Journal of The Mechanics and Physics of Solids最新文献_第6页

Material Fingerprinting for rapid discovery of hyperelastic models: First experimental validation 快速发现超弹性模型的材料指纹：首次实验验证

IF 6 2区工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY

Journal of The Mechanics and Physics of Solids

Pub Date : 2025-12-05 DOI: 10.1016/j.jmps.2025.106463

Denisa Martonová , Ellen Kuhl , Moritz Flaschel

Material Fingerprinting is an emerging approach for the rapid discovery of mechanical material models directly from experimental data. By interpreting a material’s response in standardized experiments as its fingerprint, Material Fingerprinting employs pattern recognition to match experimental data against a precomputed database, enabling real-time model discovery. This strategy is both fast and robust, as it avoids solving potentially non-convex optimization problems. Unlike traditional calibration methods, Material Fingerprinting simultaneously selects the most suitable material model and identifies its parameters. Since the fingerprint database is fully controllable, the method guarantees interpretable and physically meaningful models. In previous work, we showed the feasibility of this concept for experiments with homogeneous or heterogeneous deformation fields using synthetically generated data. Here we present the first experimental validation of Material Fingerprinting. We carefully design a fingerprint database for uniaxial tension/compression, equibiaxial tension as well as pure and simple shear experiments. Once computed in an offline phase, this database can be reused for rapid model discovery across diverse experimental datasets. We demonstrate that this single database enables the robust and efficient discovery of hyperelastic strain energy functions to accurately characterize the isotropic mechanical responses of rubber, hydrogel, and brain tissue in less than one second on a standard personal computer. To make this approach openly accessible for rapid material model discovery across laboratories, we release the database and the implementation of Material Fingerprinting as a pip-installable Python package alongside this publication.

材料指纹是一种新兴的方法，可以直接从实验数据中快速发现机械材料模型。通过将材料在标准化实验中的反应解释为其指纹，材料指纹技术采用模式识别技术将实验数据与预先计算的数据库进行匹配，从而实现实时模型发现。这种策略既快速又健壮，因为它避免了解决潜在的非凸优化问题。与传统的校准方法不同，材料指纹识别同时选择最合适的材料模型并识别其参数。由于指纹数据库是完全可控的，该方法保证了模型的可解释性和物理意义。在之前的工作中，我们使用合成生成的数据证明了该概念在均匀或非均匀变形场实验中的可行性。在这里，我们提出了材料指纹识别的第一个实验验证。我们精心设计了单轴拉伸/压缩、等双轴拉伸以及纯剪切和简单剪切实验的指纹数据库。一旦在离线阶段计算，该数据库可以被重用，用于跨不同实验数据集的快速模型发现。我们证明，这个单一的数据库能够在不到一秒的时间内，在标准的个人计算机上准确地描述橡胶、水凝胶和脑组织的各向同性力学响应，从而强大而有效地发现超弹性应变能函数。为了使这种方法能够在实验室中快速发现材料模型，我们将数据库和材料指纹的实现作为可安装的Python包与本出版物一起发布。

{"title":"Material Fingerprinting for rapid discovery of hyperelastic models: First experimental validation","authors":"Denisa Martonová , Ellen Kuhl , Moritz Flaschel","doi":"10.1016/j.jmps.2025.106463","DOIUrl":"10.1016/j.jmps.2025.106463","url":null,"abstract":"<div><div>Material Fingerprinting is an emerging approach for the rapid discovery of mechanical material models directly from experimental data. By interpreting a material’s response in standardized experiments as its fingerprint, Material Fingerprinting employs pattern recognition to match experimental data against a precomputed database, enabling real-time model discovery. This strategy is both fast and robust, as it avoids solving potentially non-convex optimization problems. Unlike traditional calibration methods, Material Fingerprinting simultaneously selects the most suitable material model and identifies its parameters. Since the fingerprint database is fully controllable, the method guarantees interpretable and physically meaningful models. In previous work, we showed the feasibility of this concept for experiments with homogeneous or heterogeneous deformation fields using synthetically generated data. Here we present the first experimental validation of Material Fingerprinting. We carefully design a fingerprint database for uniaxial tension/compression, equibiaxial tension as well as pure and simple shear experiments. Once computed in an offline phase, this database can be reused for rapid model discovery across diverse experimental datasets. We demonstrate that this single database enables the robust and efficient discovery of hyperelastic strain energy functions to accurately characterize the isotropic mechanical responses of rubber, hydrogel, and brain tissue in less than one second on a standard personal computer. To make this approach openly accessible for rapid material model discovery across laboratories, we release the database and the implementation of Material Fingerprinting as a pip-installable Python package alongside this publication.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"208 ","pages":"Article 106463"},"PeriodicalIF":6.0,"publicationDate":"2025-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145689701","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}

引用次数: 0

Fracture analysis of nonlocally homogenised solids via stochastic gradient estimates embedded in physics-informed neural networks 利用嵌入物理信息神经网络的随机梯度估计对非局部均质固体进行断裂分析

IF 6 2区工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY

Journal of The Mechanics and Physics of Solids

Pub Date : 2025-12-05 DOI: 10.1016/j.jmps.2025.106458

Rohit Sinha , Kolati Heman Sudeep , Arjun Kaithavalappil, Saikat Sarkar

Architected materials exhibit rich fracture behaviour, governed by microstructural interactions that are often difficult to capture. To overcome this challenge, we present a length-scale-informed, homogenised continuum framework in which nonlocal interactions are captured through a stochastic gradient estimator (SGE). The method substitutes explicit microstructural resolution with a radius of influence, which represents the communication distance between neighbours in a homogenised medium. This nonlocal continuum is embedded in a physics-informed neural network (PINN), which minimises a nonlocal energy functional involving displacement and phase field damage. PINN is adopted due to its computational efficiency compared to finite-element implementations of nonlocal models. Using two benchmark problems-a single-edge notched plate and a notched plate with an off-centre hole-we demonstrate that the present model recovers classic nonlocal fracture behaviours and reveals new geometric effects. In the notched plate, increasing the interaction radius produces the expected nonlocalisation of strain energy. In the plate with a hole, however, the same nonlocal mechanism leads to a geometry-induced shift in crack nucleation at the curved hole boundary, accompanied by a counterintuitive reversal of the expected stiffness reduction. This behaviour arises from curvature-assisted, nonlocal stress redistribution that cannot be produced by a local formulation. Dimensional benchmarking against existing damage models confirms the physical consistency and accuracy of the proposed approach. Overall, the study indicates that a homogenised nonlocal continuum, when coupled with an efficient solver, can capture both standard and nonintuitive fracture phenomena without explicit microstructural modelling.

建筑材料表现出丰富的断裂行为，受微观结构相互作用的支配，通常难以捕获。为了克服这一挑战，我们提出了一个长度尺度的均匀连续体框架，其中通过随机梯度估计器（SGE）捕获非局部相互作用。该方法用影响半径代替了显式微观结构分辨率，影响半径代表了均匀介质中邻居之间的通信距离。这种非局部连续体嵌入到物理信息神经网络（PINN）中，使涉及位移和相场损伤的非局部能量泛函最小化。与非局部模型的有限元实现相比，采用PINN的计算效率更高。通过对单边缺口板和带偏离中心孔的缺口板两个基准问题的分析，我们证明了该模型恢复了经典的非局部断裂行为，并揭示了新的几何效应。在缺口板中，增大相互作用半径会产生预期的应变能非局部化。然而，在有孔的板中，同样的非局部机制导致弯曲孔边界处裂纹形核的几何诱导位移，伴随着预期刚度降低的反直觉逆转。这种行为源于曲率辅助的非局部应力重分布，而局部公式无法产生这种重分布。针对现有损伤模型的尺寸基准测试证实了所提出方法的物理一致性和准确性。总的来说，研究表明，一个均匀的非局部连续体，当与一个有效的求解器相结合时，可以捕获标准和非直观的断裂现象，而无需明确的微观结构建模。

{"title":"Fracture analysis of nonlocally homogenised solids via stochastic gradient estimates embedded in physics-informed neural networks","authors":"Rohit Sinha , Kolati Heman Sudeep , Arjun Kaithavalappil, Saikat Sarkar","doi":"10.1016/j.jmps.2025.106458","DOIUrl":"10.1016/j.jmps.2025.106458","url":null,"abstract":"<div><div>Architected materials exhibit rich fracture behaviour, governed by microstructural interactions that are often difficult to capture. To overcome this challenge, we present a length-scale-informed, homogenised continuum framework in which nonlocal interactions are captured through a stochastic gradient estimator (SGE). The method substitutes explicit microstructural resolution with a radius of influence, which represents the communication distance between neighbours in a homogenised medium. This nonlocal continuum is embedded in a physics-informed neural network (PINN), which minimises a nonlocal energy functional involving displacement and phase field damage. PINN is adopted due to its computational efficiency compared to finite-element implementations of nonlocal models. Using two benchmark problems-a single-edge notched plate and a notched plate with an off-centre hole-we demonstrate that the present model recovers classic nonlocal fracture behaviours and reveals new geometric effects. In the notched plate, increasing the interaction radius produces the expected nonlocalisation of strain energy. In the plate with a hole, however, the same nonlocal mechanism leads to a geometry-induced shift in crack nucleation at the curved hole boundary, accompanied by a counterintuitive reversal of the expected stiffness reduction. This behaviour arises from curvature-assisted, nonlocal stress redistribution that cannot be produced by a local formulation. Dimensional benchmarking against existing damage models confirms the physical consistency and accuracy of the proposed approach. Overall, the study indicates that a homogenised nonlocal continuum, when coupled with an efficient solver, can capture both standard and nonintuitive fracture phenomena without explicit microstructural modelling.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"208 ","pages":"Article 106458"},"PeriodicalIF":6.0,"publicationDate":"2025-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145689697","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}

引用次数: 0

In search of constitutive conditions in isotropic hyperelasticity: polyconvexity versus true-stress-true-strain monotonicity 寻找各向同性超弹性的本构条件：多凸性与真应力-真应变单调性

IF 6 2区工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY

Journal of The Mechanics and Physics of Solids

Pub Date : 2025-12-04 DOI: 10.1016/j.jmps.2025.106465

Maximilian P. Wollner , Gerhard A. Holzapfel , Patrizio Neff

The polyconvexity of a strain-energy function is nowadays increasingly presented as the ultimate material stability condition for an idealized elastic response. While the mathematical merits of polyconvexity are clearly understood, its mechanical consequences have received less attention. In this contribution we contrast polyconvexity with the recently rediscovered true-stress-true-strain monotonicity (TSTS-M⁺⁺) condition. By way of explicit examples, we show that neither condition by itself is strong enough to guarantee physically reasonable behavior for ideal isotropic elasticity. In particular, polyconvexity does not imply a monotone trajectory of the Cauchy stress in unconstrained uniaxial extension which TSTS-M⁺⁺ ensures. On the other hand, TSTS-M⁺⁺ does not impose a monotone Cauchy shear stress response in simple shear which is enforced by Legendre-Hadamard ellipticity and in turn polyconvexity. Both scenarios are proven through the construction of appropriate strain-energy functions. Consequently, a combination of polyconvexity, ensuring Legendre-Hadamard ellipticity, and TSTS-M⁺⁺ seems to be a viable solution to Truesdell’s Hauptproblem. However, so far no isotropic strain-energy function has been identified that satisfies both constraints globally at the same time. Although we are unable to deliver a valid solution here, we provide several results that could prove helpful in the construction of such an exceptional strain-energy function. In memory of Miroslav Šilhavý (1949–2025)

应变-能量函数的多凸性现在越来越多地被认为是理想弹性响应的最终材料稳定性条件。虽然多凸性的数学优点已被清楚地理解，但它的力学后果却很少受到关注。在这篇贡献中，我们将多凸性与最近重新发现的真应力-真应变单调性（tsts - m++）条件进行了比较。通过明确的例子，我们表明，这两个条件本身都不足以保证理想各向同性弹性的物理合理行为。特别是，多凸性并不意味着柯西应力在无约束单轴拉伸中的单调轨迹，而tsts - m++保证了这一点。另一方面，tsts - m++在简单剪切中不施加单调的柯西剪应力响应，而单调的柯西剪应力响应是由legende - hadamard椭圆性和多凸性所施加的。通过构造适当的应变-能函数来证明这两种情况。因此，确保legende - hadamard椭圆性的多凸性与tsts - m++的组合似乎是解决Truesdell Hauptproblem的可行方案。然而，到目前为止，还没有发现同时满足这两个约束的各向同性应变能函数。虽然我们无法在这里提供一个有效的解决方案，但我们提供了几个结果，可以证明有助于构建这样一个特殊的应变-能量函数。纪念米罗斯拉夫Šilhavý （1949-2025）

{"title":"In search of constitutive conditions in isotropic hyperelasticity: polyconvexity versus true-stress-true-strain monotonicity","authors":"Maximilian P. Wollner , Gerhard A. Holzapfel , Patrizio Neff","doi":"10.1016/j.jmps.2025.106465","DOIUrl":"10.1016/j.jmps.2025.106465","url":null,"abstract":"<div><div>The polyconvexity of a strain-energy function is nowadays increasingly presented as the ultimate material stability condition for an idealized elastic response. While the mathematical merits of polyconvexity are clearly understood, its mechanical consequences have received less attention. In this contribution we contrast polyconvexity with the recently rediscovered true-stress-true-strain monotonicity (TSTS-M<sup>++</sup>) condition. By way of explicit examples, we show that neither condition by itself is strong enough to guarantee physically reasonable behavior for ideal isotropic elasticity. In particular, polyconvexity does not imply a monotone trajectory of the Cauchy stress in unconstrained uniaxial extension which TSTS-M<sup>++</sup> ensures. On the other hand, TSTS-M<sup>++</sup> does not impose a monotone Cauchy shear stress response in simple shear which is enforced by Legendre-Hadamard ellipticity and in turn polyconvexity. Both scenarios are proven through the construction of appropriate strain-energy functions. Consequently, a combination of polyconvexity, ensuring Legendre-Hadamard ellipticity, and TSTS-M<sup>++</sup> seems to be a viable solution to Truesdell’s Hauptproblem. However, so far no isotropic strain-energy function has been identified that satisfies both constraints globally at the same time. Although we are unable to deliver a valid solution here, we provide several results that could prove helpful in the construction of such an exceptional strain-energy function. <em>In memory of</em> Miroslav Šilhavý (1949–2025)</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"209 ","pages":"Article 106465"},"PeriodicalIF":6.0,"publicationDate":"2025-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145689708","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}

引用次数: 0

Shell-lattice metamaterials with intrinsic contact stabilization for exceptional mechanical performance and nonlinear stability 具有内在接触稳定化的壳晶格超材料，具有优异的机械性能和非线性稳定性

IF 6 2区工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY

Journal of The Mechanics and Physics of Solids

Pub Date : 2025-12-04 DOI: 10.1016/j.jmps.2025.106467

Peijie Zhang , Xueyan Chen , Penghui Yu , Kun Zhao , Hang Yin , Changguo Wang , Huifeng Tan , Muamer Kadic

Although lattice mechanical metamaterials offer low weight and tailorable properties, they face a fundamental barrier to adoption at low relative densities: optimising elastic-plastic performance usually results in reduced buckling resistance (nonlinear stability). Here, we present a novel shell-lattice metamaterial design methodology that eliminates the need to compromise between high yield strength and nonlinear stability at low relative densities. This methodology also provides high specific stiffness and high energy absorption. Our design features seamlessly integrated elliptical hollow struts and hollow spherical nodes. Leveraging a stretching-dominated mechanism augmented by contact-enhanced stabilisation, the architecture provides compensatory reinforcement under large deformations. We numerically investigate and experimentally validate the influence of key geometrical ratios on the mechanical properties. Crucially, elastic isotropy can be achieved through parameter optimisation, and broad tenability enables customised anisotropic elastic responses for diverse applications. Across relative densities ranging from 0.01 to 0.5, our proposed shell lattices demonstrate consistent superiority over conventional truss and shell lattices of equal density. At a relative density of 0.1, the designs deliver a 5 % rise in Young’s modulus, a 38 % increase in yield strength, and almost double the energy absorption capacity, significantly outperforming conventional TPMS-like shell lattices. These enhancements arise from internal contact mechanisms that stabilise post-buckling behaviour, yielding consistent or enhanced stress-strain responses. This methodology overcomes the limitations of low-density stretching-dominated lattices, paving the way for advanced, lightweight, load-bearing structures, energy absorbers, and multifunctional metamaterials.

尽管点阵机械超材料具有重量轻、可定制的性能，但在低相对密度下，它们面临着一个基本障碍：优化弹塑性性能通常会降低屈曲阻力（非线性稳定性）。在这里，我们提出了一种新的壳-晶格超材料设计方法，消除了在低相对密度下高屈服强度和非线性稳定性之间妥协的需要。这种方法还提供了高比刚度和高能量吸收。我们的设计特点是无缝集成椭圆空心支柱和空心球面节点。利用由接触增强稳定性增强的拉伸主导机制，该结构在大变形下提供补偿性加固。通过数值研究和实验验证了关键几何比对材料力学性能的影响。最重要的是，弹性各向同性可以通过参数优化来实现，广泛的可持续性可以为不同的应用定制各向异性弹性响应。在相对密度从0.01到0.5的范围内，我们提出的壳格比传统的桁架和等密度的壳格表现出一致的优势。在相对密度为0.1时，杨氏模量提高了5%，屈服强度提高了38%，能量吸收能力几乎提高了一倍，显著优于传统的tpms类壳晶格。这些增强来自于内部接触机制，该机制稳定了屈曲后行为，产生一致或增强的应力-应变响应。这种方法克服了低密度拉伸主导晶格的局限性，为先进、轻量化、承重结构、能量吸收剂和多功能超材料铺平了道路。

{"title":"Shell-lattice metamaterials with intrinsic contact stabilization for exceptional mechanical performance and nonlinear stability","authors":"Peijie Zhang , Xueyan Chen , Penghui Yu , Kun Zhao , Hang Yin , Changguo Wang , Huifeng Tan , Muamer Kadic","doi":"10.1016/j.jmps.2025.106467","DOIUrl":"10.1016/j.jmps.2025.106467","url":null,"abstract":"<div><div>Although lattice mechanical metamaterials offer low weight and tailorable properties, they face a fundamental barrier to adoption at low relative densities: optimising elastic-plastic performance usually results in reduced buckling resistance (nonlinear stability). Here, we present a novel shell-lattice metamaterial design methodology that eliminates the need to compromise between high yield strength and nonlinear stability at low relative densities. This methodology also provides high specific stiffness and high energy absorption. Our design features seamlessly integrated elliptical hollow struts and hollow spherical nodes. Leveraging a stretching-dominated mechanism augmented by contact-enhanced stabilisation, the architecture provides compensatory reinforcement under large deformations. We numerically investigate and experimentally validate the influence of key geometrical ratios on the mechanical properties. Crucially, elastic isotropy can be achieved through parameter optimisation, and broad tenability enables customised anisotropic elastic responses for diverse applications. Across relative densities ranging from 0.01 to 0.5, our proposed shell lattices demonstrate consistent superiority over conventional truss and shell lattices of equal density. At a relative density of 0.1, the designs deliver a 5 % rise in Young’s modulus, a 38 % increase in yield strength, and almost double the energy absorption capacity, significantly outperforming conventional TPMS-like shell lattices. These enhancements arise from internal contact mechanisms that stabilise post-buckling behaviour, yielding consistent or enhanced stress-strain responses. This methodology overcomes the limitations of low-density stretching-dominated lattices, paving the way for advanced, lightweight, load-bearing structures, energy absorbers, and multifunctional metamaterials.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"208 ","pages":"Article 106467"},"PeriodicalIF":6.0,"publicationDate":"2025-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145689710","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}

引用次数: 0

The broad wrinkling landscape of hyperelastic parallelogram-shaped membranes: From wrinkle migration to restabilization and their subsequent reappearance elsewhere 超弹性平行四边形膜的广泛起皱景观：从皱纹迁移到再稳定及其随后在其他地方的再现

IF 6 2区工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY

Journal of The Mechanics and Physics of Solids

Pub Date : 2025-12-04 DOI: 10.1016/j.jmps.2025.106461

Mohammad Hosein Nejabatmeimandi , Francesco Dal Corso

Wrinkling is a commonly observed out-of-plane instability in membrane structures due to their extremely low bending-to-stretching stiffness ratio. It has been extensively investigated for symmetric membrane geometries and boundary conditions that induce planar non-uniform stress states by preventing the lateral contraction at the edges, and is also known to potentially display self-restabilization. This study investigates an initially flat, parallelogram-shaped hyperelastic membrane, focusing on the effect of the inclination angle that defines its deviation from rectangular geometry. It is shown that wrinkling can occur either centrally or at the two opposite obtuse-angled corners–even for small inclination angles–during stretching with unconstrained lateral contraction, a condition under which the flat configuration for the rectangular counterpart remains always stable. Three distinct evolutions of the wrinkling pattern are numerically identified, all ultimately leading to corner-localized wrinkles. This final state may arise (i) directly, without a prior bifurcation, or after the appearance of central wrinkling that either (ii) restabilizes or (iii) separates and migrates toward the corners. A closed-form expression for the critical wrinkling condition is derived by combining a perturbation approach with an energy-based method in the framework of linear elasticity. This provides an accurate estimate of the onset and pattern of central wrinkling. The present findings reveal new pathways in wrinkling pattern evolution and introduce a novel approach to unconventional boundary-value problems, with potential applications ranging from lightweight structural systems to flexible electronics.

由于薄膜结构的弯曲-拉伸刚度比极低，起皱是一种常见的面外失稳现象。人们对对称膜的几何形状和边界条件进行了广泛的研究，这些条件通过防止边缘的侧向收缩来诱导平面非均匀应力状态，并且也知道可能显示自再稳定。本研究研究了一个最初平坦的平行四边形超弹性膜，重点研究了倾角对其偏离矩形几何形状的影响。结果表明，在无约束横向收缩拉伸过程中，褶皱既可以发生在中心，也可以发生在两个相对的钝角处，即使倾角很小，在这种条件下，矩形对应的平面构型始终保持稳定。三个不同的演变的皱纹模式被数字识别，所有最终导致角落局部皱纹。这种最终状态可能出现在(i)没有事先分叉的情况下直接出现，也可能出现在（ii）重新稳定或（iii）分离并向角落迁移的中心褶皱出现之后。在线性弹性的框架下，将微扰法与能量法相结合，导出了临界起皱条件的封闭表达式。这提供了中心起皱的开始和模式的准确估计。目前的研究结果揭示了皱纹模式演变的新途径，并引入了一种解决非常规边值问题的新方法，其潜在应用范围从轻型结构系统到柔性电子产品。

{"title":"The broad wrinkling landscape of hyperelastic parallelogram-shaped membranes: From wrinkle migration to restabilization and their subsequent reappearance elsewhere","authors":"Mohammad Hosein Nejabatmeimandi , Francesco Dal Corso","doi":"10.1016/j.jmps.2025.106461","DOIUrl":"10.1016/j.jmps.2025.106461","url":null,"abstract":"<div><div>Wrinkling is a commonly observed out-of-plane instability in membrane structures due to their extremely low bending-to-stretching stiffness ratio. It has been extensively investigated for symmetric membrane geometries and boundary conditions that induce planar non-uniform stress states by preventing the lateral contraction at the edges, and is also known to potentially display self-restabilization. This study investigates an initially flat, parallelogram-shaped hyperelastic membrane, focusing on the effect of the inclination angle that defines its deviation from rectangular geometry. It is shown that wrinkling can occur either centrally or at the two opposite obtuse-angled corners–even for small inclination angles–during stretching with unconstrained lateral contraction, a condition under which the flat configuration for the rectangular counterpart remains always stable. Three distinct evolutions of the wrinkling pattern are numerically identified, all ultimately leading to corner-localized wrinkles. This final state may arise (i) directly, without a prior bifurcation, or after the appearance of central wrinkling that either (ii) restabilizes or (iii) separates and migrates toward the corners. A closed-form expression for the critical wrinkling condition is derived by combining a perturbation approach with an energy-based method in the framework of linear elasticity. This provides an accurate estimate of the onset and pattern of central wrinkling. The present findings reveal new pathways in wrinkling pattern evolution and introduce a novel approach to unconventional boundary-value problems, with potential applications ranging from lightweight structural systems to flexible electronics.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"208 ","pages":"Article 106461"},"PeriodicalIF":6.0,"publicationDate":"2025-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145689712","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}

引用次数: 0

A probabilistic buckling model for hemispherical shells with non-interacting localized defects 具有非相互作用局部缺陷的半球形壳的概率屈曲模型

IF 6 2区工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY

Journal of The Mechanics and Physics of Solids

Pub Date : 2025-12-03 DOI: 10.1016/j.jmps.2025.106468

Zheren Baizhikova , Uba K. Ubamanyu , Fani Derveni , Roberto Ballarini , Pedro M. Reis , Jia-Liang Le

This paper presents a combined computational and analytical investigation on the probability distribution of the knockdown factor of hemispherical shells containing multiple non-interacting localized geometrical defects. In the analytical model, the statistics of the knockdown factor for shells with a single defect are explicitly linked to the statistics of the defect amplitude. The model is then extended to shells with multiple non-interacting defects of random amplitudes through a finite weakest-link formulation, which predicts how the mean and coefficient of variation of the knockdown factor depend on the number of defects on the shell surface. The results of extreme value statistics are further used to derive the limiting form of the knockdown-factor distribution. The analytical investigation is accompanied by a series of stochastic finite element (SFE) simulations of hemispherical shells of different dimensions and with different sizes of the zone containing the defects. The analytical model is shown to be in excellent agreement with the simulation results. The main outcome of the analytical model is a statistical size effect on the knockdown factor, governed by the dimensionless radius, for shells containing the maximum possible number of non-interacting defects. A similar size effect has recently been reported for hemispherical shells with continuous random imperfect surfaces. Together, these results offer a new perspective on the universal statistical role of the dimensionless radius in governing the buckling behavior of geometrically imperfect hemispherical shells.

本文对含有多个非相互作用局部几何缺陷的半球形壳体击倒因子的概率分布进行了计算与分析相结合的研究。在解析模型中，具有单一缺陷的壳体的击倒因子的统计数据与缺陷幅度的统计数据显式地联系在一起。然后，通过有限最弱链接公式将模型扩展到具有多个随机振幅的非相互作用缺陷的壳，该公式预测了击倒因子的平均值和变异系数如何依赖于壳表面缺陷的数量。利用极值统计的结果进一步导出了击倒因子分布的极限形式。在分析研究的同时，对不同尺寸和不同含缺陷区大小的半球形壳进行了一系列随机有限元模拟。分析模型与仿真结果吻合良好。分析模型的主要结果是统计尺寸对击倒因子的影响，由无量纲半径控制，对于包含最大可能数量的非相互作用缺陷的壳。最近对具有连续随机不完美表面的半球形壳体也报道了类似的尺寸效应。总之，这些结果为无量纲半径在控制几何不完美半球形壳体屈曲行为中的普遍统计作用提供了新的视角。

{"title":"A probabilistic buckling model for hemispherical shells with non-interacting localized defects","authors":"Zheren Baizhikova , Uba K. Ubamanyu , Fani Derveni , Roberto Ballarini , Pedro M. Reis , Jia-Liang Le","doi":"10.1016/j.jmps.2025.106468","DOIUrl":"10.1016/j.jmps.2025.106468","url":null,"abstract":"<div><div>This paper presents a combined computational and analytical investigation on the probability distribution of the knockdown factor of hemispherical shells containing multiple non-interacting localized geometrical defects. In the analytical model, the statistics of the knockdown factor for shells with a single defect are explicitly linked to the statistics of the defect amplitude. The model is then extended to shells with multiple non-interacting defects of random amplitudes through a finite weakest-link formulation, which predicts how the mean and coefficient of variation of the knockdown factor depend on the number of defects on the shell surface. The results of extreme value statistics are further used to derive the limiting form of the knockdown-factor distribution. The analytical investigation is accompanied by a series of stochastic finite element (SFE) simulations of hemispherical shells of different dimensions and with different sizes of the zone containing the defects. The analytical model is shown to be in excellent agreement with the simulation results. The main outcome of the analytical model is a statistical size effect on the knockdown factor, governed by the dimensionless radius, for shells containing the maximum possible number of non-interacting defects. A similar size effect has recently been reported for hemispherical shells with continuous random imperfect surfaces. Together, these results offer a new perspective on the universal statistical role of the dimensionless radius in governing the buckling behavior of geometrically imperfect hemispherical shells.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"208 ","pages":"Article 106468"},"PeriodicalIF":6.0,"publicationDate":"2025-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145689711","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}

引用次数: 0

Exploring the inverse poroelastic behavior of hydrogels: the roles of finite extensibility of polymer chains and unfolding of polymer domains 探索水凝胶的反孔弹性行为：聚合物链的有限可扩展性和聚合物结构域的展开的作用

IF 6 2区工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY

Journal of The Mechanics and Physics of Solids

Pub Date : 2025-12-03 DOI: 10.1016/j.jmps.2025.106464

Qifang Zhang , Junjie Liu , Jinglei Yang , Shaoxing Qu , Guozheng Kang

Hydrogels under stretching can exhibit pronounced deswelling—a phenomenon termed as “inverse poroelasticity”—yet its underlying mechanisms remain indistinct. In this paper, two mechanisms of the inverse poroelasticity of hydrogels are proposed: (1) the finite extensibility of polymer chains, and (2) the unfolding of polymer domains which induces a hydrophilic/hydrophobic transition of polymer chains. A novel constitutive model incorporating the two mechanisms is developed to reproduce the inverse poroelastic behavior of hydrogels. The finite extensibility of polymer chains is captured through the Langevin chain, while the unfolding of polymer domains leads to a varying chain length. Additionally, the hydrophilic/hydrophobic transition is modeled via a newly proposed mixing energy density function. The constitutive model is validated by comparing the results from the model with the experimental data of double network (DN) hydrogels and fibrin hydrogels, both of which exhibit an inverse poroelastic behavior. Furthermore, the proposed constitutive model is applied to investigate the inverse poroelastic fracture of hydrogels through the finite element method. The rate-dependent fracture and delayed fracture of hydrogels with a permeable crack are investigated. It is found that both the rate-dependent fracture and the delayed fracture differ between the hydrogels exhibiting the inverse poroelastic behavior and those displaying the conventional poroelastic behavior. This work deepens the fundamental understanding on the inverse poroelastic behavior of hydrogels and provides insights in designing mechanically robust hydrogels.

水凝胶在拉伸下会表现出明显的膨胀——一种被称为“逆孔隙弹性”的现象——但其潜在机制尚不清楚。本文提出了水凝胶反孔弹性的两种机制：(1)聚合物链的有限可扩展性；(2)聚合物结构域的展开导致聚合物链亲疏水转变。一个新的本构模型结合了这两种机制，以再现水凝胶的反孔弹性行为。聚合物链的有限延展性是通过朗之万链捕获的，而聚合物畴的展开导致了不同的链长。此外，通过新提出的混合能量密度函数来模拟亲水/疏水转变。通过将本构模型与双网（DN）水凝胶和纤维蛋白水凝胶的实验数据进行比较，验证了本构模型的有效性，双网水凝胶和纤维蛋白水凝胶均表现出反孔弹性行为。在此基础上，应用本构模型对水凝胶的反孔弹性断裂进行了有限元分析。研究了含渗透裂缝的水凝胶的速率依赖性断裂和延迟性断裂。研究发现，具有反孔隙弹性行为的水凝胶与具有常规孔隙弹性行为的水凝胶在速率相关裂缝和延迟裂缝方面存在差异。这项工作加深了对水凝胶反孔弹性行为的基本理解，并为设计机械坚固的水凝胶提供了见解。

{"title":"Exploring the inverse poroelastic behavior of hydrogels: the roles of finite extensibility of polymer chains and unfolding of polymer domains","authors":"Qifang Zhang , Junjie Liu , Jinglei Yang , Shaoxing Qu , Guozheng Kang","doi":"10.1016/j.jmps.2025.106464","DOIUrl":"10.1016/j.jmps.2025.106464","url":null,"abstract":"<div><div>Hydrogels under stretching can exhibit pronounced deswelling—a phenomenon termed as “inverse poroelasticity”—yet its underlying mechanisms remain indistinct. In this paper, two mechanisms of the inverse poroelasticity of hydrogels are proposed: (1) the finite extensibility of polymer chains, and (2) the unfolding of polymer domains which induces a hydrophilic/hydrophobic transition of polymer chains. A novel constitutive model incorporating the two mechanisms is developed to reproduce the inverse poroelastic behavior of hydrogels. The finite extensibility of polymer chains is captured through the Langevin chain, while the unfolding of polymer domains leads to a varying chain length. Additionally, the hydrophilic/hydrophobic transition is modeled via a newly proposed mixing energy density function. The constitutive model is validated by comparing the results from the model with the experimental data of double network (DN) hydrogels and fibrin hydrogels, both of which exhibit an inverse poroelastic behavior. Furthermore, the proposed constitutive model is applied to investigate the inverse poroelastic fracture of hydrogels through the finite element method. The rate-dependent fracture and delayed fracture of hydrogels with a permeable crack are investigated. It is found that both the rate-dependent fracture and the delayed fracture differ between the hydrogels exhibiting the inverse poroelastic behavior and those displaying the conventional poroelastic behavior. This work deepens the fundamental understanding on the inverse poroelastic behavior of hydrogels and provides insights in designing mechanically robust hydrogels.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"208 ","pages":"Article 106464"},"PeriodicalIF":6.0,"publicationDate":"2025-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145689713","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}

引用次数: 0

A continuum mechanics approach for the deformation of non-Euclidean origami generated by piecewise constant nematic director fields 非欧几里得折纸由分段常向列方向场产生的变形的连续介质力学方法

IF 6 2区工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY

Journal of The Mechanics and Physics of Solids

Pub Date : 2025-12-02 DOI: 10.1016/j.jmps.2025.106460

Linjuan Wang , Fan Feng

We merge classical origami concepts with active actuation by designing origami patterns whose panels undergo prescribed metric changes. These metric changes render the system non-Euclidean, inducing non-zero Gaussian curvature at the vertices after actuation. Such patterns can be realized by programming piecewise constant director fields in liquid crystal elastomer (LCE) sheets. In this work, we address the geometric design of both compatible reference director patterns and their corresponding actuated configurations. On the reference configuration, we systematically construct director patterns that satisfy metric compatibility across interfaces. We prove the existence and uniqueness of compatible director fields at a vertex for the generic case, up to orthogonal duals. The Gaussian curvature of the actuated vertex is computed based on the compatible director fields. On the actuated configuration, we develop a continuum mechanics framework to analyze the kinematics of non-Euclidean origami. In particular, we fully characterize the deformation spaces of three-fold and four-fold vertices and establish analytical relationships between their deformations and the director patterns. Building on these kinematic insights, we propose rational designs of large director patterns: one based on a quadrilateral tiling with alternating positive and negative actuated Gaussian curvature, and the other combining three-fold and four-fold vertices governed by a folding angle theorem. Remarkably, both designs achieve compatibility in both the reference and actuated states. We also propose a design strategy for active metamaterials based on the periodic non-Euclidean origami. The active metamaterials can have two modes of motions by folding or stimulating. We anticipate that our geometric framework will facilitate the design of non-Euclidean/active origami structures and broaden their application in active metamaterials, soft actuators, and robotic systems.

我们通过设计折纸图案，其面板经过规定的度量变化，将经典折纸概念与主动驱动相结合。这些度量变化使系统非欧几里得，在驱动后在顶点处诱导非零高斯曲率。这种模式可以通过在液晶弹性体（LCE）片上分段编程来实现。在这项工作中，我们讨论了兼容的参考指示器模式及其相应的驱动配置的几何设计。在参考配置上，我们系统地构建了满足跨接口度量兼容性的指令模式。我们证明了在一般情况下，直至正交对偶，在一个顶点处相容方向域的存在唯一性。基于兼容的方向域计算被驱动顶点的高斯曲率。在驱动构型上，我们建立了一个连续力学框架来分析非欧几里得折纸的运动学。特别是，我们充分表征了三重和四重顶点的变形空间，并建立了它们的变形与指向图案之间的解析关系。在这些运动学见解的基础上，我们提出了大型定向模式的合理设计：一个基于四边形平铺，具有交替的正负驱动高斯曲率，另一个结合由折叠角定理控制的三重和四重顶点。值得注意的是，两种设计在参考和驱动状态下都实现了兼容性。我们还提出了一种基于周期性非欧几里得折纸的活性超材料设计策略。活性超材料有两种运动模式：折叠运动模式和刺激运动模式。我们预计我们的几何框架将促进非欧几里得/活性折纸结构的设计，并扩大其在活性超材料，软致动器和机器人系统中的应用。

{"title":"A continuum mechanics approach for the deformation of non-Euclidean origami generated by piecewise constant nematic director fields","authors":"Linjuan Wang , Fan Feng","doi":"10.1016/j.jmps.2025.106460","DOIUrl":"10.1016/j.jmps.2025.106460","url":null,"abstract":"<div><div>We merge classical origami concepts with active actuation by designing origami patterns whose panels undergo prescribed metric changes. These metric changes render the system non-Euclidean, inducing non-zero Gaussian curvature at the vertices after actuation. Such patterns can be realized by programming piecewise constant director fields in liquid crystal elastomer (LCE) sheets. In this work, we address the geometric design of both compatible reference director patterns and their corresponding actuated configurations. On the reference configuration, we systematically construct director patterns that satisfy metric compatibility across interfaces. We prove the existence and uniqueness of compatible director fields at a vertex for the generic case, up to orthogonal duals. The Gaussian curvature of the actuated vertex is computed based on the compatible director fields. On the actuated configuration, we develop a continuum mechanics framework to analyze the kinematics of non-Euclidean origami. In particular, we fully characterize the deformation spaces of three-fold and four-fold vertices and establish analytical relationships between their deformations and the director patterns. Building on these kinematic insights, we propose rational designs of large director patterns: one based on a quadrilateral tiling with alternating positive and negative actuated Gaussian curvature, and the other combining three-fold and four-fold vertices governed by a folding angle theorem. Remarkably, both designs achieve compatibility in both the reference and actuated states. We also propose a design strategy for active metamaterials based on the periodic non-Euclidean origami. The active metamaterials can have two modes of motions by folding or stimulating. We anticipate that our geometric framework will facilitate the design of non-Euclidean/active origami structures and broaden their application in active metamaterials, soft actuators, and robotic systems.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"208 ","pages":"Article 106460"},"PeriodicalIF":6.0,"publicationDate":"2025-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145657137","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}

引用次数: 0

Peierls-Nabarro modeling of dislocations in high-entropy alloys 高熵合金中位错的Peierls-Nabarro模型

IF 6 2区工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY

Journal of The Mechanics and Physics of Solids

Pub Date : 2025-12-02 DOI: 10.1016/j.jmps.2025.106457

Xin Liu , Terrence P. Moran , Bastien F. G. Aymon , W. A. Curtin

The Peierls-Nabarro (PN) framework for modeling of dislocations is adapted and evaluated for application to high-entropy alloys. Solute-dislocation interactions in the complex alloys are introduced rigorously within elasticity theory. Detailed studies are performed on model 1/2⟨111⟩{110} edge dislocations in the BCC NbTaV high-entropy alloy. Key findings are that: (i) solute misfit stresses dominate the strengthening while fluctuations in the generalized stacking fault energy (GSFE) are negligible; (ii) the misfit stresses cannot be accurately measured using the atomic virial stress; (iii) the core spreading influences the alloy strength; (iv) the PN model using the atomistically-measured GSFE predicts a core narrower than measured atomistically; (v) correlations in atomic stresses have moderate influences on the distribution and spacing of energy barriers at the critical length scale but a small effect on the yield stress, and (vi) with increasing dislocation line length the yield stress using uncorrelated stresses converges quickly but to a value much lower than that found in direct atomistic stresses at 1100Å. Specifically, for segments at the theoretical characteristic length ζ_c ≈ 24Å, the PN model captures the energy landscape encountered by a gliding dislocation in good agreement with atomistic Nudged Elastic Band (NEB) calculations on the same atomistic realizations when the atomistic GSFE is used. Comparisons of the energy barrier distribution and barrier spacing across many simulations show reasonable agreement with NEB. Using a GSFE fitted to match the atomistic core spreading, however, the PN energy landscape is smoother. Using the atomistic GSFE, direct simulations of the

T = 0

K stress to achieve dislocation glide are also in good overall agreement with NEB results. Lower strengths are found using the fitted GSFE due to the larger barrier spacing. Strengths with and without the true spatial correlations in the misfit stresses are slightly different. PN predictions of strength of longer dislocation lines show a decrease in strength but saturating at a length of  ≈ 100Å to a value notably lower than atomistic simulations. This very detailed study of the computationally-efficient PN model for HEAs shows that it is viable for the studying dislocations in random alloys but remains imperfect. Nonetheless, the PN model provides significant flexibility to quantitatively and parametrically investigate the role of many different material parameters on many features of alloy strengthening, and enables future incorporation of additional complex metallurgical features such as short-range-order, clustering, and precipitation.

采用了用于位错建模的Peierls-Nabarro （PN）框架，并对其应用于高熵合金进行了评估。在弹性理论中严格地介绍了复杂合金中的溶质-位错相互作用。对BCC NbTaV高熵合金中的模型1/2⟨111⟩{110}边缘位错进行了详细的研究。主要发现是：(1)溶质错配应力主导强化，而广义层错能（GSFE）波动可以忽略不计；（ii）原子维里应力不能精确测量失配应力；（iii）芯的扩散影响合金的强度；（iv）使用原子测量GSFE的PN模型预测的岩心比原子测量的岩心窄；(v)原子应力的相关性对临界长度范围内能垒的分布和间距有中等程度的影响，但对屈服应力的影响很小；（vi）随着位错线长度的增加，使用不相关应力的屈服应力收敛得很快，但其值远低于1100Å处直接原子应力的值。具体来说，对于理论特征长度为ζc ≈ 24Å的段，当使用原子式GSFE时，PN模型捕获了滑动位错遇到的能量图，与原子式轻推弹性带（NEB）计算在相同的原子实现上很好地一致。在许多模拟中对能量势垒分布和势垒间距的比较显示出与NEB的合理一致。然而，使用GSFE拟合来匹配原子核心扩展，PN能量景观更加平滑。使用原子GSFE，直接模拟T=0K应力以实现位错滑动也与NEB结果总体上很好地一致。由于较大的势垒间距，使用拟合的GSFE发现较低的强度。失配应力中存在和不存在真实空间相关性的强度略有不同。较长位错线强度的PN预测显示强度下降，但在 ≈ 100Å的长度处饱和到明显低于原子模拟的值。这一非常详细的研究表明，计算效率高的PN模型对于研究随机合金中的位错是可行的，但仍有不足之处。尽管如此，PN模型提供了极大的灵活性，可以定量和参数化地研究许多不同材料参数对合金强化的许多特征的作用，并使未来能够纳入其他复杂的冶金特征，如短程有序、聚类和沉淀。

{"title":"Peierls-Nabarro modeling of dislocations in high-entropy alloys","authors":"Xin Liu , Terrence P. Moran , Bastien F. G. Aymon , W. A. Curtin","doi":"10.1016/j.jmps.2025.106457","DOIUrl":"10.1016/j.jmps.2025.106457","url":null,"abstract":"<div><div>The Peierls-Nabarro (PN) framework for modeling of dislocations is adapted and evaluated for application to high-entropy alloys. Solute-dislocation interactions in the complex alloys are introduced rigorously within elasticity theory. Detailed studies are performed on model 1/2⟨111⟩{110} edge dislocations in the BCC NbTaV high-entropy alloy. Key findings are that: (i) solute misfit stresses dominate the strengthening while fluctuations in the generalized stacking fault energy (GSFE) are negligible; (ii) the misfit stresses cannot be accurately measured using the atomic virial stress; (iii) the core spreading influences the alloy strength; (iv) the PN model using the atomistically-measured GSFE predicts a core narrower than measured atomistically; (v) correlations in atomic stresses have moderate influences on the distribution and spacing of energy barriers at the critical length scale but a small effect on the yield stress, and (vi) with increasing dislocation line length the yield stress using uncorrelated stresses converges quickly but to a value much lower than that found in direct atomistic stresses at 1100Å. Specifically, for segments at the theoretical characteristic length <em>ζ<sub>c</sub></em> ≈ 24Å, the PN model captures the energy landscape encountered by a gliding dislocation in good agreement with atomistic Nudged Elastic Band (NEB) calculations on the same atomistic realizations when the atomistic GSFE is used. Comparisons of the energy barrier distribution and barrier spacing across many simulations show reasonable agreement with NEB. Using a GSFE fitted to match the atomistic core spreading, however, the PN energy landscape is smoother. Using the atomistic GSFE, direct simulations of the <span><math><mrow><mi>T</mi><mo>=</mo><mn>0</mn></mrow></math></span>K stress to achieve dislocation glide are also in good overall agreement with NEB results. Lower strengths are found using the fitted GSFE due to the larger barrier spacing. Strengths with and without the true spatial correlations in the misfit stresses are slightly different. PN predictions of strength of longer dislocation lines show a decrease in strength but saturating at a length of  ≈ 100Å to a value notably lower than atomistic simulations. This very detailed study of the computationally-efficient PN model for HEAs shows that it is viable for the studying dislocations in random alloys but remains imperfect. Nonetheless, the PN model provides significant flexibility to quantitatively and parametrically investigate the role of many different material parameters on many features of alloy strengthening, and enables future incorporation of additional complex metallurgical features such as short-range-order, clustering, and precipitation.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"208 ","pages":"Article 106457"},"PeriodicalIF":6.0,"publicationDate":"2025-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145657138","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}

引用次数: 0

On dissipative effects in thermo-electrically coupled systems: Hill–Mandel-type homogenisation, asymptotic expansions and two-scale convergence 热电耦合系统中的耗散效应：hill - mandeltype均质化、渐近展开和双尺度收敛

IF 6 2区工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY

Journal of The Mechanics and Physics of Solids

Pub Date : 2025-12-02 DOI: 10.1016/j.jmps.2025.106427

D. Güzel , D. Wiedemann , T. Kaiser , A. Menzel

Accurately predicting the macroscopic behaviour of heterogeneous materials, particularly in thermo-electrically coupled systems, remains a challenging problem in materials science and engineering. Against this background, this study presents a comprehensive framework for the homogenisation of electrical conductors subject to strongly coupled thermo-electrical processes in (quasi-)stationary settings, with particular focus lying on Joule heating and temperature-dependent electrical conductivities. The proposed methodology combines analytical homogenisation, asymptotic expansions and Hill–Mandel-type multiscale techniques. In doing so, both, a natural physical interpretation and a rigorous mathematical justification of the governing set of effective macroscopic field equations are provided. Representative boundary value problems in two- and three dimensional settings are eventually studied to validate the effectiveness of these methods in capturing the complex behaviour of heterogeneous thermo-electric materials.

准确预测非均质材料的宏观行为，特别是在热电耦合系统中，仍然是材料科学和工程中的一个具有挑战性的问题。在此背景下，本研究提出了一个全面的框架，用于在（准）固定设置中受强耦合热电过程影响的电导体的均质化，特别关注焦耳加热和温度相关的电导率。所提出的方法结合了分析均匀化、渐近展开和hill - mandeltype多尺度技术。在这样做的过程中，提供了有效宏观场方程控制集的自然物理解释和严格的数学证明。最终研究了二维和三维环境中的代表性边值问题，以验证这些方法在捕获非均质热电材料的复杂行为方面的有效性。

{"title":"On dissipative effects in thermo-electrically coupled systems: Hill–Mandel-type homogenisation, asymptotic expansions and two-scale convergence","authors":"D. Güzel , D. Wiedemann , T. Kaiser , A. Menzel","doi":"10.1016/j.jmps.2025.106427","DOIUrl":"10.1016/j.jmps.2025.106427","url":null,"abstract":"<div><div>Accurately predicting the macroscopic behaviour of heterogeneous materials, particularly in thermo-electrically coupled systems, remains a challenging problem in materials science and engineering. Against this background, this study presents a comprehensive framework for the homogenisation of electrical conductors subject to strongly coupled thermo-electrical processes in (quasi-)stationary settings, with particular focus lying on Joule heating and temperature-dependent electrical conductivities. The proposed methodology combines analytical homogenisation, asymptotic expansions and Hill–Mandel-type multiscale techniques. In doing so, both, a natural physical interpretation and a rigorous mathematical justification of the governing set of effective macroscopic field equations are provided. Representative boundary value problems in two- and three dimensional settings are eventually studied to validate the effectiveness of these methods in capturing the complex behaviour of heterogeneous thermo-electric materials.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"208 ","pages":"Article 106427"},"PeriodicalIF":6.0,"publicationDate":"2025-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145657139","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}

引用次数: 0