Pub Date : 2026-02-01Epub Date: 2025-12-03DOI: 10.1016/j.jmps.2025.106468
Zheren Baizhikova , Uba K. Ubamanyu , Fani Derveni , Roberto Ballarini , Pedro M. Reis , Jia-Liang Le
This paper presents a combined computational and analytical investigation on the probability distribution of the knockdown factor of hemispherical shells containing multiple non-interacting localized geometrical defects. In the analytical model, the statistics of the knockdown factor for shells with a single defect are explicitly linked to the statistics of the defect amplitude. The model is then extended to shells with multiple non-interacting defects of random amplitudes through a finite weakest-link formulation, which predicts how the mean and coefficient of variation of the knockdown factor depend on the number of defects on the shell surface. The results of extreme value statistics are further used to derive the limiting form of the knockdown-factor distribution. The analytical investigation is accompanied by a series of stochastic finite element (SFE) simulations of hemispherical shells of different dimensions and with different sizes of the zone containing the defects. The analytical model is shown to be in excellent agreement with the simulation results. The main outcome of the analytical model is a statistical size effect on the knockdown factor, governed by the dimensionless radius, for shells containing the maximum possible number of non-interacting defects. A similar size effect has recently been reported for hemispherical shells with continuous random imperfect surfaces. Together, these results offer a new perspective on the universal statistical role of the dimensionless radius in governing the buckling behavior of geometrically imperfect hemispherical shells.
{"title":"A probabilistic buckling model for hemispherical shells with non-interacting localized defects","authors":"Zheren Baizhikova , Uba K. Ubamanyu , Fani Derveni , Roberto Ballarini , Pedro M. Reis , Jia-Liang Le","doi":"10.1016/j.jmps.2025.106468","DOIUrl":"10.1016/j.jmps.2025.106468","url":null,"abstract":"<div><div>This paper presents a combined computational and analytical investigation on the probability distribution of the knockdown factor of hemispherical shells containing multiple non-interacting localized geometrical defects. In the analytical model, the statistics of the knockdown factor for shells with a single defect are explicitly linked to the statistics of the defect amplitude. The model is then extended to shells with multiple non-interacting defects of random amplitudes through a finite weakest-link formulation, which predicts how the mean and coefficient of variation of the knockdown factor depend on the number of defects on the shell surface. The results of extreme value statistics are further used to derive the limiting form of the knockdown-factor distribution. The analytical investigation is accompanied by a series of stochastic finite element (SFE) simulations of hemispherical shells of different dimensions and with different sizes of the zone containing the defects. The analytical model is shown to be in excellent agreement with the simulation results. The main outcome of the analytical model is a statistical size effect on the knockdown factor, governed by the dimensionless radius, for shells containing the maximum possible number of non-interacting defects. A similar size effect has recently been reported for hemispherical shells with continuous random imperfect surfaces. Together, these results offer a new perspective on the universal statistical role of the dimensionless radius in governing the buckling behavior of geometrically imperfect hemispherical shells.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"208 ","pages":"Article 106468"},"PeriodicalIF":6.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145689711","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-11-24DOI: 10.1016/j.jmps.2025.106430
Guozhan Xia , Renwei Mao , Weiqiu Chen , Yipin Su
This study explores the tunable wrinkling of a magneto-active hydrogel (MAH) block immersed in a tank filled with a magnetic solvent. An electromagnet, with two poles positioned at the top and bottom of the tank, generates a uniform magnetic biasing field via energized coils. Within the framework of nonlinear magneto-elastic theory and non-equilibrium thermodynamics of hydrogels, the mechanical behaviors of small-amplitude wrinkling are modeled, incorporating the influence of external Maxwell stress. By employing the surface impedance matrix method combined with the Stroh formulation, the bifurcation relations governing wrinkling onset are decoupled into symmetric and antisymmetric modes. For the first time, explicit expressions are established in a compact form for compressible soft materials with general free energy functions. As representative examples, generalized neo-Hookean and Gent ideal MAH blocks are examined. Numerical results show that blocks with a smaller permeability than that of the surroundings (i.e., the normalized permeability ), exhibit wrinkling behaviors largely similar to those without an external magnetic field, albeit with minor differences in certain details. Notably, a distinct “mutation” in wrinkling is observed for extremely thick blocks, which is attributed to a geometric constraint associated with the normalized thickness of the block relative to the tank. However, for blocks with higher permeability (), the tensile Maxwell stress significantly destabilizes the system, resulting in distinct wrinkling patterns that differs from those in low-permeability blocks. Intriguingly, wrinkling can emerge during the simultaneous thickening and area expansion of the block, but this phenomenon may be suppressed by geometric constraints. These findings offer valuable insights into the behavior of magneto-active hydrogels, potentially advancing their theoretical understanding and practical applications.
{"title":"Wrinkling mechanics of immersed magneto-active hydrogels","authors":"Guozhan Xia , Renwei Mao , Weiqiu Chen , Yipin Su","doi":"10.1016/j.jmps.2025.106430","DOIUrl":"10.1016/j.jmps.2025.106430","url":null,"abstract":"<div><div>This study explores the tunable wrinkling of a magneto-active hydrogel (MAH) block immersed in a tank filled with a magnetic solvent. An electromagnet, with two poles positioned at the top and bottom of the tank, generates a uniform magnetic biasing field via energized coils. Within the framework of nonlinear magneto-elastic theory and non-equilibrium thermodynamics of hydrogels, the mechanical behaviors of small-amplitude wrinkling are modeled, incorporating the influence of external Maxwell stress. By employing the surface impedance matrix method combined with the Stroh formulation, the bifurcation relations governing wrinkling onset are decoupled into symmetric and antisymmetric modes. For the first time, explicit expressions are established in a compact form for compressible soft materials with general free energy functions. As representative examples, generalized neo-Hookean and Gent ideal MAH blocks are examined. Numerical results show that blocks with a smaller permeability than that of the surroundings (i.e., the normalized permeability <span><math><mrow><mover><mi>μ</mi><mo>¯</mo></mover><mo><</mo><mn>1</mn></mrow></math></span>), exhibit wrinkling behaviors largely similar to those without an external magnetic field, albeit with minor differences in certain details. Notably, a distinct “mutation” in wrinkling is observed for extremely thick blocks, which is attributed to a geometric constraint associated with the normalized thickness of the block relative to the tank. However, for blocks with higher permeability (<span><math><mrow><mover><mi>μ</mi><mo>¯</mo></mover><mo>></mo><mn>1</mn></mrow></math></span>), the tensile Maxwell stress significantly destabilizes the system, resulting in distinct wrinkling patterns that differs from those in low-permeability blocks. Intriguingly, wrinkling can emerge during the simultaneous thickening and area expansion of the block, but this phenomenon may be suppressed by geometric constraints. These findings offer valuable insights into the behavior of magneto-active hydrogels, potentially advancing their theoretical understanding and practical applications.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"208 ","pages":"Article 106430"},"PeriodicalIF":6.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145593063","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: 2025-11-12DOI: 10.1016/j.jmps.2025.106417
Amit Ashkenazi, Adi Shultz, Lee Jordan, Dana Solav
<div><div>Accurate quantification of soft tissue material parameters is essential for tissue mechanics simulations, medical device design, surgical planning, and non-invasive diagnostics. Finite element analysis (FEA) is commonly employed, but generating accurate simulations often requires patient- and location-specific tissue material parameters. Although soft tissue constitutive models are well-developed, practical implementation is limited by the invasive nature of experiments required for fitting model parameters. Non-invasive methods, such as indentation and suction, offer in vivo applicability but typically lack analytical solutions that would allow direct fitting of material parameters. Consequently, parameter identification becomes an inverse problem solved via FEA, which is often ill-posed, yielding multiple sets of seemingly optimal parameters, especially with limited experimental data. This non-uniqueness undermines the reliable prediction of tissue response under varying loads. This study investigates the identifiability of transversely isotropic hyperelastic material parameters through macro-scale indentation, combining simultaneous measurements of force and full-field surface deformation. We use a simplified two-parameter constitutive model to represent a soft composite phantom and compare the homogenized parameters identified through indentation with those obtained from separate analyses of the matrix and fiber materials. Our findings indicate that a measurement error of 5% leads to certainty bounds of <span><math><mrow><mo>±</mo><mn>5</mn><mo>.</mo><mn>2</mn><mtext>%</mtext></mrow></math></span> and <span><math><mrow><mo>±</mo><mn>28</mn><mtext>%</mtext></mrow></math></span> for the isotropic and anisotropic parameters, respectively, when utilizing combined force–deformation data. In contrast, when only force data is considered, they are <span><math><mrow><mo>±</mo><mn>22</mn><mo>.</mo><mn>5</mn><mtext>%</mtext></mrow></math></span> and <span><math><mrow><mo>±</mo><mn>210</mn><mtext>%</mtext></mrow></math></span>, respectively. These results demonstrate that surface deformation measurements are crucial for uniquely identifying anisotropic hyperelastic parameters through indentation. Further research is needed to evaluate identifiability in more complex models and in vivo indentation scenarios.</div><div><strong>Statement of significance</strong></div><div>Understanding how anisotropic soft tissues respond to loads is important for designing better medical devices, improving surgical planning, and developing new diagnostic tools. However, it is challenging to model and quantify the mechanical properties of these tissues without destructive procedures. This study demonstrates that combining indentation tests with 3D imaging to track surface deformations enables the identification of transversely isotropic hyperelastic material parameters with substantially smaller uncertainty compared to standard indentation. These findings can help
{"title":"Indentation-based anisotropic material parameter identifiability: Validation on a synthetic soft tissue phantom","authors":"Amit Ashkenazi, Adi Shultz, Lee Jordan, Dana Solav","doi":"10.1016/j.jmps.2025.106417","DOIUrl":"10.1016/j.jmps.2025.106417","url":null,"abstract":"<div><div>Accurate quantification of soft tissue material parameters is essential for tissue mechanics simulations, medical device design, surgical planning, and non-invasive diagnostics. Finite element analysis (FEA) is commonly employed, but generating accurate simulations often requires patient- and location-specific tissue material parameters. Although soft tissue constitutive models are well-developed, practical implementation is limited by the invasive nature of experiments required for fitting model parameters. Non-invasive methods, such as indentation and suction, offer in vivo applicability but typically lack analytical solutions that would allow direct fitting of material parameters. Consequently, parameter identification becomes an inverse problem solved via FEA, which is often ill-posed, yielding multiple sets of seemingly optimal parameters, especially with limited experimental data. This non-uniqueness undermines the reliable prediction of tissue response under varying loads. This study investigates the identifiability of transversely isotropic hyperelastic material parameters through macro-scale indentation, combining simultaneous measurements of force and full-field surface deformation. We use a simplified two-parameter constitutive model to represent a soft composite phantom and compare the homogenized parameters identified through indentation with those obtained from separate analyses of the matrix and fiber materials. Our findings indicate that a measurement error of 5% leads to certainty bounds of <span><math><mrow><mo>±</mo><mn>5</mn><mo>.</mo><mn>2</mn><mtext>%</mtext></mrow></math></span> and <span><math><mrow><mo>±</mo><mn>28</mn><mtext>%</mtext></mrow></math></span> for the isotropic and anisotropic parameters, respectively, when utilizing combined force–deformation data. In contrast, when only force data is considered, they are <span><math><mrow><mo>±</mo><mn>22</mn><mo>.</mo><mn>5</mn><mtext>%</mtext></mrow></math></span> and <span><math><mrow><mo>±</mo><mn>210</mn><mtext>%</mtext></mrow></math></span>, respectively. These results demonstrate that surface deformation measurements are crucial for uniquely identifying anisotropic hyperelastic parameters through indentation. Further research is needed to evaluate identifiability in more complex models and in vivo indentation scenarios.</div><div><strong>Statement of significance</strong></div><div>Understanding how anisotropic soft tissues respond to loads is important for designing better medical devices, improving surgical planning, and developing new diagnostic tools. However, it is challenging to model and quantify the mechanical properties of these tissues without destructive procedures. This study demonstrates that combining indentation tests with 3D imaging to track surface deformations enables the identification of transversely isotropic hyperelastic material parameters with substantially smaller uncertainty compared to standard indentation. These findings can help","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"208 ","pages":"Article 106417"},"PeriodicalIF":6.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145509551","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: 2025-12-18DOI: 10.1016/j.jmps.2025.106477
Pradeep K. Bal , Adam Ouzeri , Marino Arroyo
Epithelial tissues undergo complex morphogenetic transformations driven by cellular and cytoskeletal dynamics. To understand the emergent tissue mechanics resulting from sub-cellular mechanisms, we formulate a fully nonlinear continuum theory for epithelial shells that coarse-grains an underlying 3D vertex model, whose surfaces are in turn patches of active viscoelastic gel undergoing turnover. Our theory relies on two ingredients. First, we relate the deformation of apical, basal and lateral surfaces of cells to the continuum deformation of the tissue mid-surface and a thickness director field. We explore two variants of the theory, a Cosserat theory accommodating through-thickness tilt of cells, and a Kirchhoff theory assuming that lateral cell surfaces remain perpendicular to the mid-surface. Second, by adopting a variational formalism of irreversible thermodynamics, we construct an effective Rayleighian functional of the tissue constrained by the cellular-continuum kinematic relations, which therefore depends on continuum fields only. This functional allows us to obtain the governing equations of the continuum theory and is the basis for efficient finite element simulations. Verification against explicit 3D cellular model simulations demonstrates the accuracy of the proposed theory in capturing epithelial buckling dynamics. Furthermore, we show that the Cosserat theory is required to model tissues exhibiting apicobasal asymmetry of active tension. Our work provides a general framework for further studies integrating refined subcellular models into continuum descriptions of epithelial mechanobiology.
{"title":"Continuum theory for the mechanics of curved epithelial shells by coarse-graining an ensemble of active gel cellular surfaces","authors":"Pradeep K. Bal , Adam Ouzeri , Marino Arroyo","doi":"10.1016/j.jmps.2025.106477","DOIUrl":"10.1016/j.jmps.2025.106477","url":null,"abstract":"<div><div>Epithelial tissues undergo complex morphogenetic transformations driven by cellular and cytoskeletal dynamics. To understand the emergent tissue mechanics resulting from sub-cellular mechanisms, we formulate a fully nonlinear continuum theory for epithelial shells that coarse-grains an underlying 3D vertex model, whose surfaces are in turn patches of active viscoelastic gel undergoing turnover. Our theory relies on two ingredients. First, we relate the deformation of apical, basal and lateral surfaces of cells to the continuum deformation of the tissue mid-surface and a thickness director field. We explore two variants of the theory, a Cosserat theory accommodating through-thickness tilt of cells, and a Kirchhoff theory assuming that lateral cell surfaces remain perpendicular to the mid-surface. Second, by adopting a variational formalism of irreversible thermodynamics, we construct an effective Rayleighian functional of the tissue constrained by the cellular-continuum kinematic relations, which therefore depends on continuum fields only. This functional allows us to obtain the governing equations of the continuum theory and is the basis for efficient finite element simulations. Verification against explicit 3D cellular model simulations demonstrates the accuracy of the proposed theory in capturing epithelial buckling dynamics. Furthermore, we show that the Cosserat theory is required to model tissues exhibiting apicobasal asymmetry of active tension. Our work provides a general framework for further studies integrating refined subcellular models into continuum descriptions of epithelial mechanobiology.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"208 ","pages":"Article 106477"},"PeriodicalIF":6.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145784913","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: 2025-12-20DOI: 10.1016/j.jmps.2025.106491
Yan Yang , Qifang Zhang , Junjie Liu , Guozheng Kang , Tiejun Wang
Fluid effect on the fracture of hydrogel is of growing interest to the community of soft matter. In this work, we investigate the effect of water redistribution on the fracture of hydrogel in mechanochemical equilibrium state. The impermeable condition (e.g., in oil) and permeable condition (e.g., in water) are considered, which results in different redistributions of water in hydrogels. Here, we derive the general form of J integral incorporating the chemical potential energy of water, and then obtain the analytical forms of J integral for the fracture of hydrogel in oil and water, respectively. Also, we perform finite element calculations and experiments at an extremely large time scale to verify the theoretical predictions. It is found that the J integral of the hydrogel in oil is the sum of two parts: one part from the area under the stress-stretch curve and the other part from the area in water concentration-chemical potential curve. The J integral in oil is amplified by water redistribution, which is obvious for small deformations but becomes negligible for extremely large deformations. The J integral for the hydrogel in water is determined by the area under stress-stretch curve, which is reduced by water redistribution. This work reveals the effect of water redistribution on the fracture of hydrogel, which is fundamental for understanding fracture of hydrogels.
{"title":"Effect of water redistribution on the fracture of hydrogel in mechanochemical equilibrium state","authors":"Yan Yang , Qifang Zhang , Junjie Liu , Guozheng Kang , Tiejun Wang","doi":"10.1016/j.jmps.2025.106491","DOIUrl":"10.1016/j.jmps.2025.106491","url":null,"abstract":"<div><div>Fluid effect on the fracture of hydrogel is of growing interest to the community of soft matter. In this work, we investigate the effect of water redistribution on the fracture of hydrogel in mechanochemical equilibrium state. The impermeable condition (e.g., in oil) and permeable condition (e.g., in water) are considered, which results in different redistributions of water in hydrogels. Here, we derive the general form of <em>J</em> integral incorporating the chemical potential energy of water, and then obtain the analytical forms of <em>J</em> integral for the fracture of hydrogel in oil and water, respectively. Also, we perform finite element calculations and experiments at an extremely large time scale to verify the theoretical predictions. It is found that the <em>J</em> integral of the hydrogel in oil is the sum of two parts: one part from the area under the stress-stretch curve and the other part from the area in water concentration-chemical potential curve. The <em>J</em> integral in oil is amplified by water redistribution, which is obvious for small deformations but becomes negligible for extremely large deformations. The <em>J</em> integral for the hydrogel in water is determined by the area under stress-stretch curve, which is reduced by water redistribution. This work reveals the effect of water redistribution on the fracture of hydrogel, which is fundamental for understanding fracture of hydrogels.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"208 ","pages":"Article 106491"},"PeriodicalIF":6.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145796195","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: 2025-11-22DOI: 10.1016/j.jmps.2025.106431
Hui Li, Shanyong Wang
Phase-field modelling of compressive–shear fracture in anisotropic materials with tension-compression asymmetry remains a major challenge, despite its significance in geomechanics and structural engineering. To this end, a novel hybrid phase-field model with an orthogonality-based strain decomposition is proposed for modelling of mixed-mode brittle fracture in orthotropic/anisotropic materials. In this model, the strain is first mapped into an auxiliary space via the square root of the stiffness (ℂ1/2) and thus is orthogonally decomposed into volumetric tensile, volumetric compressive, and deviatoric parts. The deviatoric strain is further partitioned by spectral decomposition into positive and negative items. This volumetric–deviatoric–spectral strain split results in a fivefold partition of the strain energy. A new driving force is then proposed by combining the Mohr–Coulomb criterion and three fracture energies with the five energy components within the AT1 phase-field finite-element formulation. The present model is validated through 2D tension and shear tests on single-notched plates and 2D/3D compression tests on single-hole plates. It is found that the simulated results agree well with published numerical and experimental data, and the accuracy and capability of the model for modelling mixed-mode fracture in anisotropic materials under shear/compression are well validated.
{"title":"Orthogonality-based energy split for anisotropic compressive-shear brittle fracture: A hybrid phase-field model","authors":"Hui Li, Shanyong Wang","doi":"10.1016/j.jmps.2025.106431","DOIUrl":"10.1016/j.jmps.2025.106431","url":null,"abstract":"<div><div>Phase-field modelling of compressive–shear fracture in anisotropic materials with tension-compression asymmetry remains a major challenge, despite its significance in geomechanics and structural engineering. To this end, a novel hybrid phase-field model with an orthogonality-based strain decomposition is proposed for modelling of mixed-mode brittle fracture in orthotropic/anisotropic materials. In this model, the strain is first mapped into an auxiliary space via the square root of the stiffness (ℂ<sup>1/2</sup>) and thus is orthogonally decomposed into volumetric tensile, volumetric compressive, and deviatoric parts. The deviatoric strain is further partitioned by spectral decomposition into positive and negative items. This <em>volumetric–deviatoric–spectral</em> strain split results in a fivefold partition of the strain energy. A new driving force is then proposed by combining the Mohr–Coulomb criterion and three fracture energies with the five energy components within the AT<sub>1</sub> phase-field finite-element formulation. The present model is validated through 2D tension and shear tests on single-notched plates and 2D/3D compression tests on single-hole plates. It is found that the simulated results agree well with published numerical and experimental data, and the accuracy and capability of the model for modelling mixed-mode fracture in anisotropic materials under shear/compression are well validated.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"208 ","pages":"Article 106431"},"PeriodicalIF":6.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145575504","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: 2025-11-08DOI: 10.1016/j.jmps.2025.106420
Vivek Singh , Kim Pham , Arthur Geromel Fischer , Kostas Danas
This work presents a homogenization framework for modeling the mechanical behavior of three-dimensional linear elastic bodies with a periodically corrugated surface subjected to Dirichlet boundary conditions. The surface microstructure is assumed to be invariant along one spatial direction and periodic along the other. By combining asymptotic homogenization with matched asymptotic expansions near the surface corrugations, we derive an effective interface constitutive model that replaces the corrugated surface and the Dirichlet boundary condition with a flat boundary governed by a mixed (Robin-type) boundary condition. This boundary condition involves a second-order effective tensor, computed from elementary problems set on a representative periodic unit cell, hence allowing to account for the effect of the microstructure on the macroscopic response. We prove the symmetry and positive definiteness of the effective tensor and establish a uniqueness result of the effective problem. The model is assessed by comparison with 2D and 3D full-field simulations, demonstrating excellent agreement in both global and local responses. In particular, a cost-efficient post-processing strategy is proposed to reconstruct the local fields near the corrugations by use of a simple periodic unit cell, providing access to fine-scale information without the need for full-resolution computations.
{"title":"Interfacial homogenization of a periodically corrugated surface in linear elasticity","authors":"Vivek Singh , Kim Pham , Arthur Geromel Fischer , Kostas Danas","doi":"10.1016/j.jmps.2025.106420","DOIUrl":"10.1016/j.jmps.2025.106420","url":null,"abstract":"<div><div>This work presents a homogenization framework for modeling the mechanical behavior of three-dimensional linear elastic bodies with a periodically corrugated surface subjected to Dirichlet boundary conditions. The surface microstructure is assumed to be invariant along one spatial direction and periodic along the other. By combining asymptotic homogenization with matched asymptotic expansions near the surface corrugations, we derive an effective interface constitutive model that replaces the corrugated surface and the Dirichlet boundary condition with a flat boundary governed by a mixed (Robin-type) boundary condition. This boundary condition involves a second-order effective tensor, computed from elementary problems set on a representative periodic unit cell, hence allowing to account for the effect of the microstructure on the macroscopic response. We prove the symmetry and positive definiteness of the effective tensor and establish a uniqueness result of the effective problem. The model is assessed by comparison with 2D and 3D full-field simulations, demonstrating excellent agreement in both global and local responses. In particular, a cost-efficient post-processing strategy is proposed to reconstruct the local fields near the corrugations by use of a simple periodic unit cell, providing access to fine-scale information without the need for full-resolution computations.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"207 ","pages":"Article 106420"},"PeriodicalIF":6.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145461543","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}
The concurrent multi-scale methods for microstructure related macro-cracking face challenges in both physical fidelity and computational efficiency. The physical fidelity issue arises from the fact that few models can simultaneously simulate the spatial-temporal evolution of microstructures (e.g. dislocations, multi-phase) and macro-cracking. The computational efficiency issue stems from the mismatch in scale: spatially each grid of macro-simulation corresponds to the whole domain of a micro-simulation and temporally each time step of macro-simulation may encompass many time steps of micro-simulation. This disparity often results in substantial computational expense. In the present work, we significantly accelerate such simulations by developing a machine learning bridged concurrent multi-scale framework for microstructure-related macro-cracking, while preserving main micro-features. First, we establish a phase-field model to simulate the spatial-temporal co-evolution of microstructures under various stress boundary conditions. These simulations generate the data for machine learning models prior to the micro-macro concurrent multi-scale simulations. Subsequently, the well-established machine learning models efficiently provides micro-information to each macro-grid at every time step of macro-cracking, significantly reducing the computational cost. This enables a bidirectional coupling: the macro-cracking behavior is influenced by local microstructures, while the microstructures are continuously updated as macro-cracking progresses. The framework accommodates arbitrary stress-, strain-, and energy-based macro-cracking criteria. We preliminarily validate its accuracy and effectiveness by simulating microstructure-related macro-cracking during 2D high-temperature deformation of film-hole-structured single-crystal superalloys. Under the complex stress states induced by the film holes, the simulated spatial-temporal microstructure evolution and the resulting macro-cracking behavior exhibit good agreement with experimental observations. The present work highlights the possibility of machine learning to accelerate concurrent multi-scale simulations, while maintaining physical fidelity.
{"title":"A machine learning bridged concurrent multi-scale computational framework for microstructure related macro-cracking","authors":"Ronghai Wu , Yufan Zhang , Jinze Pei , Zanpeng Shangguan , Yuxin Zhang , Lei Zeng , Zichao Peng , Heng Li","doi":"10.1016/j.jmps.2025.106469","DOIUrl":"10.1016/j.jmps.2025.106469","url":null,"abstract":"<div><div>The concurrent multi-scale methods for microstructure related macro-cracking face challenges in both physical fidelity and computational efficiency. The physical fidelity issue arises from the fact that few models can simultaneously simulate the spatial-temporal evolution of microstructures (e.g. dislocations, multi-phase) and macro-cracking. The computational efficiency issue stems from the mismatch in scale: spatially each grid of macro-simulation corresponds to the whole domain of a micro-simulation and temporally each time step of macro-simulation may encompass many time steps of micro-simulation. This disparity often results in substantial computational expense. In the present work, we significantly accelerate such simulations by developing a machine learning bridged concurrent multi-scale framework for microstructure-related macro-cracking, while preserving main micro-features. First, we establish a phase-field model to simulate the spatial-temporal co-evolution of microstructures under various stress boundary conditions. These simulations generate the data for machine learning models prior to the micro-macro concurrent multi-scale simulations. Subsequently, the well-established machine learning models efficiently provides micro-information to each macro-grid at every time step of macro-cracking, significantly reducing the computational cost. This enables a bidirectional coupling: the macro-cracking behavior is influenced by local microstructures, while the microstructures are continuously updated as macro-cracking progresses. The framework accommodates arbitrary stress-, strain-, and energy-based macro-cracking criteria. We preliminarily validate its accuracy and effectiveness by simulating microstructure-related macro-cracking during 2D high-temperature deformation of film-hole-structured single-crystal superalloys. Under the complex stress states induced by the film holes, the simulated spatial-temporal microstructure evolution and the resulting macro-cracking behavior exhibit good agreement with experimental observations. The present work highlights the possibility of machine learning to accelerate concurrent multi-scale simulations, while maintaining physical fidelity.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"208 ","pages":"Article 106469"},"PeriodicalIF":6.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145689698","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: 2025-12-07DOI: 10.1016/j.jmps.2025.106462
M.A. Kumar , T. Virazels , J. García-Molleja , F. Sket , J. A. Rodríguez-Martínez Rodríguez-Martínez , K. Ravi-Chandar
<div><div>In this paper, we have conducted dynamic ring expansion tests on 3D-printed AlSi10Mg porous samples utilizing both electromagnetic and mechanical testing techniques. The electromagnetic loading setup developed by Zhang and Ravi-Chandar (2006, 2008) is employed as a benchmark for evaluating and comparing the performance of the experimental configuration recently proposed by Nieto-Fuentes et al. (2023) to investigate the fragmentation of metallic rings using a pneumatic launcher. A total of 67 experiments have been carried out covering a wide range of strain rates from <span><math><mrow><mn>2200</mn><mspace></mspace><msup><mtext>s</mtext><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math></span> to <span><math><mrow><mn>16300</mn><mspace></mspace><msup><mtext>s</mtext><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math></span>. The tests performed with both experimental techniques were imaged using high-speed cameras to obtain time-resolved information on the mechanics of sample deformation and fragmentation. The recorded data allowed us to determine the number of fragments, the elongation of the specimens at the onset of fracture, and the fragmentation time. Moreover, the fragments ejected from the samples have been soft recovered, measured, and weighed. A good correlation is observed between the results obtained from electromagnetic and mechanical loading setups regarding the fragments size distribution and the evolution of the number of fragments with the loading rate. This agreement serves as a robust validation for the experimental configuration put forth by <span><span>Nieto-Fuentes et al. (2023)</span></span>, which allowed reaching higher strain rates than the setup of <span><span>Zhang and Ravi-Chandar, 2006</span></span>, <span><span>Zhang and Ravi-Chandar, 2008</span></span>, and it is notable for its simplicity, fast operation, and quick assembly. In addition, scanning electron microscopy and X-ray tomography analysis performed on recovered fragments from tests conducted at different expansion velocities with both testing techniques has provided indications on the evolution of the porous microstructure of the material at high strain rates, showing that the porosity of 3D-printed AlSi10Mg is instrumental for the propagation of cracks leading to the fragmentation of the rings. Moreover, fractography analysis of the crack surfaces revealed that while the fractures occurred without the preceding formation of necks, yet the fracture at the microscopic level was essentially ductile. The influence of the porous microstructure on the fragmentation mechanisms has been further investigated through finite element simulations that incorporate the voids’ size distribution of the specimens obtained from X-ray tomography analysis (Marvi-Mashhadi et al., 2021). The numerical results have demonstrated both quantitative and qualitative agreement with the experiments, showing that large pores and clusters favor stress concentration and subs
在本文中，我们利用电磁和机械测试技术对3d打印的AlSi10Mg多孔样品进行了动态环膨胀测试。采用Zhang和Ravi-Chandar（2006, 2008）开发的电磁加载装置作为基准，评估和比较Nieto-Fuentes等人（2023）最近提出的实验配置的性能，以研究使用气动发射器的金属环的破碎。总共进行了67次实验，涵盖了从2200s−1到16300s−1的应变速率范围。使用这两种实验技术进行的测试使用高速摄像机进行成像，以获得关于样品变形和破碎力学的时间分辨信息。记录的数据使我们能够确定碎片的数量，断裂开始时标本的伸长率和碎片时间。此外，从样品中喷射出的碎片已被软回收、测量和称重。在电磁加载和机械加载条件下得到的碎片尺寸分布和碎片数量随加载速率的变化具有良好的相关性。该协议是对Nieto-Fuentes等人（2023）提出的实验配置的有力验证，该实验配置可以达到比Zhang和Ravi-Chandar， 2006， Zhang和Ravi-Chandar， 2008的设置更高的应变速率，并且其简单，快速操作和快速组装值得注意。此外，对两种测试技术在不同膨胀速度下进行的测试中恢复的碎片进行扫描电子显微镜和x射线断层扫描分析，提供了高应变速率下材料多孔微观结构演变的迹象，表明3d打印AlSi10Mg的孔隙率有助于裂纹的扩展，从而导致环的破碎。此外，裂纹表面的断口分析表明，虽然断裂发生时没有预先形成颈，但在微观层面上断裂基本上是延展性的。通过结合x射线断层扫描分析获得的样品的孔隙尺寸分布的有限元模拟，进一步研究了孔隙微观结构对破碎机制的影响（Marvi-Mashhadi et al., 2021）。数值计算结果与实验结果在定性和定量上都一致，表明大孔隙和大簇有利于应力集中，有利于裂缝的萌生和扩展。与Mott（1947）关于弹塑性材料无颈缩断裂的统计碎裂理论一致，从大孔缺陷和早期断裂发出的释放波似乎在确定印刷AlSi10Mg试样中碎裂尺寸分布的规模方面起着关键作用。
{"title":"High-speed fragmentation of porous metal rings","authors":"M.A. Kumar , T. Virazels , J. García-Molleja , F. Sket , J. A. Rodríguez-Martínez Rodríguez-Martínez , K. Ravi-Chandar","doi":"10.1016/j.jmps.2025.106462","DOIUrl":"10.1016/j.jmps.2025.106462","url":null,"abstract":"<div><div>In this paper, we have conducted dynamic ring expansion tests on 3D-printed AlSi10Mg porous samples utilizing both electromagnetic and mechanical testing techniques. The electromagnetic loading setup developed by Zhang and Ravi-Chandar (2006, 2008) is employed as a benchmark for evaluating and comparing the performance of the experimental configuration recently proposed by Nieto-Fuentes et al. (2023) to investigate the fragmentation of metallic rings using a pneumatic launcher. A total of 67 experiments have been carried out covering a wide range of strain rates from <span><math><mrow><mn>2200</mn><mspace></mspace><msup><mtext>s</mtext><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math></span> to <span><math><mrow><mn>16300</mn><mspace></mspace><msup><mtext>s</mtext><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math></span>. The tests performed with both experimental techniques were imaged using high-speed cameras to obtain time-resolved information on the mechanics of sample deformation and fragmentation. The recorded data allowed us to determine the number of fragments, the elongation of the specimens at the onset of fracture, and the fragmentation time. Moreover, the fragments ejected from the samples have been soft recovered, measured, and weighed. A good correlation is observed between the results obtained from electromagnetic and mechanical loading setups regarding the fragments size distribution and the evolution of the number of fragments with the loading rate. This agreement serves as a robust validation for the experimental configuration put forth by <span><span>Nieto-Fuentes et al. (2023)</span></span>, which allowed reaching higher strain rates than the setup of <span><span>Zhang and Ravi-Chandar, 2006</span></span>, <span><span>Zhang and Ravi-Chandar, 2008</span></span>, and it is notable for its simplicity, fast operation, and quick assembly. In addition, scanning electron microscopy and X-ray tomography analysis performed on recovered fragments from tests conducted at different expansion velocities with both testing techniques has provided indications on the evolution of the porous microstructure of the material at high strain rates, showing that the porosity of 3D-printed AlSi10Mg is instrumental for the propagation of cracks leading to the fragmentation of the rings. Moreover, fractography analysis of the crack surfaces revealed that while the fractures occurred without the preceding formation of necks, yet the fracture at the microscopic level was essentially ductile. The influence of the porous microstructure on the fragmentation mechanisms has been further investigated through finite element simulations that incorporate the voids’ size distribution of the specimens obtained from X-ray tomography analysis (Marvi-Mashhadi et al., 2021). The numerical results have demonstrated both quantitative and qualitative agreement with the experiments, showing that large pores and clusters favor stress concentration and subs","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"208 ","pages":"Article 106462"},"PeriodicalIF":6.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145689691","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: 2025-12-03DOI: 10.1016/j.jmps.2025.106464
Qifang Zhang , Junjie Liu , Jinglei Yang , Shaoxing Qu , Guozheng Kang
Hydrogels under stretching can exhibit pronounced deswelling—a phenomenon termed as “inverse poroelasticity”—yet its underlying mechanisms remain indistinct. In this paper, two mechanisms of the inverse poroelasticity of hydrogels are proposed: (1) the finite extensibility of polymer chains, and (2) the unfolding of polymer domains which induces a hydrophilic/hydrophobic transition of polymer chains. A novel constitutive model incorporating the two mechanisms is developed to reproduce the inverse poroelastic behavior of hydrogels. The finite extensibility of polymer chains is captured through the Langevin chain, while the unfolding of polymer domains leads to a varying chain length. Additionally, the hydrophilic/hydrophobic transition is modeled via a newly proposed mixing energy density function. The constitutive model is validated by comparing the results from the model with the experimental data of double network (DN) hydrogels and fibrin hydrogels, both of which exhibit an inverse poroelastic behavior. Furthermore, the proposed constitutive model is applied to investigate the inverse poroelastic fracture of hydrogels through the finite element method. The rate-dependent fracture and delayed fracture of hydrogels with a permeable crack are investigated. It is found that both the rate-dependent fracture and the delayed fracture differ between the hydrogels exhibiting the inverse poroelastic behavior and those displaying the conventional poroelastic behavior. This work deepens the fundamental understanding on the inverse poroelastic behavior of hydrogels and provides insights in designing mechanically robust hydrogels.
{"title":"Exploring the inverse poroelastic behavior of hydrogels: the roles of finite extensibility of polymer chains and unfolding of polymer domains","authors":"Qifang Zhang , Junjie Liu , Jinglei Yang , Shaoxing Qu , Guozheng Kang","doi":"10.1016/j.jmps.2025.106464","DOIUrl":"10.1016/j.jmps.2025.106464","url":null,"abstract":"<div><div>Hydrogels under stretching can exhibit pronounced deswelling—a phenomenon termed as “inverse poroelasticity”—yet its underlying mechanisms remain indistinct. In this paper, two mechanisms of the inverse poroelasticity of hydrogels are proposed: (1) the finite extensibility of polymer chains, and (2) the unfolding of polymer domains which induces a hydrophilic/hydrophobic transition of polymer chains. A novel constitutive model incorporating the two mechanisms is developed to reproduce the inverse poroelastic behavior of hydrogels. The finite extensibility of polymer chains is captured through the Langevin chain, while the unfolding of polymer domains leads to a varying chain length. Additionally, the hydrophilic/hydrophobic transition is modeled via a newly proposed mixing energy density function. The constitutive model is validated by comparing the results from the model with the experimental data of double network (DN) hydrogels and fibrin hydrogels, both of which exhibit an inverse poroelastic behavior. Furthermore, the proposed constitutive model is applied to investigate the inverse poroelastic fracture of hydrogels through the finite element method. The rate-dependent fracture and delayed fracture of hydrogels with a permeable crack are investigated. It is found that both the rate-dependent fracture and the delayed fracture differ between the hydrogels exhibiting the inverse poroelastic behavior and those displaying the conventional poroelastic behavior. This work deepens the fundamental understanding on the inverse poroelastic behavior of hydrogels and provides insights in designing mechanically robust hydrogels.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"208 ","pages":"Article 106464"},"PeriodicalIF":6.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145689713","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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