Journal of The Mechanics and Physics of Solids最新文献

{"title":"Characterizing hydrogel behavior under compression with gel-freezing osmometry","authors":"Yanxia Feng ,&nbsp;Dominic Gerber ,&nbsp;Stefanie Heyden ,&nbsp;Martin Kröger ,&nbsp;Eric R. Dufresne ,&nbsp;Lucio Isa ,&nbsp;Robert W. Style","doi":"10.1016/j.jmps.2025.106166","DOIUrl":"10.1016/j.jmps.2025.106166","url":null,"abstract":"<div><div>Hydrogels are particularly versatile materials that are widely found in both Nature and industry. One key reason for this versatility is their high water content, which lets them dramatically change their volume and many of their mechanical properties – often by orders of magnitude – as they swell and dry out. Currently, we lack techniques that can precisely characterize how these properties change with water content. To overcome this challenge, here we develop Gel-Freezing Osmometry (GelFrO): an extension of freezing-point osmometry. We show how GelFrO can measure a hydrogel’s mechanical response to compression and shrinkage in response to an applied osmotic pressure, while only using small, <span><math><mi>O</mi></math></span> (<span><math><mrow><mn>100</mn><mspace></mspace><mi>μ</mi></mrow></math></span>L) samples. Because the technique allows measurement of properties over an unusually wide range of water contents, it allows us to accurately test theoretical predictions. We find simple, power-law behavior for both mechanical and osmotic responses, while these are not well-captured by classical Flory–Huggins theory. We interpret this power-law behavior as a hallmark of a microscopic fractal structure of the gel’s polymer network, and propose a simple way to connect the gel’s fractal dimension to its mechanical and osmotic properties. This connection is supported by observations of hydrogel microstructures using small-angle X-ray scattering. Finally, our results motivate simplifications to common models for hydrogel mechanics, and we propose an updated hydrogel constitutive model.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"201 ","pages":"Article 106166"},"PeriodicalIF":5.0,"publicationDate":"2025-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143918234","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":"Universal pull-off force for separating a rigid sphere from a membrane","authors":"Wanying Zheng,&nbsp;Zhaohe Dai","doi":"10.1016/j.jmps.2025.106163","DOIUrl":"10.1016/j.jmps.2025.106163","url":null,"abstract":"<div><div>A pull-off force <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>c</mi></mrow></msub></math></span> is required to separate two objects in adhesive contact. For a rigid sphere on an elastic slab, the classic Johnson–Kendall–Roberts (JKR) theory predicts <span><math><mrow><msub><mrow><mi>F</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>=</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mi>π</mi><mi>γ</mi><msub><mrow><mi>R</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow></math></span>, where <span><math><mi>γ</mi></math></span> represents the interface adhesion or toughness and <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>s</mi></mrow></msub></math></span> is the radius of the sphere. Here, we investigate an alternative, extreme scenario: the pull-off force required to detach a rigid, frictionless sphere from a thin membrane, a scenario observed in a wide range of nature and engineering systems, such as nanoparticles on cell membranes, atomic force microscopy probes on atomically thin 2D material sheets, and electronic devices on flexible films. We show that, within the JKR framework, the pull-off forces in axisymmetric soap films, linearly elastic membranes, and nonlinear hyperelastic membranes are all given by <span><math><mrow><msub><mrow><mi>F</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>=</mo><mi>π</mi><mi>γ</mi><msub><mrow><mi>R</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow></math></span>. This result is remarkable as it indicates that the pull-off force for membranes is independent of the material’s constitutive law, size, pretension, and solid surface tension.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"201 ","pages":"Article 106163"},"PeriodicalIF":5.0,"publicationDate":"2025-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143904248","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":"Thermal fluctuations effects on crack nucleation and propagation","authors":"Claudia Binetti ,&nbsp;Giuseppe Florio ,&nbsp;Nicola M. Pugno ,&nbsp;Stefano Giordano ,&nbsp;Giuseppe Puglisi","doi":"10.1016/j.jmps.2025.106157","DOIUrl":"10.1016/j.jmps.2025.106157","url":null,"abstract":"<div><div>This paper investigates the impact of thermal effects on fracture propagation, a subject that poses significant theoretical and experimental challenges across multiple scales. While previous experimental and numerical studies have explored the relationship between temperature fluctuations and mechanical behavior, a comprehensive theoretical framework in fracture mechanics that rigorously incorporates temperature effects is still absent. Building upon the Griffith energetic approach and equilibrium statistical mechanics, we incorporate entropic effects into the overall energy balance of the system and replace the total mechanical energy with free energies. Indeed, our model captures the energetic interplay between elastic deformation, external loads, fracture energy, and entropic contributions. We propose a simplified approach in which both discrete and continuum representations are formulated concurrently, reflecting a multiscale paradigm. The discrete model leverages statistical mechanics to account for temperature effects, while the continuum model provides a mesoscopic description of the fracture process. This framework provides (temperature dependent) analytical expressions for key mechanical parameters, such as the stress and displacement fracture thresholds, the energy release rate, the fracture surface energy, and the J-integral. Notably, we identify a critical temperature at which the system undergoes a phase transition from an intact to a fractured state in the absence of mechanical loading. We believe that this approach lays the foundation for a new theoretical framework, enabling a rigorous multiscale understanding of thermal fluctuations in fracture mechanics. We finally propose a comparison with numerical data concerning the fracture of graphene as a function of temperature exhibiting the efficiency of the model in describing thermal effects in fracture behavior.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"201 ","pages":"Article 106157"},"PeriodicalIF":5.0,"publicationDate":"2025-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143948477","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":"Microstructure-based machine learning of damage models including anisotropy, irreversibility and evolution","authors":"Julien Yvonnet,&nbsp;Qi-Chang He","doi":"10.1016/j.jmps.2025.106160","DOIUrl":"10.1016/j.jmps.2025.106160","url":null,"abstract":"<div><div>A homogenization framework for materials incorporating evolving cracks is proposed, with machine learning to discover the evolution laws of the internal variables describing the homogenized anisotropic damage. The damage model is constructed using data-driven harmonic analysis of damage (DDHAD). First, simulations on Representative Volume Elements (RVEs) with local crack initiation and propagation are performed along different loading trajectories. The elastic tensor is homogenized for each loading increment and step, and recorded as data. Macroscopic internal variables defining arbitrary anisotropic damage are extracted by calculating orientation-dependent damage functions and expanding them into spherical harmonics, the independent coefficients of which are used as macroscopic internal variables. A reduction step is performed to minimize the number of internal variables using Proper Orthogonal Decomposition. A simple Feed-Forward neural network is used to discover the evolution laws of these internal variables, and an algorithm is proposed to manage loading/unloading scenarios. The technique is applied to different RVEs so as to construct anisotropic damage models, including initial and induced anisotropy, progressive and compressive damage.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"200 ","pages":"Article 106160"},"PeriodicalIF":5.0,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143891970","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 finite strain model for fiber angle plasticity of textile fabrics based on isogeometric shell finite elements","authors":"Thang X. Duong ,&nbsp;Roger A. Sauer","doi":"10.1016/j.jmps.2025.106158","DOIUrl":"10.1016/j.jmps.2025.106158","url":null,"abstract":"<div><div>This work presents a shear elastoplasticity model for textile fabrics within the theoretical framework of anisotropic Kirchhoff–Love shells with bending of embedded fibers proposed by Duong et al. (2023). The plasticity model aims at capturing the rotational inter-ply frictional sliding between fiber families in textile composites undergoing large deformation. Such effects are usually dominant in dry textile fabrics such as woven and non-crimp fabrics. The model explicitly uses relative angles between fiber families as strain measures for the kinematics. The plasticity model is formulated directly with surface invariants without resorting to thickness integration. Motivated by experimental observations from the picture frame test, a yield function is proposed with isotropic hardening and a simple evolution equation. A classical return mapping algorithm is employed to solve the elastoplastic problem within the isogeometric finite shell element formulation of Duong et al. (2022). The verification of the implementation is facilitated by the analytical solution for the picture frame test. The proposed plasticity model is calibrated from the picture frame test and is then validated by the bias extension test, considering available experimental data for different samples from the literature. Good agreement between model prediction and experimental data is obtained. Finally, the applicability of the elastoplasticity model to 3D shell problems is demonstrated.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"200 ","pages":"Article 106158"},"PeriodicalIF":5.0,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143902538","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":"Micromechanics-inspired granular thermodynamics: A constitutive model for multidirectional cyclic shearing","authors":"Zhichao Zhang ,&nbsp;Kenichi Soga","doi":"10.1016/j.jmps.2025.106170","DOIUrl":"10.1016/j.jmps.2025.106170","url":null,"abstract":"<div><div>A new micromechanics-inspired thermodynamic constitutive model is developed for fluid-saturated granular materials. The model development begins with the conceptual assumption that a granular material, when subjected to an external load, is supported by networks of microscopic force chains, including strong and weak force networks. The model also considers the heterogeneous nature of the fabrics in these force networks and describes these micro-level fabrics as a set of distributed fabric tensors. Using non-equilibrium thermodynamic principles, the micro-level behaviors in the strong and weak force networks are homogenized into two macro-level spaces: fabric-transformed space and real space. The model employs fabric-dependent granular hyperelasticity with free and residual elastic potentials, which leads to a fabric-dependent yielding criterion evaluated from the instability of micro-level elasticity. The granular plastic relationships are thermodynamically derived in combination with the concepts of fluidization index and granular temperature. Consequently, the thermodynamic transformations of stresses, strains, and plastic dissipative flows in the two macro-level spaces are derived. The model developed is capable of simulating granular fluidization (i.e., cyclic liquefaction). Its performance is validated by simulating undrained cyclic tests of Monterey No. 0/30 sand under different types of multidirectional non-proportional cyclic paths. The analysis of the developments in yielding and various internal factors of this model provides valuable insights into the mechanisms governing the critical state and non-coaxial cyclic behavior of granular materials.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"200 ","pages":"Article 106170"},"PeriodicalIF":5.0,"publicationDate":"2025-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143895251","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":"Hypo-elasticity, Cauchy-elasticity, corotational stability and monotonicity in the logarithmic strain","authors":"Patrizio Neff ,&nbsp;Sebastian Holthausen ,&nbsp;Marco Valerio d’Agostino ,&nbsp;Davide Bernardini ,&nbsp;Adam Sky ,&nbsp;Ionel-Dumitrel Ghiba ,&nbsp;Robert J. Martin","doi":"10.1016/j.jmps.2025.106074","DOIUrl":"10.1016/j.jmps.2025.106074","url":null,"abstract":"&lt;div&gt;&lt;div&gt;We combine the rate formulation for the objective, corotational Zaremba–Jaumann rate &lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;ZJ&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;ZJ&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;sym&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ξ&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; operating on the Cauchy stress &lt;span&gt;&lt;math&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, the Eulerian rate of deformation &lt;span&gt;&lt;math&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; and the spatial velocity &lt;span&gt;&lt;math&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; with the novel “corotational stability postulate” &lt;span&gt;&lt;span&gt;&lt;span&gt;(CSP)&lt;/span&gt;&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;〈&lt;/mo&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;ZJ&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;〉&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mo&gt;∀&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mo&gt;Sym&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;∖&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;to show that for a given isotropic Cauchy-elastic constitutive law &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo&gt;↦&lt;/mo&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; in terms of the left Cauchy–Green tensor &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;F&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;F&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, the induced fourth-order tangent stiffness tensor &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;ZJ&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; is positive definite if and only if for &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;̂&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;log&lt;/mo&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, the strong True-Stress–True-Strain monotonicity condition &lt;span&gt;&lt;span&gt;(TSTS-M&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;)&lt;/span&gt;&lt;/span&gt; in the logarithmic strain is satisfied: &lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;span&gt;(TSTS-M++)&lt;/span&gt;&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;sym&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;log&lt;/mo&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;̂&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;log&lt;/mo&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mo&gt;Sym&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;⟹&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mrow&gt;&lt;mo&gt;〈&lt;/mo&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;̂&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;log&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/mro","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"202 ","pages":"Article 106074"},"PeriodicalIF":5.0,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144137697","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":"Learning constitutive relations from experiments: 1. PDE constrained optimization","authors":"Andrew Akerson ,&nbsp;Aakila Rajan ,&nbsp;Kaushik Bhattacharya","doi":"10.1016/j.jmps.2025.106128","DOIUrl":"10.1016/j.jmps.2025.106128","url":null,"abstract":"<div><div>We propose a method to accurately and efficiently identify the constitutive behavior of complex materials through full-field observations. We formulate the problem of inferring constitutive relations from experiments as an indirect inverse problem that is constrained by the balance laws. Specifically, we seek to find a constitutive relation that minimizes the difference between the experimental observation and the corresponding quantities computed with the model, while enforcing the balance laws. We formulate the forward problem as a boundary value problem corresponding to the experiment, and compute the sensitivity of the objective with respect to model using the adjoint method. The resulting method is robust and can be applied to constitutive models with arbitrary complexity. We focus on elasto-viscoplasticity, but the approach can be extended to other settings. In this part one, we formulate the method and demonstrate it using synthetic data on two problems, one quasistatic and the other dynamic.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"201 ","pages":"Article 106128"},"PeriodicalIF":5.0,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143907822","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":"Hybrid variable spiking graph neural networks for energy-efficient scientific machine learning","authors":"Isha Jain ,&nbsp;Shailesh Garg ,&nbsp;Shaurya Shriyam ,&nbsp;Souvik Chakraborty","doi":"10.1016/j.jmps.2025.106152","DOIUrl":"10.1016/j.jmps.2025.106152","url":null,"abstract":"<div><div>Graph-based representations for samples of computational mechanics-related datasets can prove instrumental when dealing with problems like irregular domains or molecular structures of materials, etc. To effectively analyze and process such datasets, deep learning offers Graph Neural Networks (GNNs) that utilize techniques like message-passing within their architecture. The issue, however, is that as the individual graph scales and/ or GNN architecture becomes increasingly complex, the increased energy budget of the overall deep learning model makes it unsustainable and restricts its applications in applications like edge computing. To overcome this, we propose in this paper Variable Spiking Graph Neural Networks (VS-GNNs) and their hybrid variants, collectively termed VS-GNN architectures, that utilize Variable Spiking Neurons (VSNs) within their architecture to promote sparse communication and hence reduce the overall energy budget. VSNs, while promoting sparse event-driven computations, also perform well for regression tasks, which are often encountered in computational mechanics applications and are the main target of this paper. Three examples dealing with the prediction of mechanical properties of materials based on their microscale/ mesoscale structures are shown to test the performance of the proposed VS-GNNs architectures in regression tasks. We have compared the performance of VS-GNN architectures with the performance of vanilla GNNs, GNNs utilizing leaky integrate and fire neurons, and GNNs utilizing recurrent leaky integrate and fire neurons. The results produced show that VS-GNN architectures perform well for regression tasks, all while promoting sparse communication and, hence, energy efficiency.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"200 ","pages":"Article 106152"},"PeriodicalIF":5.0,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143879076","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":"The geometric nature of homeostatic stress in biological growth","authors":"A. Erlich ,&nbsp;G. Zurlo","doi":"10.1016/j.jmps.2025.106155","DOIUrl":"10.1016/j.jmps.2025.106155","url":null,"abstract":"<div><div>Morphogenesis, the process of growth and shape formation in biological tissues, is driven by complex interactions between mechanical, biochemical, and genetic factors. Traditional models of biological growth often rely on the concept of homeostatic Eshelby stress, which defines an ideal target state for the growing body. Any local deviation from this state triggers growth and remodelling, aimed at restoring balance between mechanical forces and biological adaptation. Despite its relevance in the biomechanical context, the nature of homeostatic stress remains elusive, with its value and spatial distribution often chosen arbitrarily, lacking a clear biological interpretation or understanding of its connection to the lower scales of the tissue. To bring clarity on the nature of homeostatic stress, we shift the focus from Eshelby stress to growth incompatibility, a measure of geometric frustration in the tissue that is the primary source of residual stresses in the developing body. Incompatibility, which is measured by the Ricci tensor of the growth metric at the continuous level, can be potentially regulated at the cell level through the formation of appropriate networks and connections with the surrounding cells, making it a more meaningful concept than homeostatic stress as a fixed target. In this geometric perspective, achieving a homeostatic state corresponds to the establishment of a physiological level of frustration in the body, a process leading to the generation and maintenance of the mechanical stresses that are crucial to tissue functionality. While residual stress can be induced through either active contraction or differential growth, the latter is the focus of this work. In this work we present a formulation of biological growth that penalises deviations from a desired state of incompatibility, similar to the way the Einstein–Hilbert action operates in General Relativity. The proposed framework offers a clear and physically grounded approach that elucidates the regulation of size and shape, while providing a means to link cellular and tissue scales in biological systems.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"201 ","pages":"Article 106155"},"PeriodicalIF":5.0,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143904247","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}