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}
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: 2025-11-14DOI: 10.1016/j.jmps.2025.106425
Mohammadali Behboodi, Yida Zhang
Adsorption-induced swelling occurs in a wide spectrum of natural and engineered porous materials. A key underlying mechanism is the monotonic reduction of solid-fluid surface energy upon fluid adsorption, which lowers the contractive adsorption stress and causes the porous skeleton to swell (Bangham and Fakhoury, 1928). Some mesoporous materials, however, deviate from the monotonic swelling pattern predicted by this mechanism, exhibiting an abrupt shrinkage at intermediate adsorbate partial pressures before swelling resumes and continues to full saturation. This behavior is commonly attributed to capillary condensation of the adsorbate from the vapor to the liquid phase within the pores. Understanding the stresses and the shrinkage induced by capillary condensation is critical in various industrial applications including micro-/nanofabrication, geotechnical engineering in collapsible soils, and sorption-driven actuation technologies. This work aims to develop a unified poromechanics theory that captures the full sequence of adsorption-induced deformation, including initial swelling, contraction during capillary condensation, and resumed expansion near full saturation. The formulation begins with a thermodynamic analysis of an unsaturated deformable porous solid, acknowledging the energetics of the solid-fluid (sl), solid-vapor (sv), and liquid-vapor (lv) interfaces. The resulting free energy balance permits the simultaneous derivation of the liquid retention characteristics curve and the coupled mechanical effects driven by adsorption and partial saturation. Within this framework, two strategies for constructing constitutive relations are examined: one explicitly resolves the dynamic evolution of sl-sv-lv interfacial areas to emphasize the underlying physics, while the other partially lumps the surface energies into a macroscopic capillary potential to facilitate model calibration using standard laboratory tests. The models are evaluated using datasets from two markedly different solid-fluid systems: N2 gas adsorption on a hierarchical porous silica at 77 K and water adsorption on a carbon xerogel at 298 K. Both approaches effectively capture the complex, non-monotonic strain isotherms exhibited by the adsorbent. The adsorption-desorption hysteresis is also addressed in a thermodynamically consistent framework. The proposed theory demonstrates both robustness and unifying power in explaining the complex strain isotherms of porous materials along adsorption and desorption paths, covering the entire spectrum from vacuum-dry to fully liquid-saturated states.
{"title":"Interfacial evolution explains the complex swelling-shrinkage responses of porous materials from vacuum-dry to full liquid saturation","authors":"Mohammadali Behboodi, Yida Zhang","doi":"10.1016/j.jmps.2025.106425","DOIUrl":"10.1016/j.jmps.2025.106425","url":null,"abstract":"<div><div>Adsorption-induced swelling occurs in a wide spectrum of natural and engineered porous materials. A key underlying mechanism is the monotonic reduction of solid-fluid surface energy upon fluid adsorption, which lowers the contractive adsorption stress and causes the porous skeleton to swell (Bangham and Fakhoury, 1928). Some mesoporous materials, however, deviate from the monotonic swelling pattern predicted by this mechanism, exhibiting an abrupt shrinkage at intermediate adsorbate partial pressures before swelling resumes and continues to full saturation. This behavior is commonly attributed to capillary condensation of the adsorbate from the vapor to the liquid phase within the pores. Understanding the stresses and the shrinkage induced by capillary condensation is critical in various industrial applications including micro-/nanofabrication, geotechnical engineering in collapsible soils, and sorption-driven actuation technologies. This work aims to develop a unified poromechanics theory that captures the full sequence of adsorption-induced deformation, including initial swelling, contraction during capillary condensation, and resumed expansion near full saturation. The formulation begins with a thermodynamic analysis of an unsaturated deformable porous solid, acknowledging the energetics of the solid-fluid (<em>sl</em>), solid-vapor (<em>sv</em>), and liquid-vapor (<em>lv</em>) interfaces. The resulting free energy balance permits the simultaneous derivation of the liquid retention characteristics curve and the coupled mechanical effects driven by adsorption and partial saturation. Within this framework, two strategies for constructing constitutive relations are examined: one explicitly resolves the dynamic evolution of <em>sl-sv-lv</em> interfacial areas to emphasize the underlying physics, while the other partially lumps the surface energies into a macroscopic capillary potential to facilitate model calibration using standard laboratory tests. The models are evaluated using datasets from two markedly different solid-fluid systems: N<sub>2</sub> gas adsorption on a hierarchical porous silica at 77 K and water adsorption on a carbon xerogel at 298 K. Both approaches effectively capture the complex, non-monotonic strain isotherms exhibited by the adsorbent. The adsorption-desorption hysteresis is also addressed in a thermodynamically consistent framework. The proposed theory demonstrates both robustness and unifying power in explaining the complex strain isotherms of porous materials along adsorption and desorption paths, covering the entire spectrum from vacuum-dry to fully liquid-saturated states.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"207 ","pages":"Article 106425"},"PeriodicalIF":6.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145545472","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-11-17DOI: 10.1016/j.jmps.2025.106421
Anh Tuan Le , Xavier Bruant , Ngoc Tram Phung , François Ozanam , Michel Rosso , Laurent Guin
We report operando measurements and concurrent modeling of the stress dependence of the chemical potential of lithium in a silicon electrode. An experimental study is carried out on hydrogenated amorphous silicon thin films in which the electrode stress state is modified operando during electrochemical lithiation and delithiation by applying an external mechanical load. During galvanostatic cycling, the electrode is periodically subjected to a tensile strain, inducing stress variations that are reflected in voltage changes. The measured stress-induced voltage changes are interpreted using a well-established chemomechanical model of lithium insertion in silicon. Comparison of voltage measurements with model predictions allows us to determine the concentration-dependent Young’s modulus (from 29 GPa to 26 GPa with increasing lithium content) and some of the viscoplastic parameters of lithiated silicon. The calibrated model shows good predictive capability when applied to lithiation cycles performed at a C-rate different from that of the calibration cycle. However, it shows limitations in explaining voltage changes under delithiation. These results show that thermodynamically-consistent chemomechanical models of lithiation not only adequately describe the effect of lithium insertion and deinsertion on stress, as already shown in the literature, but also capture the reverse effect of stress on lithium chemical potential in silicon. In this respect, this work opens up new perspectives for the quantitative validation and calibration of existing diffusion-deformation theories, notably by highlighting their possible limitations.
{"title":"Stress dependence of the chemical potential of lithium in a silicon electrode","authors":"Anh Tuan Le , Xavier Bruant , Ngoc Tram Phung , François Ozanam , Michel Rosso , Laurent Guin","doi":"10.1016/j.jmps.2025.106421","DOIUrl":"10.1016/j.jmps.2025.106421","url":null,"abstract":"<div><div>We report <em>operando</em> measurements and concurrent modeling of the stress dependence of the chemical potential of lithium in a silicon electrode. An experimental study is carried out on hydrogenated amorphous silicon thin films in which the electrode stress state is modified <em>operando</em> during electrochemical lithiation and delithiation by applying an external mechanical load. During galvanostatic cycling, the electrode is periodically subjected to a tensile strain, inducing stress variations that are reflected in voltage changes. The measured stress-induced voltage changes are interpreted using a well-established chemomechanical model of lithium insertion in silicon. Comparison of voltage measurements with model predictions allows us to determine the concentration-dependent Young’s modulus (from 29 GPa to 26 GPa with increasing lithium content) and some of the viscoplastic parameters of lithiated silicon. The calibrated model shows good predictive capability when applied to lithiation cycles performed at a C-rate different from that of the calibration cycle. However, it shows limitations in explaining voltage changes under delithiation. These results show that thermodynamically-consistent chemomechanical models of lithiation not only adequately describe the effect of lithium insertion and deinsertion on stress, as already shown in the literature, but also capture the reverse effect of stress on lithium chemical potential in silicon. In this respect, this work opens up new perspectives for the quantitative validation and calibration of existing diffusion-deformation theories, notably by highlighting their possible limitations.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"207 ","pages":"Article 106421"},"PeriodicalIF":6.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145546297","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 mechanical instabilities of clamped helical elastic rods under controlled rotation and extension, featuring perversion, are studied experimentally, numerically and theoretically. Perversion appears at a winding lower than the intrinsic one. When the extension and winding are varied, the perversion is involved in three main instabilities. They can all be identified visually as abrupt qualitative modifications of the conformation. Singularities in the axial force and torque acting on the clamps are observed at critical winding and/or extension. (i) Transitioning from a pure helix to a configuration with perversion (and vice versa) is accompanied by a snapping instability. (ii) At zero net turns, the rod undergoes a writhing bifurcation from a straight to a writhed configuration. (iii) The perversion jumps to self-contact at critical extension. While the transitions (i) and (iii) are subcritical bifurcations, the writhing bifurcation is continuous and supercritical. The singularity at the creation of the perversion is reproduced numerically by incorporating clamping effects within path-following methods. A shooting technique, path-following method and finite element simulations are employed to assess the stability of the perversion and the associated snapping towards self-contact.An analogy with first-order phase transitions is discussed.
{"title":"Mechanical instabilities and snapping phenomena in helical rods with perversion","authors":"Émilien Dilly , Sébastien Neukirch , Julien Derr , Williams Brett , Dražen Zanchi","doi":"10.1016/j.jmps.2025.106402","DOIUrl":"10.1016/j.jmps.2025.106402","url":null,"abstract":"<div><div>The mechanical instabilities of clamped helical elastic rods under controlled rotation and extension, featuring perversion, are studied experimentally, numerically and theoretically. Perversion appears at a winding lower than the intrinsic one. When the extension and winding are varied, the perversion is involved in three main instabilities. They can all be identified visually as abrupt qualitative modifications of the conformation. Singularities in the axial force and torque acting on the clamps are observed at critical winding and/or extension. (i) Transitioning from a pure helix to a configuration with perversion (and vice versa) is accompanied by a snapping instability. (ii) At zero net turns, the rod undergoes a writhing bifurcation from a straight to a writhed configuration. (iii) The perversion jumps to self-contact at critical extension. While the transitions (i) and (iii) are subcritical bifurcations, the writhing bifurcation is continuous and supercritical. The singularity at the creation of the perversion is reproduced numerically by incorporating clamping effects within path-following methods. A shooting technique, path-following method and finite element simulations are employed to assess the stability of the perversion and the associated snapping towards self-contact.An analogy with first-order phase transitions is discussed.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"207 ","pages":"Article 106402"},"PeriodicalIF":6.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145461549","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: 2025-11-13DOI: 10.1016/j.jmps.2025.106419
Yanni Chen , Zhongxuan Yang , Itai Einav
Stresses and pressures are used to represent the hydromechanical state of deformable porous media. Past formulations often adopt the effective stress principle, usually in an empirical and energetically inconsistent way. Using the rigorous hydrodynamic procedure, this study pursues an alternative energy-consistent formulation for the full characterisation of both saturated and unsaturated porous materials. An elastic stress is consistently linked to its energy-conjugated elastic strain and, in the absence of viscous stress, has a structure that was previously interpreted as an effective stress. Here, it is emphasised that this similarity does not imply that the elastic stress is ‘effective’ in the classical sense, namely that it can replace total stress in dry soils to represent the mechanical behaviour of saturated or unsaturated soils. The dependence of the elastic stress on the deformability of the solid is incorporated constitutively using a general elastic strain energy of pressure- and density-dependent media, excluding energy costs from solid density changes due to volumetric elastic straining. By adopting the resulting internal energy that is convex for physically realistic porous materials, the proposed formulation yields a rigorous quantification of the elastic stress, and the pressures of the air, water, and solid required for characterising saturated and unsaturated soils, including the Biot stress correction coefficient for deformable porous media at variable saturation. The formulation also reveals the intrinsic dependence of the stress coefficients on material elasticity and the characteristics of water retention responses.
{"title":"Hydrodynamics of stresses and pressures in saturated and unsaturated deformable porous media","authors":"Yanni Chen , Zhongxuan Yang , Itai Einav","doi":"10.1016/j.jmps.2025.106419","DOIUrl":"10.1016/j.jmps.2025.106419","url":null,"abstract":"<div><div>Stresses and pressures are used to represent the hydromechanical state of deformable porous media. Past formulations often adopt the effective stress principle, usually in an empirical and energetically inconsistent way. Using the rigorous hydrodynamic procedure, this study pursues an alternative energy-consistent formulation for the full characterisation of both saturated and unsaturated porous materials. An elastic stress is consistently linked to its energy-conjugated elastic strain and, in the absence of viscous stress, has a structure that was previously interpreted as an effective stress. Here, it is emphasised that this similarity does not imply that the elastic stress is ‘effective’ in the classical sense, namely that it can replace total stress in dry soils to represent the mechanical behaviour of saturated or unsaturated soils. The dependence of the elastic stress on the deformability of the solid is incorporated constitutively using a general elastic strain energy of pressure- and density-dependent media, excluding energy costs from solid density changes due to volumetric elastic straining. By adopting the resulting internal energy that is convex for physically realistic porous materials, the proposed formulation yields a rigorous quantification of the elastic stress, and the pressures of the air, water, and solid required for characterising saturated and unsaturated soils, including the Biot stress correction coefficient for deformable porous media at variable saturation. The formulation also reveals the intrinsic dependence of the stress coefficients on material elasticity and the characteristics of water retention responses.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"207 ","pages":"Article 106419"},"PeriodicalIF":6.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145519062","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: 2025-11-04DOI: 10.1016/j.jmps.2025.106411
Shuvrangsu Das
This work investigates the effects of multiscale substructure on the mechanical response of porous materials. First, we consider porous materials consisting of two populations of cylindrical pores embedded in an incompressible anisotropic viscous matrix and obtain analytical estimates for the overall response and field statistics under plane-strain loading in transverse plane. We demonstrate that the effective bulk viscosity of three-scale porous materials is lower compared to that of two-scale porous materials, whereas the effective shear viscosity remains unaffected. However, the stress and strain-rate fields become substantially more heterogeneous because of the multiscale substructure, with the enhancement increasing with the anisotropy of the viscous matrix, the total pore volume fraction, and the relative volume fraction of large and small pores. Next, we consider porous polycrystals in which the pores of two populations are distributed in a polycrystalline material composed of anisotropic viscous grains. Depending on the relative sizes of the pores to the grains, three types of porous polycrystals are considered: porous polycrystals containing intergranular pores and voids; porous polycrystals with porous grains and intergranular pores; and porous polycrystals with porous grains and voids. As before, the overall deviatoric response remains largely independent of the relative sizes of pores and grains, but the polycrystals containing porous grains show a softer dilatational response than the other two types of porous polycrystals. Moreover, the polycrystals consisting of intragranular pores exhibit substantially more heterogeneity of the stress and strain-rate fields, compared to polycrystals containing only voids or intergranular pores. While this work focuses on multiscale porous viscous materials, the framework to derive the overall response and field statistics is quite general and, with an appropriate linearization scheme, it can be extended to multiscale porous viscoplastic materials. In this work, however, we considered porous materials with anisotropic viscous phases and focused on uncovering the effects of multiscale substructures, which are found to significantly influence the field statistics of porous materials with strongly anisotropic phases.
{"title":"Effects of multiscale substructures on the effective behavior and field statistics of porous materials","authors":"Shuvrangsu Das","doi":"10.1016/j.jmps.2025.106411","DOIUrl":"10.1016/j.jmps.2025.106411","url":null,"abstract":"<div><div>This work investigates the effects of multiscale substructure on the mechanical response of porous materials. First, we consider porous materials consisting of two populations of cylindrical pores embedded in an incompressible anisotropic viscous matrix and obtain analytical estimates for the overall response and field statistics under plane-strain loading in transverse plane. We demonstrate that the effective bulk viscosity of three-scale porous materials is lower compared to that of two-scale porous materials, whereas the effective shear viscosity remains unaffected. However, the stress and strain-rate fields become substantially more heterogeneous because of the multiscale substructure, with the enhancement increasing with the anisotropy of the viscous matrix, the total pore volume fraction, and the relative volume fraction of large and small pores. Next, we consider porous polycrystals in which the pores of two populations are distributed in a polycrystalline material composed of anisotropic viscous grains. Depending on the relative sizes of the pores to the grains, three types of porous polycrystals are considered: porous polycrystals containing intergranular pores and voids; porous polycrystals with porous grains and intergranular pores; and porous polycrystals with porous grains and voids. As before, the overall deviatoric response remains largely independent of the relative sizes of pores and grains, but the polycrystals containing porous grains show a softer dilatational response than the other two types of porous polycrystals. Moreover, the polycrystals consisting of intragranular pores exhibit substantially more heterogeneity of the stress and strain-rate fields, compared to polycrystals containing only voids or intergranular pores. While this work focuses on multiscale porous viscous materials, the framework to derive the overall response and field statistics is quite general and, with an appropriate linearization scheme, it can be extended to multiscale porous viscoplastic materials. In this work, however, we considered porous materials with anisotropic viscous phases and focused on uncovering the effects of multiscale substructures, which are found to significantly influence the field statistics of porous materials with strongly anisotropic phases.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"207 ","pages":"Article 106411"},"PeriodicalIF":6.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145434316","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}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号