows the existence of a nonlinear dynamical “size effect”, where, given a protective layer of some thickness and otherwise identical quasi-static mechanical properties and total mass, <em>e.g.</em>, a <span><math><mrow><mn>1</mn><mspace></mspace><mi>mm</mi></mrow></math></span> thick layer having 200 unit cells of 5 <span><math><mrow><mi>μ</mi><mi>m</mi></mrow></math></span> thickness is predicted to perform significantly better than one having 20 unit cells of 50 <span><math><mrow><mi>μ</mi><mi>m</mi></mrow></math></span> thickness. The complex dynamics revealed herein could help guide the future design and application of bistable, and perhaps more generally nonlinear, metamaterials in various domains including signal processing, shape changing devices, and shock and impact protection, with particular benefits in the latter case predicted for scenarios where constituent materials with low intrinsic viscosity are needed (<em>e.g.</em>, wherein metals or ceramics would be used).</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"200 ","pages":"Article 106105"},"PeriodicalIF":5.0,"publicationDate":"2025-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143675593","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":"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}