Pub Date : 2026-01-10DOI: 10.1016/j.jmps.2026.106504
S. Mohammad Mousavi, Jason Mulderrig, Brandon Talamini, Nikolaos Bouklas
This study aims to examine modeling flaw sensitivity in elastomers. The direct incorporation of polymer chain statistical mechanics considerations into a continuum stretch-based gradient-enhanced damage formulation, in turn, allows a representation of diffuse chain damage and fracture events that align with known micromechanical mechanisms. Through a series of numerical experiments, we simulate crack propagation and extract the fracture energy as an output of the model, while keeping track of the micromechanical signatures of diffuse chain damage that accommodate fracture propagation and eventually influence flaw sensitivity. Finally, by combining the fracture toughness and the work to rupture, we identify a fractocohesive length of the material, corresponding to the full width of the damage process zone. As the damage-to-fracture cascade in the proposed GED model is influenced by the the introduction of a length scale associated with network imperfection and long-range load transfer, the emerging relationship of the two length scales is discussed, providing a potential link between microscopic damage mechanisms and the observed macroscopic fracture response.
{"title":"Capturing the fractocohesive length scale in elastomers through a statistical mechanics-based gradient enhanced damage model","authors":"S. Mohammad Mousavi, Jason Mulderrig, Brandon Talamini, Nikolaos Bouklas","doi":"10.1016/j.jmps.2026.106504","DOIUrl":"https://doi.org/10.1016/j.jmps.2026.106504","url":null,"abstract":"This study aims to examine modeling flaw sensitivity in elastomers. The direct incorporation of polymer chain statistical mechanics considerations into a continuum stretch-based gradient-enhanced damage formulation, in turn, allows a representation of diffuse chain damage and fracture events that align with known micromechanical mechanisms. Through a series of numerical experiments, we simulate crack propagation and extract the fracture energy as an output of the model, while keeping track of the micromechanical signatures of diffuse chain damage that accommodate fracture propagation and eventually influence flaw sensitivity. Finally, by combining the fracture toughness and the work to rupture, we identify a fractocohesive length of the material, corresponding to the full width of the damage process zone. As the damage-to-fracture cascade in the proposed GED model is influenced by the the introduction of a length scale associated with network imperfection and long-range load transfer, the emerging relationship of the two length scales is discussed, providing a potential link between microscopic damage mechanisms and the observed macroscopic fracture response.","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"15 1","pages":""},"PeriodicalIF":5.3,"publicationDate":"2026-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145956828","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 : 2026-01-09DOI: 10.1016/j.jmps.2026.106512
Jidu Yu, Jidong Zhao, Weijian Liang
This study presents a hybrid continuum-discrete multiscale computational framework that integrates the material point method (MPM) and the discrete element method (DEM) to model fully coupled thermo-hydro-mechanical-chemical (THMC) behavior of hydrate-bearing sediments (HBS). Key innovation of the framework lies in its direct use of DEM to model microscale mechanisms, such as hydrate bond degradation, particle rearrangement, and pore evolution, thereby bypassing the need for conventional elastoplastic constitutive models to define effective stress. We show that a simple hydrate saturation-dependent contact model within the DEM can effectively reproduce characteristic shear and volumetric responses of HBS under various hydrate saturation and confining stresses. By embedding a DEM-based representative volume element (RVE) at each material point in the MPM grid, microscale mechanical behaviors are seamlessly homogenized to inform large-deformation macroscale multiphysics processes. Numerical simulations of biaxial compression and indenter penetration demonstrate the framework’s capability to capture critical phenomena, including shear band formation, shear-induced dilation, and the generation of negative excess pore pressure that drives localized hydrate dissociation. The results further reveal that while higher hydrate saturation enhances shear strength, it also promotes brittle failure and intensified dissociation. Conversely, increased confining stress suppresses volumetric dilation and stabilizes the sediment by mitigating the development of negative pore pressure. This multiscale approach provides a powerful new tool for elucidating complex THMC interactions in HBS, with important implications for assessing hydrate-related geohazards and optimizing gas extraction strategies.
{"title":"Multiscale Modeling of Coupled Thermo-Hydro-Mechanical-Chemical Behavior in Hydrate-Bearing Sediment","authors":"Jidu Yu, Jidong Zhao, Weijian Liang","doi":"10.1016/j.jmps.2026.106512","DOIUrl":"https://doi.org/10.1016/j.jmps.2026.106512","url":null,"abstract":"This study presents a hybrid continuum-discrete multiscale computational framework that integrates the material point method (MPM) and the discrete element method (DEM) to model fully coupled thermo-hydro-mechanical-chemical (THMC) behavior of hydrate-bearing sediments (HBS). Key innovation of the framework lies in its direct use of DEM to model microscale mechanisms, such as hydrate bond degradation, particle rearrangement, and pore evolution, thereby bypassing the need for conventional elastoplastic constitutive models to define effective stress. We show that a simple hydrate saturation-dependent contact model within the DEM can effectively reproduce characteristic shear and volumetric responses of HBS under various hydrate saturation and confining stresses. By embedding a DEM-based representative volume element (RVE) at each material point in the MPM grid, microscale mechanical behaviors are seamlessly homogenized to inform large-deformation macroscale multiphysics processes. Numerical simulations of biaxial compression and indenter penetration demonstrate the framework’s capability to capture critical phenomena, including shear band formation, shear-induced dilation, and the generation of negative excess pore pressure that drives localized hydrate dissociation. The results further reveal that while higher hydrate saturation enhances shear strength, it also promotes brittle failure and intensified dissociation. Conversely, increased confining stress suppresses volumetric dilation and stabilizes the sediment by mitigating the development of negative pore pressure. This multiscale approach provides a powerful new tool for elucidating complex THMC interactions in HBS, with important implications for assessing hydrate-related geohazards and optimizing gas extraction strategies.","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"10 1","pages":""},"PeriodicalIF":5.3,"publicationDate":"2026-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145956831","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 : 2026-01-05DOI: 10.1016/j.jmps.2026.106501
Adeline Wihardja , Juan Carlos Nieto-Fuentes , Daniel Rittel , Kaushik Bhattacharya
Liquid crystal elastomers are rubbery solids that couple liquid crystalline order and deformation. This coupling leads to properties that are attractive for a number of applications in soft robotics and energy absorption. This paper is motivated by the latter application, and provides a systematic experimental study of a particular class of liquid crystal elastomers – the isotropic genesis polydomain liquid crystal elastomers – over a wide range of strain rates in tension and compression. An important aspect of this study is a novel tensile drop-tower that enables tensile strain rates of 100 s that are important to application but previously inaccessible. The paper also extends a recently proposed constitutive model to the high strain rate regime, and shows that it can be fit to describe the observed behavior across the full spectrum of loading conditions and strain rates examined.
{"title":"High strain rate behavior of liquid crystal elastomers","authors":"Adeline Wihardja , Juan Carlos Nieto-Fuentes , Daniel Rittel , Kaushik Bhattacharya","doi":"10.1016/j.jmps.2026.106501","DOIUrl":"10.1016/j.jmps.2026.106501","url":null,"abstract":"<div><div>Liquid crystal elastomers are rubbery solids that couple liquid crystalline order and deformation. This coupling leads to properties that are attractive for a number of applications in soft robotics and energy absorption. This paper is motivated by the latter application, and provides a systematic experimental study of a particular class of liquid crystal elastomers – the isotropic genesis polydomain liquid crystal elastomers – over a wide range of strain rates in tension and compression. An important aspect of this study is a novel tensile drop-tower that enables tensile strain rates of 100 s<span><math><msup><mrow></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></math></span> that are important to application but previously inaccessible. The paper also extends a recently proposed constitutive model to the high strain rate regime, and shows that it can be fit to describe the observed behavior across the full spectrum of loading conditions and strain rates examined.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"209 ","pages":"Article 106501"},"PeriodicalIF":6.0,"publicationDate":"2026-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145902452","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 : 2026-01-05DOI: 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":"2026-01-05","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}
Pub Date : 2026-01-02DOI: 10.1016/j.jmps.2025.106497
Beijun Shen , Yuefeng Jiang , Christopher M. Yakacki , Sung Hoon Kang , Thao D. Nguyen
Architected materials that exploit buckling to trap energy are effective for impact protection, and their performance can be enhanced by incorporating liquid crystal elastomers (LCEs). Beyond conventional viscoelasticity, LCEs exhibit a highly dissipative, rate-dependent soft stress response in tension associated with mesogen rotation. Because buckling typically occurs at strains below the onset of this soft stress behavior, we introduced an LCE horizontal bar into a hexagonal structure composed of tilted LCE beams. Under compression, stretching of the horizontal bar reduces the angle of the tilted beams and suppresses buckling; however, the viscoelastic softening behavior of LCEs creates the opportunity to design geometries that activate both the buckling of the tilted beams and the large stretching of the horizontal bar. In this work, we characterized the rate-dependent uniaxial tensile response of two monodomain LCE materials with different crosslink densities and used these data to parameterize a nonlinear viscoelastic model for monodomain LCEs implemented in Abaqus/Standard as a user-defined element. Finite element simulations of the compression response of the hexagonal structures showed that energy absorption is maximized at an optimal thickness ratio between the horizontal bar and the tilted beams, which shifts with the relative moduli of the two structural components. This optimized configuration allows the beams to buckle before substantial stretching develops in the bar and absorbs up to 2.5 times the energy of a rigid-bar counterpart, depending on the effective strain rate and material pairing. The same optimized thickness ratio applies to lattices composed of stacked unit cells, which undergo sequential buckling and lateral stretching across adjacent layers. These interactions create local load-unload-reload cycles that increase per-layer dissipation with increasing number of layers and become more pronounced under repeated loading. Together, these results demonstrate that LCE-based lattice structures can be designed to hierarchically nest competing dissipation mechanisms across unit-cell and lattice length scales, providing a new strategy for optimizing energy absorption.
{"title":"Combining stretching-dominated and bending-dominated dissipation behavior to optimize energy absorption in liquid crystal elastomer-based lattice structures","authors":"Beijun Shen , Yuefeng Jiang , Christopher M. Yakacki , Sung Hoon Kang , Thao D. Nguyen","doi":"10.1016/j.jmps.2025.106497","DOIUrl":"10.1016/j.jmps.2025.106497","url":null,"abstract":"<div><div>Architected materials that exploit buckling to trap energy are effective for impact protection, and their performance can be enhanced by incorporating liquid crystal elastomers (LCEs). Beyond conventional viscoelasticity, LCEs exhibit a highly dissipative, rate-dependent soft stress response in tension associated with mesogen rotation. Because buckling typically occurs at strains below the onset of this soft stress behavior, we introduced an LCE horizontal bar into a hexagonal structure composed of tilted LCE beams. Under compression, stretching of the horizontal bar reduces the angle of the tilted beams and suppresses buckling; however, the viscoelastic softening behavior of LCEs creates the opportunity to design geometries that activate both the buckling of the tilted beams and the large stretching of the horizontal bar. In this work, we characterized the rate-dependent uniaxial tensile response of two monodomain LCE materials with different crosslink densities and used these data to parameterize a nonlinear viscoelastic model for monodomain LCEs implemented in Abaqus/Standard as a user-defined element. Finite element simulations of the compression response of the hexagonal structures showed that energy absorption is maximized at an optimal thickness ratio between the horizontal bar and the tilted beams, which shifts with the relative moduli of the two structural components. This optimized configuration allows the beams to buckle before substantial stretching develops in the bar and absorbs up to 2.5 times the energy of a rigid-bar counterpart, depending on the effective strain rate and material pairing. The same optimized thickness ratio applies to lattices composed of stacked unit cells, which undergo sequential buckling and lateral stretching across adjacent layers. These interactions create local load-unload-reload cycles that increase per-layer dissipation with increasing number of layers and become more pronounced under repeated loading. Together, these results demonstrate that LCE-based lattice structures can be designed to hierarchically nest competing dissipation mechanisms across unit-cell and lattice length scales, providing a new strategy for optimizing energy absorption.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"209 ","pages":"Article 106497"},"PeriodicalIF":6.0,"publicationDate":"2026-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145894532","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 : 2026-01-01DOI: 10.1016/j.jmps.2025.106499
Qinghua Zhang , Stephan Ritzert , Jian Zhang , Jannick Kehls , Stefanie Reese , Tim Brepols
In multiphysics damage problems, material degradation is often modeled using local and/or global damage variables, whose evolution introduces strong nonlinearities and significant computational costs. Linear projection-based reduced-order models (ROMs) are widely used to accelerate these simulations but often fail to capture complex nonlinear damage evolution effectively. This limitation arises from the slow decay of the Kolmogorov n-width, which leads to a phenomenon known as the Kolmogorov barrier in linear approximation. To overcome this challenge, this study proposes a novel unified multi-perspective (multi-field and multi-state) quadratic manifold-based ROM framework for thermo-mechanically coupled damage-plasticity problems. A key feature lies in a multi-field and multi-state decomposition strategy that is grounded in the material’s physical response to guide the selection of mode numbers for each coupled field. Moreover, the framework decouples both material states and physical fields, providing clearer insights into the contributions and interactions of each field within the overall multiphysics simulation. Benchmark tests demonstrate that the proposed approach mitigates the Kolmogorov barrier of linear projection-based ROMs by ensuring a smooth and monotonic decrease in error as the number of modes increases. The proposed multi-perspective quadratic manifold framework offers a robust and flexible approach for efficiently reducing complex damage-involved multiphysics problems and shows the potential for industrial applications.
{"title":"A unified multi-perspective quadratic manifold for mitigating the Kolmogorov barrier in multiphysics damage","authors":"Qinghua Zhang , Stephan Ritzert , Jian Zhang , Jannick Kehls , Stefanie Reese , Tim Brepols","doi":"10.1016/j.jmps.2025.106499","DOIUrl":"10.1016/j.jmps.2025.106499","url":null,"abstract":"<div><div>In multiphysics damage problems, material degradation is often modeled using local and/or global damage variables, whose evolution introduces strong nonlinearities and significant computational costs. Linear projection-based reduced-order models (ROMs) are widely used to accelerate these simulations but often fail to capture complex nonlinear damage evolution effectively. This limitation arises from the slow decay of the Kolmogorov <em>n</em>-width, which leads to a phenomenon known as the Kolmogorov barrier in linear approximation. To overcome this challenge, this study proposes a novel unified multi-perspective (multi-field and multi-state) quadratic manifold-based ROM framework for thermo-mechanically coupled damage-plasticity problems. A key feature lies in a multi-field and multi-state decomposition strategy that is grounded in the material’s physical response to guide the selection of mode numbers for each coupled field. Moreover, the framework decouples both material states and physical fields, providing clearer insights into the contributions and interactions of each field within the overall multiphysics simulation. Benchmark tests demonstrate that the proposed approach mitigates the Kolmogorov barrier of linear projection-based ROMs by ensuring a smooth and monotonic decrease in error as the number of modes increases. The proposed multi-perspective quadratic manifold framework offers a robust and flexible approach for efficiently reducing complex damage-involved multiphysics problems and shows the potential for industrial applications.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"209 ","pages":"Article 106499"},"PeriodicalIF":6.0,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145894534","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 : 2025-12-31DOI: 10.1016/j.jmps.2025.106498
Zhengyu Wei, Fan Shi
Elastic wave diffraction is strongly affected by both the finite size and geometric complexity of edges. Previous studies have primarily focused on diffraction from finite straight edges, particularly in applications such as seismic wave exploration, ultrasonic imaging and noise control. However, modeling of elastodynamic diffraction from three-dimensional edges with arbitrary shapes remains underdeveloped, despite its importance in understanding the diffraction behavior of realistic defect geometries for accurate defect characterization. In this work, we develop an edge-segment stationary phase-based theory of diffraction (SPTD) for the accurate calculation of elastic wave diffraction from arbitrarily shaped 3D edges. Conventional edge-diffraction formulations, such as the incremental theory of diffraction (ITD), may suffer from non-physical amplitude fluctuations and even singular behavior when applied to rough or irregular edges, primarily due to the breakdown of the stationary-phase approximation at the elemental edge-segment level. To address this limitation, the proposed SPTD enforces the stationary-phase condition by projecting discretized edge segments onto virtual edges determined by the local diffraction Snell’s law. This formulation effectively suppresses non-physical amplitude fluctuations and singular contributions, thereby significantly improving the accuracy of predictions of diffraction waves. The SPTD model delivers consistently accurate results for a variety of edge geometries, such as straight, elliptical, and sinusoidal shapes, over a broad range of diffraction angles. In addition, the proposed SPTD model is used to examine the limitation of classical modeling methods. Notably, the classical geometrical theory of diffraction (GTD) is rederived within this framework, yielding a refined expression that extends its applicability to finite-length straight and curved edges, though it remains less general than the SPTD model.
{"title":"A stationary phase-based theory of diffraction: Modeling three-dimensional elastic wave diffraction from defect edges with arbitrary shapes","authors":"Zhengyu Wei, Fan Shi","doi":"10.1016/j.jmps.2025.106498","DOIUrl":"10.1016/j.jmps.2025.106498","url":null,"abstract":"<div><div>Elastic wave diffraction is strongly affected by both the finite size and geometric complexity of edges. Previous studies have primarily focused on diffraction from finite straight edges, particularly in applications such as seismic wave exploration, ultrasonic imaging and noise control. However, modeling of elastodynamic diffraction from three-dimensional edges with arbitrary shapes remains underdeveloped, despite its importance in understanding the diffraction behavior of realistic defect geometries for accurate defect characterization. In this work, we develop an edge-segment stationary phase-based theory of diffraction (SPTD) for the accurate calculation of elastic wave diffraction from arbitrarily shaped 3D edges. Conventional edge-diffraction formulations, such as the incremental theory of diffraction (ITD), may suffer from non-physical amplitude fluctuations and even singular behavior when applied to rough or irregular edges, primarily due to the breakdown of the stationary-phase approximation at the elemental edge-segment level. To address this limitation, the proposed SPTD enforces the stationary-phase condition by projecting discretized edge segments onto virtual edges determined by the local diffraction Snell’s law. This formulation effectively suppresses non-physical amplitude fluctuations and singular contributions, thereby significantly improving the accuracy of predictions of diffraction waves. The SPTD model delivers consistently accurate results for a variety of edge geometries, such as straight, elliptical, and sinusoidal shapes, over a broad range of diffraction angles. In addition, the proposed SPTD model is used to examine the limitation of classical modeling methods. Notably, the classical geometrical theory of diffraction (GTD) is rederived within this framework, yielding a refined expression that extends its applicability to finite-length straight and curved edges, though it remains less general than the SPTD model.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"209 ","pages":"Article 106498"},"PeriodicalIF":6.0,"publicationDate":"2025-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145894538","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 : 2025-12-30DOI: 10.1016/j.jmps.2025.106490
Bin Wu , Linghao Kong , Weiqiu Chen , Davide Riccobelli , Michel Destrade
Active control of wrinkling in soft film-substrate composites using electric fields is a critical challenge in tunable material systems. Here, we investigate the electro-mechanical instability of a soft dielectric film bonded to a hyperelastic substrate, revealing the fundamental mechanisms that enable on-demand surface patterning. For the linearized stability analysis, we use the Stroh formalism and the surface impedance method to obtain exact and sixth-order approximate bifurcation equations that signal the onset of wrinkles. We derive the explicit bifurcation equations giving the critical stretch and critical voltage for wrinkling, as well as the corresponding critical wavenumber. We look at scenarios where the voltage is kept constant and the stretch changes, and vice versa. We provide the thresholds of the shear modulus ratio or pre-stretch below which the film-substrate system wrinkles mechanically, prior to the application of a voltage. These predictions offer theoretical guidance for practical structural design, as the shear modulus ratio r and/or the pre-stretch λ can be chosen to be slightly greater than and/or , so that the film-substrate system wrinkles with a small applied voltage. Finally, we simulate the full nonlinear behavior using the Finite Element method (FEniCS) to validate our formulas and conduct a post-buckling analysis. This work advances the fundamental understanding of electro-mechanical wrinkling instabilities in soft material systems. By enabling active control of surface morphologies via applied electric fields, our findings open new avenues for adaptive technologies in soft robotics, flexible electronics, smart surfaces, and bioinspired systems.
{"title":"Electro-mechanical wrinkling of soft dielectric films bonded to hyperelastic substrates","authors":"Bin Wu , Linghao Kong , Weiqiu Chen , Davide Riccobelli , Michel Destrade","doi":"10.1016/j.jmps.2025.106490","DOIUrl":"10.1016/j.jmps.2025.106490","url":null,"abstract":"<div><div>Active control of wrinkling in soft film-substrate composites using electric fields is a critical challenge in tunable material systems. Here, we investigate the electro-mechanical instability of a soft dielectric film bonded to a hyperelastic substrate, revealing the fundamental mechanisms that enable on-demand surface patterning. For the linearized stability analysis, we use the Stroh formalism and the surface impedance method to obtain exact and sixth-order approximate bifurcation equations that signal the onset of wrinkles. We derive the explicit bifurcation equations giving the critical stretch and critical voltage for wrinkling, as well as the corresponding critical wavenumber. We look at scenarios where the voltage is kept constant and the stretch changes, and vice versa. We provide the thresholds of the shear modulus ratio <span><math><msubsup><mi>r</mi><mrow><mrow><mi>c</mi></mrow></mrow><mn>0</mn></msubsup></math></span> or pre-stretch <span><math><msubsup><mi>λ</mi><mrow><mrow><mi>c</mi></mrow></mrow><mn>0</mn></msubsup></math></span> below which the film-substrate system wrinkles mechanically, prior to the application of a voltage. These predictions offer theoretical guidance for practical structural design, as the shear modulus ratio <em>r</em> and/or the pre-stretch <em>λ</em> can be chosen to be slightly greater than <span><math><msubsup><mi>r</mi><mrow><mrow><mi>c</mi></mrow></mrow><mn>0</mn></msubsup></math></span> and/or <span><math><msubsup><mi>λ</mi><mrow><mrow><mi>c</mi></mrow></mrow><mn>0</mn></msubsup></math></span>, so that the film-substrate system wrinkles with a small applied voltage. Finally, we simulate the full nonlinear behavior using the Finite Element method (<span>FEniCS</span>) to validate our formulas and conduct a post-buckling analysis. This work advances the fundamental understanding of electro-mechanical wrinkling instabilities in soft material systems. By enabling active control of surface morphologies via applied electric fields, our findings open new avenues for adaptive technologies in soft robotics, flexible electronics, smart surfaces, and bioinspired systems.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"209 ","pages":"Article 106490"},"PeriodicalIF":6.0,"publicationDate":"2025-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145894540","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 : 2025-12-29DOI: 10.1016/j.jmps.2025.106500
Ziying Yin , Yuxuan Jiang , Yuxi Guo , Jiayi Pu , Shiyu Ma , Guo-Yang Li , Yanping Cao
Tissue viscoelasticity has been recognized as a crucial biomechanical indicator for disease diagnosis and therapeutic monitoring. Conventional shear wave elastography techniques depend on dispersion analysis and face fundamental limitations in clinical scenarios. Particularly, limited wave propagation data with low signal-to-noise ratios, along with challenges in discriminating between dual dispersion sources stemming from viscoelasticity and finite tissue dimensions, pose great difficulties for extracting the dispersion relation. In this study, we introduce SWVE-Net, a framework for shear wave viscoelasticity imaging based on a physics-informed neural network (PINN). SWVE-Net circumvents dispersion analysis by directly incorporating the viscoelasticity wave motion equation into the loss functions of the PINN. Finite element simulations have revealed that SWVE-Net allows for the quantification of viscosity parameters within a wide range (e.g., 0.5 – 5 Pa·s). Remarkably, it can achieve this even for samples as small as a few millimeters, where substantial wave reflections and dispersion take place. Ex vivo experiments have demonstrated the broad applicability of SWVE-Net across various organ types, with shear moduli ranging from 2.13 to 5.96 kPa and viscosities from 1.26 to 2.00 Pa·s. In in vivo human experiments, SWVE-Net quantified breast and skeletal muscle tissues with shear moduli of 4.94 and 2.99 kPa and viscosities of 0.78 and 0.82 Pa·s, respectively. These results highlight the method's robustness under real-world imaging constraints. SWVE-Net overcomes the fundamental limitations of conventional elastography and enables reliable viscoelastic characterization in situations where traditional methods fall short. Therefore, it may have potential applications, for example in grading the severity of hepatic lipid accumulation, detecting myocardial infarction boundaries, and assisting in distinguishing between malignant and benign tumors.
{"title":"Physics-informed neural networks enable quantitative characterization of viscoelastic properties from shear waves in multiple organs","authors":"Ziying Yin , Yuxuan Jiang , Yuxi Guo , Jiayi Pu , Shiyu Ma , Guo-Yang Li , Yanping Cao","doi":"10.1016/j.jmps.2025.106500","DOIUrl":"10.1016/j.jmps.2025.106500","url":null,"abstract":"<div><div>Tissue viscoelasticity has been recognized as a crucial biomechanical indicator for disease diagnosis and therapeutic monitoring. Conventional shear wave elastography techniques depend on dispersion analysis and face fundamental limitations in clinical scenarios. Particularly, limited wave propagation data with low signal-to-noise ratios, along with challenges in discriminating between dual dispersion sources stemming from viscoelasticity and finite tissue dimensions, pose great difficulties for extracting the dispersion relation. In this study, we introduce SWVE-Net, a framework for shear wave viscoelasticity imaging based on a physics-informed neural network (PINN). SWVE-Net circumvents dispersion analysis by directly incorporating the viscoelasticity wave motion equation into the loss functions of the PINN. Finite element simulations have revealed that SWVE-Net allows for the quantification of viscosity parameters within a wide range (e.g., 0.5 – 5 Pa·s). Remarkably, it can achieve this even for samples as small as a few millimeters, where substantial wave reflections and dispersion take place. <em>Ex vivo</em> experiments have demonstrated the broad applicability of SWVE-Net across various organ types, with shear moduli ranging from 2.13 to 5.96 kPa and viscosities from 1.26 to 2.00 Pa·s. In <em>in vivo</em> human experiments, SWVE-Net quantified breast and skeletal muscle tissues with shear moduli of 4.94 and 2.99 kPa and viscosities of 0.78 and 0.82 Pa·s, respectively. These results highlight the method's robustness under real-world imaging constraints. SWVE-Net overcomes the fundamental limitations of conventional elastography and enables reliable viscoelastic characterization in situations where traditional methods fall short. Therefore, it may have potential applications, for example in grading the severity of hepatic lipid accumulation, detecting myocardial infarction boundaries, and assisting in distinguishing between malignant and benign tumors.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"209 ","pages":"Article 106500"},"PeriodicalIF":6.0,"publicationDate":"2025-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145894541","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 : 2025-12-29DOI: 10.1016/j.jmps.2025.106495
Elizabeth Livingston , Siddhartha Srivastava , Jamie Holber , Hashem M. Mourad , Krishna Garikipati
The phase field approach to modeling fracture uses a diffuse damage field to represent cracks. This representation mollifies singularities that arise in computations with sharp interface models and some of the resultant difficulties in the mathematical and numerical treatment of fracture. Phase field fracture models have proven effective at representing crack propagation, branching, and merging. Specific formulations, beginning with brittle fracture, have also been shown to converge to classical solutions. Extensions to cover the range of material failure, including ductile and cohesive fracture, lead to an array of possible models. There exists a large body of literature focusing on this class of models and on the impact of model form on the predicted crack evolution. However, there have not been systematic studies into how optimal models may be chosen. Here, we take a first step in this direction by developing formal methods for identification of the best parsimonious model of phase field fracture given full-field data on the damage and deformation fields. We consider some of the main models that have been used for the degradation of elastic response due to damage and its propagation. Our approach builds upon Variational System Identification (VSI), a weak form variant of the Sparse Identification of Nonlinear Dynamics (SINDy). In this first communication we focus on synthetically generated data but we also consider central issues associated with the use of experimental full-field data, such as data sparsity and noise.
{"title":"Inference of phase field fracture models","authors":"Elizabeth Livingston , Siddhartha Srivastava , Jamie Holber , Hashem M. Mourad , Krishna Garikipati","doi":"10.1016/j.jmps.2025.106495","DOIUrl":"10.1016/j.jmps.2025.106495","url":null,"abstract":"<div><div>The phase field approach to modeling fracture uses a diffuse damage field to represent cracks. This representation mollifies singularities that arise in computations with sharp interface models and some of the resultant difficulties in the mathematical and numerical treatment of fracture. Phase field fracture models have proven effective at representing crack propagation, branching, and merging. Specific formulations, beginning with brittle fracture, have also been shown to converge to classical solutions. Extensions to cover the range of material failure, including ductile and cohesive fracture, lead to an array of possible models. There exists a large body of literature focusing on this class of models and on the impact of model form on the predicted crack evolution. However, there have not been systematic studies into how optimal models may be chosen. Here, we take a first step in this direction by developing formal methods for identification of the best parsimonious model of phase field fracture given full-field data on the damage and deformation fields. We consider some of the main models that have been used for the degradation of elastic response due to damage and its propagation. Our approach builds upon Variational System Identification (VSI), a weak form variant of the Sparse Identification of Nonlinear Dynamics (SINDy). In this first communication we focus on synthetically generated data but we also consider central issues associated with the use of experimental full-field data, such as data sparsity and noise.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"209 ","pages":"Article 106495"},"PeriodicalIF":6.0,"publicationDate":"2025-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145894542","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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