Biological vessels are often enveloped by connective tissues that exhibit markedly different mechanical properties from the vessel wall, including high compressibility and nonlinear strain stiffening. While these composite structures are ubiquitous in soft tissue systems, the role of surrounding connective tissue in modulating vascular buckling behavior remains poorly understood. In this study, we develop a theoretical framework to investigate how connective tissue regulate mechanical stability in bilayer vessel–tissue systems. Moving beyond conventional models that assume homogeneous and incompressible materials, we introduce a more physiologically representative structure composed of a compliant, compressible outer tissue layer enclosing a stiff, incompressible vascular core. A bifurcation analysis based on incremental theory is performed to predict critical buckling performance, with results validated by both experiments and finite element simulations. The results reveal that connective tissue’s compressibility substantially increases the buckling threshold by redistributing stress across the interface and mitigating stress concentration within the vessel layer. Furthermore, comparison with actual aortic tissue reveals a stress-deconcentrating mechanism that enhances the structural resistance to buckling, a behavior not captured by idealized neoHookean models. These findings might provide mechanistic insights into tissue-mediated buckling suppression and offer design guidelines in soft biological interfaces and vascular-mimetic materials.
{"title":"Instability of vascular bilayer reveals the protective role of connective tissue","authors":"Dong Wu , Benzhu Guo , Yafei Yin , Shuai Zuo , Hongshuai Lei , Zeang Zhao , Daining Fang","doi":"10.1016/j.jmps.2025.106466","DOIUrl":"10.1016/j.jmps.2025.106466","url":null,"abstract":"<div><div>Biological vessels are often enveloped by connective tissues that exhibit markedly different mechanical properties from the vessel wall, including high compressibility and nonlinear strain stiffening. While these composite structures are ubiquitous in soft tissue systems, the role of surrounding connective tissue in modulating vascular buckling behavior remains poorly understood. In this study, we develop a theoretical framework to investigate how connective tissue regulate mechanical stability in bilayer vessel–tissue systems. Moving beyond conventional models that assume homogeneous and incompressible materials, we introduce a more physiologically representative structure composed of a compliant, compressible outer tissue layer enclosing a stiff, incompressible vascular core. A bifurcation analysis based on incremental theory is performed to predict critical buckling performance, with results validated by both experiments and finite element simulations. The results reveal that connective tissue’s compressibility substantially increases the buckling threshold by redistributing stress across the interface and mitigating stress concentration within the vessel layer. Furthermore, comparison with actual aortic tissue reveals a stress-deconcentrating mechanism that enhances the structural resistance to buckling, a behavior not captured by idealized neoHookean models. These findings might provide mechanistic insights into tissue-mediated buckling suppression and offer design guidelines in soft biological interfaces and vascular-mimetic materials.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"208 ","pages":"Article 106466"},"PeriodicalIF":6.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145657136","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-11-29DOI: 10.1016/j.jmps.2025.106456
Wei Tang , Lingfeng Wang , Shen Sun , Liucheng Zhou , Marco Paggi , Min Yi
Laser additive manufacturing (LAM) is increasingly employed as an in-situ repair technique for restoring the structural integrity and fatigue performance of metallic components. The fatigue and fracture behavior of LAM repaired components are significantly affected by defects introduced during the repair process, which poses challenges for predicting fatigue properties after LAM repair. Herein, we demonstrate the fatigue strength enhancement and fatigue crack growth (FCG) mechanisms in LAM repaired titanium-alloy blades by integrating vibration-based bending fatigue experiments with phase-field modeling (PFM). It is found that LAM repair of the notched TC17 forged blade could improve the fatigue strength by 94%. Fatigue cracks are revealed to initiate at internal defects within the LAM repair and propagate along transgranular paths influenced by defect clusters, deviating from the surface-initiated cracks in the forged counterparts. X-ray computed tomography reveals that the defect is dominated by small pores, with over 80% exhibiting an equivalent diameter below 60 µm. Furthermore, a macroscopic PFM incorporating fatigue life model that considers repair-induced pore defects is applied to predict the fatigue performance after LAM repair. Phase-field simulation results are shown to agree well with the experimental ones in terms of fatigue strength (error < 6%), critical crack length (error < 8%), and fracture surface morphology. Impact of defect features, material and model parameters on fatigue properties are investigated using our PFM, and the repair-induced pore size is shown to govern fatigue crack initiation and growth behavior of LAM repaired blade. Our work highlights the governing role of LAM repair-induced pore defects in high-cycle fatigue performance and enables a predictive PFM framework applicable to the fatigue evaluation of LAM repaired metallic components.
{"title":"Additive-manufacturing repair towards restoring fatigue performance of metallic component: Experiment and phase-field model prediction","authors":"Wei Tang , Lingfeng Wang , Shen Sun , Liucheng Zhou , Marco Paggi , Min Yi","doi":"10.1016/j.jmps.2025.106456","DOIUrl":"10.1016/j.jmps.2025.106456","url":null,"abstract":"<div><div>Laser additive manufacturing (LAM) is increasingly employed as an in-situ repair technique for restoring the structural integrity and fatigue performance of metallic components. The fatigue and fracture behavior of LAM repaired components are significantly affected by defects introduced during the repair process, which poses challenges for predicting fatigue properties after LAM repair. Herein, we demonstrate the fatigue strength enhancement and fatigue crack growth (FCG) mechanisms in LAM repaired titanium-alloy blades by integrating vibration-based bending fatigue experiments with phase-field modeling (PFM). It is found that LAM repair of the notched TC17 forged blade could improve the fatigue strength by 94%. Fatigue cracks are revealed to initiate at internal defects within the LAM repair and propagate along transgranular paths influenced by defect clusters, deviating from the surface-initiated cracks in the forged counterparts. X-ray computed tomography reveals that the defect is dominated by small pores, with over 80% exhibiting an equivalent diameter below 60 µm. Furthermore, a macroscopic PFM incorporating fatigue life model that considers repair-induced pore defects is applied to predict the fatigue performance after LAM repair. Phase-field simulation results are shown to agree well with the experimental ones in terms of fatigue strength (error < 6%), critical crack length (error < 8%), and fracture surface morphology. Impact of defect features, material and model parameters on fatigue properties are investigated using our PFM, and the repair-induced pore size is shown to govern fatigue crack initiation and growth behavior of LAM repaired blade. Our work highlights the governing role of LAM repair-induced pore defects in high-cycle fatigue performance and enables a predictive PFM framework applicable to the fatigue evaluation of LAM repaired metallic components.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"208 ","pages":"Article 106456"},"PeriodicalIF":6.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145619692","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 aim of this work is to study the effect of cyclic loadings including shear on the ductile behavior of porous materials. We use the recent model of Roubaud et al. (2024), based on the sequential limit-analysis of an ellipsoidal cell containing an ellipsoidal cavity, in which the heterogeneous distribution of hardening is accounted for by considering a finite number of ellipsoidal layers. The model is implemented numerically in order to study the combined effects of hardening and void shape on cyclic ductile behavior. The predictions of the model are compared to finite element micromechanical unit-cell calculations with initially spherical voids, for various loading cases and hardening laws. Under cyclic loadings at low stress triaxiality levels, significant ratcheting effects in porosity, void shape and void orientation are observed. Overall, the predictions of the model are in agreement with the results of unit-cell calculations.
{"title":"Combined effects of hardening and void shape on the plasticity of porous solids under cyclic loadings including shear","authors":"François Roubaud , Cihan Tekoğlu , Almahdi Remmal , Léo Morin , Jean-Baptiste Leblond","doi":"10.1016/j.jmps.2025.106415","DOIUrl":"10.1016/j.jmps.2025.106415","url":null,"abstract":"<div><div>The aim of this work is to study the effect of cyclic loadings including shear on the ductile behavior of porous materials. We use the recent model of Roubaud et al. (2024), based on the sequential limit-analysis of an ellipsoidal cell containing an ellipsoidal cavity, in which the heterogeneous distribution of hardening is accounted for by considering a finite number of ellipsoidal layers. The model is implemented numerically in order to study the combined effects of hardening and void shape on cyclic ductile behavior. The predictions of the model are compared to finite element micromechanical unit-cell calculations with initially spherical voids, for various loading cases and hardening laws. Under cyclic loadings at low stress triaxiality levels, significant ratcheting effects in porosity, void shape and void orientation are observed. Overall, the predictions of the model are in agreement with the results of unit-cell calculations.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"207 ","pages":"Article 106415"},"PeriodicalIF":6.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145478104","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.2025.106484
Ranny R. Zhao, Kevin T. Turner, John L. Bassani
Surface force-mediated adhesion, e.g. via van der Waals intermolecular forces, can lead to direct bonding between two bulk solids, but many analyses of this phenomenon only consider normal surface stresses. However, when finite size effects are accounted for, an interface shear traction generally arises from a mismatch in Poisson contraction, which can reduce the interface adhesion significantly from its ideal strength. The underlying mechanism of detachment is crack propagation along the interface. The understanding of the interplay between normal and shear surface stresses unlocks opportunities to control interfacial strength and toughness in various applications, including micro-transfer printing, MEMS/NEMS, manufacturing advanced 3D integrated circuits, and robotic grippers. We propose potential-based, coupled normal and shear traction-separation-sliding relations (TSSRs) and show that cohesive shear stresses have a significant effect of the detachment force and behavior of adhered pillars. Detailed finite element simulations utilizing cohesive elements based on the coupled TSSR are used to study the failure mechanism of an elastic pillar adhered to a rigid substrate. The effects of coupled normal and shear cohesive stresses are investigated in detail. A non-dimensional parameter, which incorporates the effect of cohesive shear stresses, is defined to describe the transition between strength-based failure and fracture-based failure. Preliminary experiments demonstrate how the TSSR properties can be determined.
{"title":"Resistance to interface sliding and effects on detachment of directly-bonded pillars","authors":"Ranny R. Zhao, Kevin T. Turner, John L. Bassani","doi":"10.1016/j.jmps.2025.106484","DOIUrl":"10.1016/j.jmps.2025.106484","url":null,"abstract":"<div><div>Surface force-mediated adhesion, e.g. via van der Waals intermolecular forces, can lead to direct bonding between two bulk solids, but many analyses of this phenomenon only consider normal surface stresses. However, when finite size effects are accounted for, an interface shear traction generally arises from a mismatch in Poisson contraction, which can reduce the interface adhesion significantly from its ideal strength. The underlying mechanism of detachment is crack propagation along the interface. The understanding of the interplay between normal and shear surface stresses unlocks opportunities to control interfacial strength and toughness in various applications, including micro-transfer printing, MEMS/NEMS, manufacturing advanced 3D integrated circuits, and robotic grippers. We propose potential-based, coupled normal and shear traction-separation-sliding relations (TSSRs) and show that cohesive shear stresses have a significant effect of the detachment force and behavior of adhered pillars. Detailed finite element simulations utilizing cohesive elements based on the coupled TSSR are used to study the failure mechanism of an elastic pillar adhered to a rigid substrate. The effects of coupled normal and shear cohesive stresses are investigated in detail. A non-dimensional parameter, which incorporates the effect of cohesive shear stresses, is defined to describe the transition between strength-based failure and fracture-based failure. Preliminary experiments demonstrate how the TSSR properties can be determined.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"208 ","pages":"Article 106484"},"PeriodicalIF":6.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145784911","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.2025.106468
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: 2025-12-20DOI: 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}
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