Pub Date : 2026-03-01Epub Date: 2026-01-05DOI: 10.1016/j.jmps.2026.106503
Angelo Amorosi , Yang Yu , Zhongxuan Yang , Fabio Rollo
Clays are natural materials characterised by a nonlinear and irreversible mechanical behaviour that originates from the complex internal microstructure composed by particles often arranged to form clusters. Despite the increasing availability of accurate laboratory techniques to measure the properties of clays at the microscale, most of the existing macroscopic constitutive models disregard their particulate nature, adopting scalar and tensorial variables that are treated as pure mathematical entities aimed at reproducing the mechanical response of this class of materials. In this paper, we develop a new constitutive model formulated within the framework of thermodynamics with internal variables, in which we have selected two scalar internal variables, intra- and inter-cluster void ratios, and a second order fabric tensor, to link the evolution of the porosity and the particles orientation at the microscale with the macroscopic mechanical behaviour of clays. Through a new strategy of initialisation of the internal variables based on direct microscale measurements, and incorporating the two interacting scales of porosity and fabric, the formulation can capture some relevant features of clays behaviour, such as small strain irreversibility, anisotropy and critical state, while maintaining the simplicity and the computational efficiency of a single-surface elasto-plastic model.
{"title":"A micro-informed thermodynamically consistent plasticity model for clays accounting for double porosity and fabric","authors":"Angelo Amorosi , Yang Yu , Zhongxuan Yang , Fabio Rollo","doi":"10.1016/j.jmps.2026.106503","DOIUrl":"10.1016/j.jmps.2026.106503","url":null,"abstract":"<div><div>Clays are natural materials characterised by a nonlinear and irreversible mechanical behaviour that originates from the complex internal microstructure composed by particles often arranged to form clusters. Despite the increasing availability of accurate laboratory techniques to measure the properties of clays at the microscale, most of the existing macroscopic constitutive models disregard their particulate nature, adopting scalar and tensorial variables that are treated as pure mathematical entities aimed at reproducing the mechanical response of this class of materials. In this paper, we develop a new constitutive model formulated within the framework of thermodynamics with internal variables, in which we have selected two scalar internal variables, intra- and inter-cluster void ratios, and a second order fabric tensor, to link the evolution of the porosity and the particles orientation at the microscale with the macroscopic mechanical behaviour of clays. Through a new strategy of initialisation of the internal variables based on direct microscale measurements, and incorporating the two interacting scales of porosity and fabric, the formulation can capture some relevant features of clays behaviour, such as small strain irreversibility, anisotropy and critical state, while maintaining the simplicity and the computational efficiency of a single-surface elasto-plastic model.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"209 ","pages":"Article 106503"},"PeriodicalIF":6.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145897489","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}
As an emerging method for simulating fracture in solids, the variational damage model is currently still mainly limited to the study of brittle fracture. To simulate the quasi-brittle failure of solids, this work proposes an efficient and unified variational damage model (vdczm) within a variational framework, together with its corresponding phase-field model (Tpfczm) that is insensitive to the length scale parameter. Specifically, a crack geometric function associated with the unified phase-field model and a purely geometric rational degradation function are introduced. The introduced constitutive functions are capable of recovering both the classical variational damage model and the phase-field models (including pfczm), thus ensuring the unification of the theoretical framework. This work also demonstrates the specific implementation of incorporating the cohesive zone model into the variational damage framework. The procedure includes deriving an analytical solution for quasi-brittle fracture in the one-dimensional case, based on which an equivalent cohesive zone model is constructed. This equivalent model can accurately reproduce exponential, hyperbolic, and Cornelissen softening laws, and typical constitutive parameters can be obtained by fitting these classical softening laws. Furthermore, this work proposes an efficient hybrid formulation of the unified variational damage model (vdczm), which provides greater advantages in energy decomposition. The effectiveness of the two proposed theories is verified through a series of numerical examples. The results show that both vdczm and Tpfczm are insensitive to mesh size, and Tpfczm is also insensitive to the length scale parameter when it is well resolved by the mesh. The comparison of computational efficiency indicates that vdczm is significantly more efficient than both Tpfczm and pfczm, while Tpfczm is also noticeably more efficient than pfczm.
{"title":"A unified variational damage model and an efficient length scale insensitive phase-field model","authors":"Ya Duan , Huilong Ren , Yehui Bie , Xiaoying Zhuang , Timon Rabczuk","doi":"10.1016/j.jmps.2025.106494","DOIUrl":"10.1016/j.jmps.2025.106494","url":null,"abstract":"<div><div>As an emerging method for simulating fracture in solids, the variational damage model is currently still mainly limited to the study of brittle fracture. To simulate the quasi-brittle failure of solids, this work proposes an efficient and unified variational damage model (vdczm) within a variational framework, together with its corresponding phase-field model (Tpfczm) that is insensitive to the length scale parameter. Specifically, a crack geometric function associated with the unified phase-field model and a purely geometric rational degradation function are introduced. The introduced constitutive functions are capable of recovering both the classical variational damage model and the phase-field models (including pfczm), thus ensuring the unification of the theoretical framework. This work also demonstrates the specific implementation of incorporating the cohesive zone model into the variational damage framework. The procedure includes deriving an analytical solution for quasi-brittle fracture in the one-dimensional case, based on which an equivalent cohesive zone model is constructed. This equivalent model can accurately reproduce exponential, hyperbolic, and Cornelissen softening laws, and typical constitutive parameters can be obtained by fitting these classical softening laws. Furthermore, this work proposes an efficient hybrid formulation of the unified variational damage model (vdczm), which provides greater advantages in energy decomposition. The effectiveness of the two proposed theories is verified through a series of numerical examples. The results show that both vdczm and Tpfczm are insensitive to mesh size, and Tpfczm is also insensitive to the length scale parameter when it is well resolved by the mesh. The comparison of computational efficiency indicates that vdczm is significantly more efficient than both Tpfczm and pfczm, while Tpfczm is also noticeably more efficient than pfczm.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"208 ","pages":"Article 106494"},"PeriodicalIF":6.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145845100","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}
Pub Date : 2026-02-01Epub Date: 2025-12-23DOI: 10.1016/j.jmps.2025.106493
Juan Michael Sargado, Joachim Mathiesen
The enforcement of global energy conservation in phase-field fracture simulations has been an open problem for the last 25 years. Specifically, the occurrence of unstable fracture is accompanied by a loss in total potential energy, which suggests a violation of the energy conservation law. This phenomenon can occur even with purely quasi-static, displacement-driven loading conditions, where finite crack growth arises from an infinitesimal increase in load. While such behavior is typically seen in crack nucleation, it may also occur in other situations. Initial efforts to enforce energy conservation involved backtracking schemes based on global minimization, however in recent years it has become clearer that unstable fracture, being an inherently dynamic phenomenon, cannot be adequately resolved within a purely quasi-static framework. Despite this, it remains uncertain whether transitioning to a fully dynamic framework would sufficiently address the issue. In this work, we propose a pseudo-dynamic framework designed to enforce energy balance without relying on global minimization. This approach incorporates dynamic effects heuristically into an otherwise quasi-static model, allowing us to bypass solving the full dynamic linear momentum equation. It offers the flexibility to simulate crack evolution along a spectrum, ranging from full energy conservation at one extreme to maximal energy loss at the other. Using data from recent experiments, we demonstrate that our framework can closely replicate experimental load-displacement curves, achieving results that are unattainable with classical phase-field models.
{"title":"A pseudo-dynamic phase-field model for brittle fracture","authors":"Juan Michael Sargado, Joachim Mathiesen","doi":"10.1016/j.jmps.2025.106493","DOIUrl":"10.1016/j.jmps.2025.106493","url":null,"abstract":"<div><div>The enforcement of global energy conservation in phase-field fracture simulations has been an open problem for the last 25 years. Specifically, the occurrence of unstable fracture is accompanied by a loss in total potential energy, which suggests a violation of the energy conservation law. This phenomenon can occur even with purely quasi-static, displacement-driven loading conditions, where finite crack growth arises from an infinitesimal increase in load. While such behavior is typically seen in crack nucleation, it may also occur in other situations. Initial efforts to enforce energy conservation involved backtracking schemes based on global minimization, however in recent years it has become clearer that unstable fracture, being an inherently dynamic phenomenon, cannot be adequately resolved within a purely quasi-static framework. Despite this, it remains uncertain whether transitioning to a fully dynamic framework would sufficiently address the issue. In this work, we propose a pseudo-dynamic framework designed to enforce energy balance without relying on global minimization. This approach incorporates dynamic effects heuristically into an otherwise quasi-static model, allowing us to bypass solving the full dynamic linear momentum equation. It offers the flexibility to simulate crack evolution along a spectrum, ranging from full energy conservation at one extreme to maximal energy loss at the other. Using data from recent experiments, we demonstrate that our framework can closely replicate experimental load-displacement curves, achieving results that are unattainable with classical phase-field models.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"208 ","pages":"Article 106493"},"PeriodicalIF":6.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145823047","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}
Pub Date : 2026-02-01Epub Date: 2025-12-12DOI: 10.1016/j.jmps.2025.106478
Xin Liu , Hyunsoo Lee , Yang Li , Liam Myhill , David Rodney , Pierre-Antoine Geslin , Nikhil Chandra Admal , Giacomo Po , Enrique Martinez , Yinan Cui
Multi-principal element alloys (MPEAs) continue to attract considerable attention. However, one fundamental question regarding their plasticity remains far from well understood, namely, how the nanoscale heterogeneity and chemical short-range order (SRO) control dislocation motion and plasticity. Different from previous studies incorporating statistical variations of the energy landscape into full dislocation dynamics, the current work proposes an innovative atomistically informed partial dislocation dynamics (PDD) method, which directly considers the spatially-correlated non-uniform planar fault energy (PFE) at the atomic scale, and at the same time benefits from the larger temporal and spatial scales of the dislocation dynamics methods. Through systematic analysis, we find that the PFE field exhibits a negative correlation along the atomic slip direction, which reduces the critical stress required for dislocation motion in that direction. In contrast, the correlation characteristics along other directions can be approximated as uncorrelated noise, which also contributes to strengthening. In addition, it is found that SRO only slightly enhances the correlation strength along certain crystallographic directions, while it weakens the degree of negative correlation along the slip direction. Overall, the increase in the mean PFE induced by SRO significantly contributes to the strengthening of the dislocation depinning transition. The proposed model provides new opportunities for designing MPEAs with tailored macroscopic mechanical properties by manipulating their atomic distribution and spatial correlations.
{"title":"Atomistically informed partial dislocation dynamics of multi-principal element alloys","authors":"Xin Liu , Hyunsoo Lee , Yang Li , Liam Myhill , David Rodney , Pierre-Antoine Geslin , Nikhil Chandra Admal , Giacomo Po , Enrique Martinez , Yinan Cui","doi":"10.1016/j.jmps.2025.106478","DOIUrl":"10.1016/j.jmps.2025.106478","url":null,"abstract":"<div><div>Multi-principal element alloys (MPEAs) continue to attract considerable attention. However, one fundamental question regarding their plasticity remains far from well understood, namely, how the nanoscale heterogeneity and chemical short-range order (SRO) control dislocation motion and plasticity. Different from previous studies incorporating statistical variations of the energy landscape into full dislocation dynamics, the current work proposes an innovative atomistically informed partial dislocation dynamics (PDD) method, which directly considers the spatially-correlated non-uniform planar fault energy (PFE) at the atomic scale, and at the same time benefits from the larger temporal and spatial scales of the dislocation dynamics methods. Through systematic analysis, we find that the PFE field exhibits a negative correlation along the atomic slip direction, which reduces the critical stress required for dislocation motion in that direction. In contrast, the correlation characteristics along other directions can be approximated as uncorrelated noise, which also contributes to strengthening. In addition, it is found that SRO only slightly enhances the correlation strength along certain crystallographic directions, while it weakens the degree of negative correlation along the slip direction. Overall, the increase in the mean PFE induced by SRO significantly contributes to the strengthening of the dislocation depinning transition. The proposed model provides new opportunities for designing MPEAs with tailored macroscopic mechanical properties by manipulating their atomic distribution and spatial correlations.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"208 ","pages":"Article 106478"},"PeriodicalIF":6.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145731147","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}
Pub Date : 2026-02-01Epub Date: 2025-11-23DOI: 10.1016/j.jmps.2025.106445
Dinghuai Yang , Zhichao Liu , Jian Cheng , Mingjun Chen , Linjie Zhao , Shengfei Wang , Feng Geng , Yazhou Sun , Qiao Xu
Spallation and thermal damage limit the application of fused silica under extremely intense lasers. Herein, the unclear underlying mechanisms, including extreme-irradiation-induced plasticity-related behaviors were studied based on first-constructed cross-scale models, molecular dynamics simulation, and multimodal characterization. Material spallation originated from the anomalous “quasiplasticity” and phased propagation of micro-cracks under quadruplex elastoplastic waves. Although the fastest primary wave could not cause macroscopic deformation, it could lead to micro-plasticity phenomena (ring-structure transformation and point-defect proliferation) due to material phase transformation and destabilizing effects. Subsequently, conjugate secondary and head elastoplastic waves governed initialization processes of micro-cracks, where primary-wave-induced E’-Center and NBOHC defects played roles of “damage precursors”. Concomitantly, transitional deformation zones containing massive strip-like-distributed cavities (similar to “immature” micro-cracks) were generated around micro-cracks. There was a cascading evolution process of point defects, cavities, and micro-cracks under phased energy input from waves, causing an anomalous “quasiplasticity” process within brittle fused silica. It differs from transient fracture processes of brittle materials. Finally, the Rayleigh waves trapped on surfaces attracted micro-cracks towards them, causing disastrous surface damage. The thermal damage originated from the volcanic vents formed within 3∼4 ns, which was induced under the comprehensive action of the impact of elastoplastic waves, cascading solid-liquid-gas phase transition, GPa-level pressure difference between ablated zones and air, and fluidic flow disturbances. The whole time-evolution sequence axis diagram of the material failure process was drawn based on these. Summarily, this work could offer novel insights into the anomalous “quasiplasticity”, spallation, and thermal damage phenomena of fused silica under intense lasers.
{"title":"Anomalous quasiplasticity, spallation, and thermal damage in fused silica under laser-induced quadruple stress waves and multi-field coupling effects","authors":"Dinghuai Yang , Zhichao Liu , Jian Cheng , Mingjun Chen , Linjie Zhao , Shengfei Wang , Feng Geng , Yazhou Sun , Qiao Xu","doi":"10.1016/j.jmps.2025.106445","DOIUrl":"10.1016/j.jmps.2025.106445","url":null,"abstract":"<div><div>Spallation and thermal damage limit the application of fused silica under extremely intense lasers. Herein, the unclear underlying mechanisms, including extreme-irradiation-induced plasticity-related behaviors were studied based on first-constructed cross-scale models, molecular dynamics simulation, and multimodal characterization. Material spallation originated from the anomalous “quasiplasticity” and phased propagation of micro-cracks under quadruplex elastoplastic waves. Although the fastest primary wave could not cause macroscopic deformation, it could lead to micro-plasticity phenomena (ring-structure transformation and point-defect proliferation) due to material phase transformation and destabilizing effects. Subsequently, conjugate secondary and head elastoplastic waves governed initialization processes of micro-cracks, where primary-wave-induced E’-Center and NBOHC defects played roles of “damage precursors”. Concomitantly, transitional deformation zones containing massive strip-like-distributed cavities (similar to “immature” micro-cracks) were generated around micro-cracks. There was a cascading evolution process of point defects, cavities, and micro-cracks under phased energy input from waves, causing an anomalous “quasiplasticity” process within brittle fused silica. It differs from transient fracture processes of brittle materials. Finally, the Rayleigh waves trapped on surfaces attracted micro-cracks towards them, causing disastrous surface damage. The thermal damage originated from the volcanic vents formed within 3∼4 ns, which was induced under the comprehensive action of the impact of elastoplastic waves, cascading solid-liquid-gas phase transition, GPa-level pressure difference between ablated zones and air, and fluidic flow disturbances. The whole time-evolution sequence axis diagram of the material failure process was drawn based on these. Summarily, this work could offer novel insights into the anomalous “quasiplasticity”, spallation, and thermal damage phenomena of fused silica under intense lasers.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"208 ","pages":"Article 106445"},"PeriodicalIF":6.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145575496","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}
Liquid crystal elastomers (LCEs) combine the anisotropic self-ordering behavior of liquid crystals with the dissipative viscoelastic behavior of elastomers. This combination produces unique behaviors, including a large strain response to cooling past the nematic–isotropic transition temperature, rate-dependent soft stress response, and enhanced dissipation compared to traditional elastomers. To capture these phenomena, we develop a finite-deformation viscoelastic micro-stretch theory for monodomain nematic elastomers, which describes the coupled mechanisms of viscous mesogen ordering, viscous director rotation, and viscoelastic network deformation. We then specialize the general theory to model the thermomechanical behavior of uniaxial nematic elastomers, and examine its predictions through material-point and boundary-value computations. The latter employs a finite element framework that includes the Frank-like energy terms. The numerical examples explore the thermal deformation response to temperature cycling across the nematic–isotropic transition at different temperature scan rates and mechanical pre-loads, as well as the isothermal uniaxial tension stress response. We further present new experimental results that investigate the effect of mechanical loading on thermally driven phase transformations. These experiments reveal an unexpected phenomenon wherein samples cooled into the nematic state under a perpendicular pre-load exhibit a dramatic mode switch in their anisotropic thermal deformation response. The proposed model successfully predicts this effect and further provides a plausible microstructural explanation. Altogether, these studies demonstrate the rich and complex phenomena that emerge from the full coupling of the evolving scalar order parameter, rotating director, and mechanical deformation.
{"title":"A viscoelastic micro-stretch theory for monodomain nematic liquid crystal elastomers","authors":"Yuefeng Jiang , Zengting Xu , Rui Xiao , Sanjay Govindjee , Thao D. Nguyen","doi":"10.1016/j.jmps.2025.106412","DOIUrl":"10.1016/j.jmps.2025.106412","url":null,"abstract":"<div><div>Liquid crystal elastomers (LCEs) combine the anisotropic self-ordering behavior of liquid crystals with the dissipative viscoelastic behavior of elastomers. This combination produces unique behaviors, including a large strain response to cooling past the nematic–isotropic transition temperature, rate-dependent soft stress response, and enhanced dissipation compared to traditional elastomers. To capture these phenomena, we develop a finite-deformation viscoelastic micro-stretch theory for monodomain nematic elastomers, which describes the coupled mechanisms of viscous mesogen ordering, viscous director rotation, and viscoelastic network deformation. We then specialize the general theory to model the thermomechanical behavior of uniaxial nematic elastomers, and examine its predictions through material-point and boundary-value computations. The latter employs a finite element framework that includes the Frank-like energy terms. The numerical examples explore the thermal deformation response to temperature cycling across the nematic–isotropic transition at different temperature scan rates and mechanical pre-loads, as well as the isothermal uniaxial tension stress response. We further present new experimental results that investigate the effect of mechanical loading on thermally driven phase transformations. These experiments reveal an unexpected phenomenon wherein samples cooled into the nematic state under a perpendicular pre-load exhibit a dramatic mode switch in their anisotropic thermal deformation response. The proposed model successfully predicts this effect and further provides a plausible microstructural explanation. Altogether, these studies demonstrate the rich and complex phenomena that emerge from the full coupling of the evolving scalar order parameter, rotating director, and mechanical deformation.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"207 ","pages":"Article 106412"},"PeriodicalIF":6.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145442031","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}
Pub Date : 2026-02-01Epub Date: 2025-11-29DOI: 10.1016/j.jmps.2025.106459
Qiancheng Ren , Yilan Xu , Jinglan Liu , Xiaochu Chen , Qi Yang , Jiayuan Fang , Pei Zhao
The evolution of a solid interface from coupling to friction and its mechanisms still face challenges. Here, we use large-twist-angle bilayer graphene combined with isotope-labeling-assisted Raman spectroscopy to measure the mechanical behaviors of its two layers from coupling to friction. Results show that as the strain of the bottom graphene layer increases, the interfacial interaction gradually weakens from the edge region and finally achieves the superlubricity state. A modified multi-adhesive shear-lag model is established based on the experiments, and its numerical analysis supports the experimental data. Molecular simulations demonstrate that after a critical strain, the interfacial force of large-twist-angle bilayer graphene decreases rapidly to enter the multiple adhesive state and finally stabilizes for friction, attributed to the generation and movements of interfacial dislocations, which reduce the interfacial interaction and promote the layer sliding.
{"title":"Transition from coupling to friction at the interface of large-twist-angle bilayer graphene","authors":"Qiancheng Ren , Yilan Xu , Jinglan Liu , Xiaochu Chen , Qi Yang , Jiayuan Fang , Pei Zhao","doi":"10.1016/j.jmps.2025.106459","DOIUrl":"10.1016/j.jmps.2025.106459","url":null,"abstract":"<div><div>The evolution of a solid interface from coupling to friction and its mechanisms still face challenges. Here, we use large-twist-angle bilayer graphene combined with isotope-labeling-assisted Raman spectroscopy to measure the mechanical behaviors of its two layers from coupling to friction. Results show that as the strain of the bottom graphene layer increases, the interfacial interaction gradually weakens from the edge region and finally achieves the superlubricity state. A modified multi-adhesive shear-lag model is established based on the experiments, and its numerical analysis supports the experimental data. Molecular simulations demonstrate that after a critical strain, the interfacial force of large-twist-angle bilayer graphene decreases rapidly to enter the multiple adhesive state and finally stabilizes for friction, attributed to the generation and movements of interfacial dislocations, which reduce the interfacial interaction and promote the layer sliding.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"208 ","pages":"Article 106459"},"PeriodicalIF":6.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145614043","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}
Pub Date : 2026-02-01Epub Date: 2025-11-14DOI: 10.1016/j.jmps.2025.106424
F. Vicentini, J. Heinzmann, P. Carrara, L. De Lorenzis
Variational phase-field models of brittle fracture are powerful tools for studying Griffith-type crack propagation in complex scenarios. However, as approximations of Griffith’s theory — which does not incorporate a strength criterion — these models lack flexibility in prescribing material-specific strength surfaces. Consequently, they struggle to accurately capture crack nucleation under multiaxial stress conditions. In this paper, inspired by Alessi et al. (2014), we propose a variational phase-field model that approximates cohesive fracture. The model accommodates an arbitrary (convex) strength surface, independent of the regularization length scale, and allows for flexible tuning of the cohesive response. Our formulation results in sharp cohesive cracks and naturally enforces a sharp non-interpenetration condition, thereby eliminating the need for additional energy decomposition strategies. It inherently satisfies stress softening and produces ”crack-like” residual stresses by construction. To ensure strain hardening, the ratio of the regularization length to the material’s cohesive length must be sufficiently small; however, if crack nucleation is desired, this ratio must also be large enough to make the homogeneous damaged state unstable. We investigate the model in one and three dimensions, establishing first- and second-order stability results. The theoretical findings are validated through numerical simulations using the finite element method, employing standard discretization and solution techniques.
脆性断裂的变分相场模型是研究复杂情况下griffith型裂纹扩展的有力工具。然而，作为格里菲斯理论的近似值（不包含强度标准），这些模型在规定材料特定强度表面方面缺乏灵活性。因此，他们很难准确地捕捉多轴应力条件下的裂纹形核。在本文中，受Alessi et al.（2014）的启发，我们提出了一个近似于内聚断裂的变分相场模型。该模型可容纳任意（凸）强度表面，独立于正则化长度尺度，并允许灵活调整内聚响应。我们的配方产生尖锐的粘性裂缝，并自然地强制执行尖锐的非相互渗透条件，从而消除了对额外能量分解策略的需要。它本质上满足应力软化，并通过施工产生“裂纹状”残余应力。为保证应变硬化，正则化长度与材料内聚长度之比必须足够小；然而，如果想要裂纹成核，这个比率也必须足够大，以使均匀损伤状态不稳定。我们在一维和三维上研究了模型，建立了一阶和二阶稳定性结果。采用有限元方法，采用标准离散化和求解技术，通过数值模拟验证了理论结果。
{"title":"Variational phase-field modeling of cohesive fracture with flexibly tunable strength surface","authors":"F. Vicentini, J. Heinzmann, P. Carrara, L. De Lorenzis","doi":"10.1016/j.jmps.2025.106424","DOIUrl":"10.1016/j.jmps.2025.106424","url":null,"abstract":"<div><div>Variational phase-field models of brittle fracture are powerful tools for studying Griffith-type crack propagation in complex scenarios. However, as approximations of Griffith’s theory — which does not incorporate a strength criterion — these models lack flexibility in prescribing material-specific strength surfaces. Consequently, they struggle to accurately capture crack nucleation under multiaxial stress conditions. In this paper, inspired by Alessi et al. (2014), we propose a variational phase-field model that approximates cohesive fracture. The model accommodates an arbitrary (convex) strength surface, independent of the regularization length scale, and allows for flexible tuning of the cohesive response. Our formulation results in sharp cohesive cracks and naturally enforces a sharp non-interpenetration condition, thereby eliminating the need for additional energy decomposition strategies. It inherently satisfies stress softening and produces ”crack-like” residual stresses by construction. To ensure strain hardening, the ratio of the regularization length to the material’s cohesive length must be sufficiently small; however, if crack nucleation is desired, this ratio must also be large enough to make the homogeneous damaged state unstable. We investigate the model in one and three dimensions, establishing first- and second-order stability results. The theoretical findings are validated through numerical simulations using the finite element method, employing standard discretization and solution techniques.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"207 ","pages":"Article 106424"},"PeriodicalIF":6.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145545471","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}
Pub Date : 2026-02-01Epub Date: 2025-11-17DOI: 10.1016/j.jmps.2025.106428
Yang Zhao , Anh T. Nguyen , Hoang T. Nguyen , Zdeněk P. Bažant
The geological genesis of natural cracks in sedimentary rocks such as shale is a problem that needs to be understood to improve the technology of hydraulic fracturing as well as deep sequestration of harmful fluids. Why are the vertical natural cracks roughly parallel and equidistant, and why is the spacing roughly 10 cm rather than 1 cm or 100 cm? Fracture mechanics of critical cracks cannot answer this question. Neither can the material heterogeneity. The growth of critical parallel cracks is impossible because the relative crack face displacements would immediately localize into one crack, leading to an earthquake. The cracks must have formed, on the tectonic time scale, by a slow growth of subcritical shear cracks governed by the Charles-Evans law. The idea advanced here is that what controls the crack spacing is the balance between the reduction, due to shear dilatancy, of the concentration of ions such as Na and Cl in each fracture process zone (PFZ), which decelerates the cracks, and the restoration of ion concentration by diffusion of ions from the space between the cracks into the FPZ. This diffusion of water is driven mainly by the osmotic pressure gradient, which offsets the deceleration and depends strongly on the crack spacing. A simple analytical solution of the steady state is rendered possible by approximating the ion concentration profiles between adjacent cracks by parabolic arcs. Applying this theory to Woodford shale yields the approximate crack spacing of 10 cm, which is realistic. The stability of unlimited parallel mode II frictional crack growth is proven by examining the second variation of the free energy. Water concentration drop in the FPZ due to shear dilatancy and its restoration by water diffusion from the inter-crack space have similar effect, although probably much weaker.
{"title":"Osmotic control of the spacing of parallel shear cracks in shale growing subcritically in geologic past","authors":"Yang Zhao , Anh T. Nguyen , Hoang T. Nguyen , Zdeněk P. Bažant","doi":"10.1016/j.jmps.2025.106428","DOIUrl":"10.1016/j.jmps.2025.106428","url":null,"abstract":"<div><div>The geological genesis of natural cracks in sedimentary rocks such as shale is a problem that needs to be understood to improve the technology of hydraulic fracturing as well as deep sequestration of harmful fluids. Why are the vertical natural cracks roughly parallel and equidistant, and why is the spacing roughly 10 cm rather than 1 cm or 100 cm? Fracture mechanics of critical cracks cannot answer this question. Neither can the material heterogeneity. The growth of critical parallel cracks is impossible because the relative crack face displacements would immediately localize into one crack, leading to an earthquake. The cracks must have formed, on the tectonic time scale, by a slow growth of subcritical shear cracks governed by the Charles-Evans law. The idea advanced here is that what controls the crack spacing is the balance between the reduction, due to shear dilatancy, of the concentration of ions such as Na<span><math><msup><mrow></mrow><mrow><mo>+</mo></mrow></msup></math></span> and Cl<span><math><msup><mrow></mrow><mrow><mo>−</mo></mrow></msup></math></span> in each fracture process zone (PFZ), which decelerates the cracks, and the restoration of ion concentration by diffusion of ions from the space between the cracks into the FPZ. This diffusion of water is driven mainly by the osmotic pressure gradient, which offsets the deceleration and depends strongly on the crack spacing. A simple analytical solution of the steady state is rendered possible by approximating the ion concentration profiles between adjacent cracks by parabolic arcs. Applying this theory to Woodford shale yields the approximate crack spacing of 10 cm, which is realistic. The stability of unlimited parallel mode II frictional crack growth is proven by examining the second variation of the free energy. Water concentration drop in the FPZ due to shear dilatancy and its restoration by water diffusion from the inter-crack space have similar effect, although probably much weaker.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"207 ","pages":"Article 106428"},"PeriodicalIF":6.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145546347","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}
Pub Date : 2026-02-01Epub Date: 2025-12-23DOI: 10.1016/j.jmps.2025.106492
Changyi Yang , Jidong Zhao , Fan Zhu
This paper presents a thermo-hydrodynamic-mechanical (THM) peridynamics (PD) method for thermal fluid-solid interaction (FSI) involving fracturing in solids. Both fluid and solid materials are treated using the PD formulation. For solids, we employ a total-Lagrangian description consistent with classical PD, while for fluids, we develop a semi-Lagrangian approach with non-local operators to solve the Navier-Stokes equations under large deformations. The coupling method is achieved through a simple yet efficient two-way fictitious point method, ensuring accurate thermal and mechanical coupling across moving interfaces as discontinuities evolve. This approach also facilitates fluid flow through openings between crack surfaces. The THM PD framework is validated through various multi-physics simulations, including natural and mixed convection, quenching processes, and the injection of cold water into hot dry rock. These examples demonstrate its robust capabilities for modeling complex thermal FSI problems with evolving discontinuities. This framework bridges the application gap of PD in solids and fluids, allowing us to solve multi-physics problems using a single solver.
{"title":"Coupled thermo-hydrodynamic-mechanical peridynamics for thermal fluid-solid interactions with fracturing","authors":"Changyi Yang , Jidong Zhao , Fan Zhu","doi":"10.1016/j.jmps.2025.106492","DOIUrl":"10.1016/j.jmps.2025.106492","url":null,"abstract":"<div><div>This paper presents a thermo-hydrodynamic-mechanical (THM) peridynamics (PD) method for thermal fluid-solid interaction (FSI) involving fracturing in solids. Both fluid and solid materials are treated using the PD formulation. For solids, we employ a total-Lagrangian description consistent with classical PD, while for fluids, we develop a semi-Lagrangian approach with non-local operators to solve the Navier-Stokes equations under large deformations. The coupling method is achieved through a simple yet efficient two-way fictitious point method, ensuring accurate thermal and mechanical coupling across moving interfaces as discontinuities evolve. This approach also facilitates fluid flow through openings between crack surfaces. The THM PD framework is validated through various multi-physics simulations, including natural and mixed convection, quenching processes, and the injection of cold water into hot dry rock. These examples demonstrate its robust capabilities for modeling complex thermal FSI problems with evolving discontinuities. This framework bridges the application gap of PD in solids and fluids, allowing us to solve multi-physics problems using a single solver.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"208 ","pages":"Article 106492"},"PeriodicalIF":6.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145823048","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}
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