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}
Pub Date : 2025-12-28DOI: 10.1016/j.jmps.2025.106496
Pramod Kumar Patel, Sumit Basu
The intrinsic uniaxial stress-strain response of a glassy amorphous polymer exhibits a set of generic features that determine its toughness under monotonic or cyclic loads. Phenomenological constitutive models successfully mimic these generic features and often insightfully allude to their micromechanical origins. On the other hand, atomistic simulations, notwithstanding their well-known limitations, are also successful in capturing these features using a variety of force fields. This motivates us to delve deeper into these simulations and attempt to identify the micromechanical events that synergistically give rise to these very distinctive features. Especially, we study the roles of the evolution of the free volume and the entanglement network formed by the macromolecules. We show that the small-strain response is largely governed by how free volume proliferates in the material. At larger strains, entanglement slips and disentanglement events decide the extent of plastic strain that will accumulate and the reversibility of the material on unloading. The cohesive strength of the non-bonded interactions between monomers and the energy barrier between torsional flips are the most important underlying features of the force field that affect both evolution of free volume and behaviour of the entanglement network. By perturbing these parameters, we can, control the extent of strain softening, hardening, accumulation of plastic strains and reversibility on unloading. The parameters of the force field, which are determined by the macromolecular architecture, can be used to ‘sculpt’ a targeted stress-strain response.
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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.
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