Pub Date : 2025-10-26DOI: 10.1016/j.jmps.2025.106410
Minglu Lin , Haonan Sui , Yin Zhang , Huiling Duan
Predicting spall strength for designing enhanced performance materials under extreme conditions requires understanding microstructural features due to their role in void nucleation and growth. In single crystal metals, spallation primarily results from void growth initiated by vacancy clusters via dislocation nucleation at void surfaces, necessitating a comprehensive understanding of void growth mechanisms for accurate modeling. The energy barrier for dislocation nucleation is calculated through atomistic simulations as a function of the stress tensor, enabling the development of a general dislocation nucleation criterion for face-centered cubic (FCC) metals. Results indicate that the local stress state at void surfaces governs dislocation-mediated void growth by modulating the nucleation energy barrier. By integrating this microscopic criterion—explicitly parameterized by local stress—into macroscopic spallation models through the Steigmann–Ogden interface model, the model captures the temperature and strain-rate sensitivities of spall strength. Furthermore, it reveals the competition between thermally activated dislocation nucleation and inertial effects during void growth, and effectively explains the reduction in spall strength observed in metals containing gas bubbles. The significance of this study lies in developing an atomistically-informed model that enables realistic incorporation of microscopic defect responses into macroscopic spallation predictions.
{"title":"Atomistically-informed modeling of void growth in spallation of FCC metals","authors":"Minglu Lin , Haonan Sui , Yin Zhang , Huiling Duan","doi":"10.1016/j.jmps.2025.106410","DOIUrl":"10.1016/j.jmps.2025.106410","url":null,"abstract":"<div><div>Predicting spall strength for designing enhanced performance materials under extreme conditions requires understanding microstructural features due to their role in void nucleation and growth. In single crystal metals, spallation primarily results from void growth initiated by vacancy clusters via dislocation nucleation at void surfaces, necessitating a comprehensive understanding of void growth mechanisms for accurate modeling. The energy barrier for dislocation nucleation is calculated through atomistic simulations as a function of the stress tensor, enabling the development of a general dislocation nucleation criterion for face-centered cubic (FCC) metals. Results indicate that the local stress state at void surfaces governs dislocation-mediated void growth by modulating the nucleation energy barrier. By integrating this microscopic criterion—explicitly parameterized by local stress—into macroscopic spallation models through the Steigmann–Ogden interface model, the model captures the temperature and strain-rate sensitivities of spall strength. Furthermore, it reveals the competition between thermally activated dislocation nucleation and inertial effects during void growth, and effectively explains the reduction in spall strength observed in metals containing gas bubbles. The significance of this study lies in developing an atomistically-informed model that enables realistic incorporation of microscopic defect responses into macroscopic spallation predictions.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"206 ","pages":"Article 106410"},"PeriodicalIF":6.0,"publicationDate":"2025-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145382948","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-24DOI: 10.1016/j.jmps.2025.106403
Qingxiang Ji , Jinliang Wang , Brahim Lemkalli , Gwenn Ulliac , Changguo Wang , Sébastien Guenneau , Muamer Kadic
Mechanical metamaterials have recently driven significant advancements, and this field has currently been extended to break the reciprocity principle in static mechanics and wave propagation. Here, we demonstrate a type of three-dimensional mechanical metamaterials that possess nonreciprocal static elastic behaviors and tunable dynamic wave properties. The metamaterial is designed with suitably tailored microstructure asymmetry, which exhibits vastly different deformation configurations upon loading from different sides. Such contrast in deformation induces distinct force–displacement responses, which gives nonlinear elastic moduli that are dependent on both the magnitude and direction of applied loads. We fabricate such metamaterials with 3D printing technique at the microscale. The non-reciprocal mechanical behavior is validated by analytical means, simulations, and experiments. Besides, tunable band structure characteristics are obtained when the metamaterial is loaded in opposite directions or by different magnitudes. The band structure deforms in asymmetrical ways, which indicates flexible control on transmit–prohibit switching of elastic waves propagation (in certain frequency ranges), and this is realized by only switching the external mechanical loading direction. These peculiar behaviors show great prospects in enabling unidirectional elasticity and wave transmission within a solid material, paving avenues to new one-way functional devices.
{"title":"Non-reciprocal three-dimensional mechanical metamaterials","authors":"Qingxiang Ji , Jinliang Wang , Brahim Lemkalli , Gwenn Ulliac , Changguo Wang , Sébastien Guenneau , Muamer Kadic","doi":"10.1016/j.jmps.2025.106403","DOIUrl":"10.1016/j.jmps.2025.106403","url":null,"abstract":"<div><div>Mechanical metamaterials have recently driven significant advancements, and this field has currently been extended to break the reciprocity principle in static mechanics and wave propagation. Here, we demonstrate a type of three-dimensional mechanical metamaterials that possess nonreciprocal static elastic behaviors and tunable dynamic wave properties. The metamaterial is designed with suitably tailored microstructure asymmetry, which exhibits vastly different deformation configurations upon loading from different sides. Such contrast in deformation induces distinct force–displacement responses, which gives nonlinear elastic moduli that are dependent on both the magnitude and direction of applied loads. We fabricate such metamaterials with 3D printing technique at the microscale. The non-reciprocal mechanical behavior is validated by analytical means, simulations, and experiments. Besides, tunable band structure characteristics are obtained when the metamaterial is loaded in opposite directions or by different magnitudes. The band structure deforms in asymmetrical ways, which indicates flexible control on transmit–prohibit switching of elastic waves propagation (in certain frequency ranges), and this is realized by only switching the external mechanical loading direction. These peculiar behaviors show great prospects in enabling unidirectional elasticity and wave transmission within a solid material, paving avenues to new one-way functional devices.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"206 ","pages":"Article 106403"},"PeriodicalIF":6.0,"publicationDate":"2025-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145339780","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-24DOI: 10.1016/j.jmps.2025.106406
Corentin Thouénon , Alizée Dubois , Etienne Barraud , Théo Géral , Nicolas Bruzy , Jacques Besson , François Willot
Spallation in ductile metals involves complex void nucleation and growth mechanisms, but the interactions between voids and the resulting statistical structure of fracture surfaces remain a persistent challenge for both experimental and theoretical modeling. This study develops a generative model to capture the statistical features of spall-induced fracture surfaces in high-purity aluminum. Aluminum samples were subjected to nanosecond laser-induced spallation, and the resulting fracture surfaces were imaged via scanning electron microscopy (SEM) and reconstructed in 3D. Individual dimples were segmented and analyzed to extract void size distributions and the spatial arrangement of nucleation sites. Boolean models and Gaussian random fields were then used to generate synthetic surfaces and compared against the experimental data using one- and two-point statistics. The analysis revealed a Poisson distribution of nucleation centers within the spall plane but significant out-of-plane spatial correlations in nucleation depth. The extended generative model successfully reproduces both the surface height distribution and the spatial covariance observed experimentally. These results emphasize the need to incorporate large-scale spatial correlations in predictive models of dynamic ductile damage. The proposed framework provides a basis for future studies of collective void growth and spall surface formation in dynamic ductile fracture.
{"title":"Statistical modeling and generation of inertial ductile fracture surfaces","authors":"Corentin Thouénon , Alizée Dubois , Etienne Barraud , Théo Géral , Nicolas Bruzy , Jacques Besson , François Willot","doi":"10.1016/j.jmps.2025.106406","DOIUrl":"10.1016/j.jmps.2025.106406","url":null,"abstract":"<div><div>Spallation in ductile metals involves complex void nucleation and growth mechanisms, but the interactions between voids and the resulting statistical structure of fracture surfaces remain a persistent challenge for both experimental and theoretical modeling. This study develops a generative model to capture the statistical features of spall-induced fracture surfaces in high-purity aluminum. Aluminum samples were subjected to nanosecond laser-induced spallation, and the resulting fracture surfaces were imaged via scanning electron microscopy (SEM) and reconstructed in 3D. Individual dimples were segmented and analyzed to extract void size distributions and the spatial arrangement of nucleation sites. Boolean models and Gaussian random fields were then used to generate synthetic surfaces and compared against the experimental data using one- and two-point statistics. The analysis revealed a Poisson distribution of nucleation centers within the spall plane but significant out-of-plane spatial correlations in nucleation depth. The extended generative model successfully reproduces both the surface height distribution and the spatial covariance observed experimentally. These results emphasize the need to incorporate large-scale spatial correlations in predictive models of dynamic ductile damage. The proposed framework provides a basis for future studies of collective void growth and spall surface formation in dynamic ductile fracture.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"206 ","pages":"Article 106406"},"PeriodicalIF":6.0,"publicationDate":"2025-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145382952","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-24DOI: 10.1016/j.jmps.2025.106408
Bernardo P. Ferreira, Miguel A. Bessa
We introduce an Automatically Differentiable Model Updating (ADiMU) framework that finds any history-independent or history-dependent material model from full-field displacement and global force data (global, indirect discovery) or from strain-stress data (local, direct discovery). We show that ADiMU can update conventional (physics-based), neural network (data-driven), and hybrid material models. Moreover, this framework requires no fine-tuning of hyperparameters or additional quantities beyond those inherent to the user-selected material model architecture and optimizer. The robustness and versatility of ADiMU is extensively exemplified by updating different models spanning tens to millions of parameters, in both local and global discovery settings. Relying on fully differentiable code, the algorithmic implementation leverages vectorizing maps that enable history-dependent automatic differentiation via efficient batched execution of shared computation graphs. This contribution also aims to facilitate the integration, evaluation and application of future material model architectures by openly supporting the research community. Therefore, ADiMU is released as an open-source computational tool, integrated into a carefully designed and documented software named HookeAI.
{"title":"Automatically Differentiable Model Updating (ADiMU): Conventional, hybrid, and neural network material model discovery including history-dependency","authors":"Bernardo P. Ferreira, Miguel A. Bessa","doi":"10.1016/j.jmps.2025.106408","DOIUrl":"10.1016/j.jmps.2025.106408","url":null,"abstract":"<div><div>We introduce an Automatically Differentiable Model Updating (ADiMU) framework that finds any history-independent or history-dependent material model from full-field displacement and global force data (global, indirect discovery) or from strain-stress data (local, direct discovery). We show that ADiMU can update conventional (physics-based), neural network (data-driven), and hybrid material models. Moreover, this framework requires no fine-tuning of hyperparameters or additional quantities beyond those inherent to the user-selected material model architecture and optimizer. The robustness and versatility of ADiMU is extensively exemplified by updating different models spanning tens to millions of parameters, in both local and global discovery settings. Relying on fully differentiable code, the algorithmic implementation leverages vectorizing maps that enable history-dependent automatic differentiation via efficient batched execution of shared computation graphs. This contribution also aims to facilitate the integration, evaluation and application of future material model architectures by openly supporting the research community. Therefore, ADiMU is released as an open-source computational tool, integrated into a carefully designed and documented software named HookeAI.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"206 ","pages":"Article 106408"},"PeriodicalIF":6.0,"publicationDate":"2025-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145382953","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-22DOI: 10.1016/j.jmps.2025.106392
Manon Thbaut , Basile Audoly , Claire Lestringant
The goal of periodic homogenization is to identify an effective model specified by an energy functional depending on the macroscopic displacement . We consider second-order homogenization, a case where the effective energy depends not only on the strain but also on its gradients and . Functionals obtained in prior work are typically made stationary order by order in the expansion parameter, and are not positive when truncated: they are not proper strain-gradient theories. Starting from a functional produced by linear, second-order homogenization of a periodic elastic lattice in dimension 1, we propose a systematic method to upgrade it to a positive strain-gradient energy . This enables us to formulate second-order homogenization as a variational problem. Boundary layers are represented in an effective and asymptotically correct way by boundary terms in the energy .
{"title":"Asymptotic strain-gradient theory for one-dimensional continua","authors":"Manon Thbaut , Basile Audoly , Claire Lestringant","doi":"10.1016/j.jmps.2025.106392","DOIUrl":"10.1016/j.jmps.2025.106392","url":null,"abstract":"<div><div>The goal of periodic homogenization is to identify an effective model specified by an energy functional <span><math><mrow><msub><mrow><mi>Φ</mi></mrow><mrow><mi>ɛ</mi></mrow></msub><mrow><mo>[</mo><mi>u</mi><mo>]</mo></mrow></mrow></math></span> depending on the macroscopic displacement <span><math><mi>u</mi></math></span>. We consider second-order homogenization, a case where the effective energy depends not only on the strain <span><math><msup><mrow><mi>u</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span> but also on its gradients <span><math><msup><mrow><mi>u</mi></mrow><mrow><mo>′</mo><mo>′</mo></mrow></msup></math></span> and <span><math><msup><mrow><mi>u</mi></mrow><mrow><mo>′</mo><mo>′</mo><mo>′</mo></mrow></msup></math></span>. Functionals <span><math><mrow><msub><mrow><mi>Φ</mi></mrow><mrow><mi>ɛ</mi></mrow></msub><mrow><mo>[</mo><mi>u</mi><mo>]</mo></mrow></mrow></math></span> obtained in prior work are typically made stationary <em>order by order</em> in the expansion parameter, and are not positive when truncated: they are not proper strain-gradient theories. Starting from a functional <span><math><mrow><msub><mrow><mi>Φ</mi></mrow><mrow><mi>ɛ</mi></mrow></msub><mrow><mo>[</mo><mi>u</mi><mo>]</mo></mrow></mrow></math></span> produced by linear, second-order homogenization of a periodic elastic lattice in dimension 1, we propose a systematic method to upgrade it to a positive strain-gradient energy <span><math><mrow><msub><mrow><mi>Ψ</mi></mrow><mrow><mi>ɛ</mi></mrow></msub><mrow><mo>[</mo><mi>u</mi><mo>]</mo></mrow></mrow></math></span>. This enables us to formulate second-order homogenization as a variational problem. Boundary layers are represented in an effective and asymptotically correct way by boundary terms in the energy <span><math><mrow><msub><mrow><mi>Ψ</mi></mrow><mrow><mi>ɛ</mi></mrow></msub><mrow><mo>[</mo><mi>u</mi><mo>]</mo></mrow></mrow></math></span>.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"206 ","pages":"Article 106392"},"PeriodicalIF":6.0,"publicationDate":"2025-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145416732","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-22DOI: 10.1016/j.jmps.2025.106407
Darshan Bamney, Laurent Capolungo
Twinning is a key deformation mechanism in hexagonal close-packed (hcp) metals, which are typified by a lack of easily activated slip systems that can accommodate a general state of loading. Pragmatically, the nucleation and evolution of twin domains occurs concomitantly with slip, such that the eventual twin network is conditioned by both external and internal stresses resulting, among others, from the evolution of dislocations. However our understanding of the interplay between dislocations, and twin nucleation and stability remains limited. This work focuses on elucidating the influence of dislocation-mediated plasticity on the formation, growth, and stability of twin embryos. First, a new mesoscale spectral crystal plasticity-twinning framework is developed and used to quantify the change in the free energy landscape following the nucleation of twins in Mg. Representative twin morphologies are modeled under conditions of limited and profuse slip activity, which are emulative of small- and bulk-scale samples, respectively. Then, the driving traction profiles around twin embryos are investigated via a sharp interface approach to obtain insights into how concurrent slip-mediated plasticity can influence the growth/stabilization of nanometric twins. The driving traction profiles are further utilized to determine the stability of twin embryos post loading. The initial dislocation density in the samples, and within the different domains (i.e., twin vs. parent), is seen to have a significant effect on the twin nucleation stress. Namely, the activation of high levels of concomitant plasticity in the parent grain is seen to significantly drive the formation of nanometric twin nuclei at stresses as low as . Further, the sharp interface analysis reveals that profuse plasticity in the parent grain simultaneously alters the forward and back stresses, such that the magnitude/polarity of the driving tractions become increasingly favorable for nanometric twin growth when slip is active. Finally, prior plasticity in the parent grain is seen to result in favorable driving tractions for nanometric twin growth, even at applied stresses as low as . These results are in stark contrast to a case without any dislocations, wherein applied stresses as high as are necessary to grow the twin domains.
{"title":"Twin nucleation and growth in hexagonal close-packed metals: The role of slip-mediated plasticity on twin embryo formation and evolution","authors":"Darshan Bamney, Laurent Capolungo","doi":"10.1016/j.jmps.2025.106407","DOIUrl":"10.1016/j.jmps.2025.106407","url":null,"abstract":"<div><div>Twinning is a key deformation mechanism in hexagonal close-packed (hcp) metals, which are typified by a lack of easily activated slip systems that can accommodate a general state of loading. Pragmatically, the nucleation and evolution of twin domains occurs concomitantly with slip, such that the eventual twin network is conditioned by both external and internal stresses resulting, among others, from the evolution of dislocations. However our understanding of the interplay between dislocations, and twin nucleation and stability remains limited. This work focuses on elucidating the influence of dislocation-mediated plasticity on the formation, growth, and stability of twin embryos. First, a new mesoscale spectral crystal plasticity-twinning framework is developed and used to quantify the change in the free energy landscape following the nucleation of <span><math><mrow><mo>{</mo><mn>10</mn><mover><mrow><mn>1</mn></mrow><mrow><mo>̄</mo></mrow></mover><mn>2</mn><mo>}</mo></mrow></math></span> twins in Mg. Representative twin morphologies are modeled under conditions of limited and profuse slip activity, which are emulative of small- and bulk-scale samples, respectively. Then, the driving traction profiles around twin embryos are investigated via a sharp interface approach to obtain insights into how concurrent slip-mediated plasticity can influence the growth/stabilization of nanometric twins. The driving traction profiles are further utilized to determine the stability of twin embryos post loading. The initial dislocation density in the samples, and within the different domains (i.e., twin vs. parent), is seen to have a significant effect on the twin nucleation stress. Namely, the activation of high levels of concomitant plasticity in the parent grain is seen to significantly drive the formation of nanometric twin nuclei at stresses as low as <span><math><mrow><mn>250</mn><mspace></mspace><mi>MPa</mi></mrow></math></span>. Further, the sharp interface analysis reveals that profuse plasticity in the parent grain simultaneously alters the forward and back stresses, such that the magnitude/polarity of the driving tractions become increasingly favorable for nanometric twin growth when slip is active. Finally, prior plasticity in the parent grain is seen to result in favorable driving tractions for nanometric twin growth, even at applied stresses as low as <span><math><mrow><mo>∼</mo><mn>100</mn><mspace></mspace><mi>MPa</mi></mrow></math></span>. These results are in stark contrast to a case without any dislocations, wherein applied stresses as high as <span><math><mrow><mo>∼</mo><mn>500</mn><mspace></mspace><mi>MPa</mi></mrow></math></span> are necessary to grow the twin domains.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"206 ","pages":"Article 106407"},"PeriodicalIF":6.0,"publicationDate":"2025-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145416729","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-21DOI: 10.1016/j.jmps.2025.106396
Bruno Masseron , Giuseppe Rastiello , Rodrigue Desmorat , Nicolas Moës
Variational approaches for damage and fracture are now well established. Most of them are restricted to isotropic (scalar) damage, but tensorial internal variables are needed to properly account for loading-induced damage anisotropy. The objective of the present work is to present a theoretical framework for the variational formulation of second-order tensorial damage, in order to exploit the finesse and physical consistency of an anisotropic modeling of damage. Theoretical developments are conducted in order to investigate conceptual locks for such a type of formulation. A regularized anisotropic damage model is developed in a Lip-field framework, using the concept of accumulated damage. This quantity is introduced to define a scalar dissipation potential, whereas the tensorial damage variable appears in the free-energy potential. The proposed constitutive modeling serves both as a proof of concept and as a support for the analysis of the advantages and disadvantages of explicitly accounting for damage anisotropy through a tensorial damage variable. The proposed formulation is implemented in an ad-hoc finite element code in order to perform simple computations.
{"title":"Variational formulation of loading-induced damage anisotropy: Theoretical framework for second-order anisotropic damage and Lip-field regularization","authors":"Bruno Masseron , Giuseppe Rastiello , Rodrigue Desmorat , Nicolas Moës","doi":"10.1016/j.jmps.2025.106396","DOIUrl":"10.1016/j.jmps.2025.106396","url":null,"abstract":"<div><div>Variational approaches for damage and fracture are now well established. Most of them are restricted to isotropic (scalar) damage, but tensorial internal variables are needed to properly account for loading-induced damage anisotropy. The objective of the present work is to present a theoretical framework for the variational formulation of second-order tensorial damage, in order to exploit the finesse and physical consistency of an anisotropic modeling of damage. Theoretical developments are conducted in order to investigate conceptual locks for such a type of formulation. A regularized anisotropic damage model is developed in a Lip-field framework, using the concept of accumulated damage. This quantity is introduced to define a scalar dissipation potential, whereas the tensorial damage variable appears in the free-energy potential. The proposed constitutive modeling serves both as a proof of concept and as a support for the analysis of the advantages and disadvantages of explicitly accounting for damage anisotropy through a tensorial damage variable. The proposed formulation is implemented in an ad-hoc finite element code in order to perform simple computations.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"206 ","pages":"Article 106396"},"PeriodicalIF":6.0,"publicationDate":"2025-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145416727","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-21DOI: 10.1016/j.jmps.2025.106397
Zhengping Su, Yeqiang Bu, Wei Yang
Cracking represents a fundamental mode of failure in solids and structures, with mechanisms from catastrophic cleavage to fully ductile separation, as extensively investigated in materials spanning brittle ceramics and rocks to ductile metals and composites. However, for superhard materials, extreme hardness and brittleness result in exceptionally formidable challenges to mechanical testing and microstructural characterization, leaving their underlying cracking mechanisms and corresponding mechanical models largely unexplored. Herein, by employing a homemade in situ transmission electron microscopy mechanical stage, we observed two distinct cracking mechanisms in superhard cubic boron nitride (cBN), including the conventional brittle cleavage and a fundamentally different layered decohesion mechanism characterized by the formation of stacked hexagonal planes formed via a cubic-to-graphitic phase transition on the crack surfaces. Combining experimental observations and molecular dynamics simulations, it was revealed that the activation of the two cracking mechanisms depends on the surface flaw depth, with mechanistically distinct layered decohesion pathway occurring only when the flaw depth is below the critical flaw size. Building on the elucidated cracking mechanisms in cBN, a double-phase field model including both the descriptions of cleavage and the transition from cubic to graphitic phases is proposed. The presented phase field model endeavors to predict brittle or ductile fractures as occurred in cBN under severe strain, and provides a novel methodology to simulate the cracking in superhard covalent materials.
{"title":"A double-phase field formulation for cracking in cubic boron nitride: Coupling cleavage and a mechanistically distinct layered decohesion pathway","authors":"Zhengping Su, Yeqiang Bu, Wei Yang","doi":"10.1016/j.jmps.2025.106397","DOIUrl":"10.1016/j.jmps.2025.106397","url":null,"abstract":"<div><div>Cracking represents a fundamental mode of failure in solids and structures, with mechanisms from catastrophic cleavage to fully ductile separation, as extensively investigated in materials spanning brittle ceramics and rocks to ductile metals and composites. However, for superhard materials, extreme hardness and brittleness result in exceptionally formidable challenges to mechanical testing and microstructural characterization, leaving their underlying cracking mechanisms and corresponding mechanical models largely unexplored. Herein, by employing a homemade <em>in situ</em> transmission electron microscopy mechanical stage, we observed two distinct cracking mechanisms in superhard cubic boron nitride (cBN), including the conventional brittle cleavage and a fundamentally different layered decohesion mechanism characterized by the formation of stacked hexagonal planes formed via a cubic-to-graphitic phase transition on the crack surfaces. Combining experimental observations and molecular dynamics simulations, it was revealed that the activation of the two cracking mechanisms depends on the surface flaw depth, with mechanistically distinct layered decohesion pathway occurring only when the flaw depth is below the critical flaw size. Building on the elucidated cracking mechanisms in cBN, a double-phase field model including both the descriptions of cleavage and the transition from cubic to graphitic phases is proposed. The presented phase field model endeavors to predict brittle or ductile fractures as occurred in cBN under severe strain, and provides a novel methodology to simulate the cracking in superhard covalent materials.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"206 ","pages":"Article 106397"},"PeriodicalIF":6.0,"publicationDate":"2025-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145416730","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-17DOI: 10.1016/j.jmps.2025.106400
J. Hure
A homogenized model is proposed for describing ductile porous materials in which voids are embedded in an inhomogeneous isotropic matrix. First, limit analysis is used to derive yield criteria for spherical voids in a matrix material with an inhomogeneous yield stress. A three-parameter yield stress spatial distribution is considered, which generalizes special cases already considered in the literature. Three distinct yield criteria are derived, that correspond to void growth/low stress triaxiality, void growth/large stress triaxiality, and void necking coalescence. These criteria are combined using a regularized multi-surface plasticity framework. Evolution laws are proposed for the spatial distribution of yield stress as a function of the material’s hardening behaviour. The model is evaluated against a comprehensive database of porous unit cell FFT simulations for axisymmetric loading conditions, validating the yield criterion and demonstrating the model’s ability to reproduce stress–strain curves and porosity evolution. The model’s key output is that it greatly improves the predictions for stress triaxiality values relevant in the presence of cracks, surpassing the standard approach used in the literature. The model is used to perform non local finite element simulations of the ductile tearing of Compact Tension samples for different hardening behaviour, demonstrating its potential application in structural calculations. Finally, the implications of the power law regularization used to combine the yield criteria are discussed, as well as the model’s potential for physical modelling of void nucleation.
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Pub Date : 2025-10-17DOI: 10.1016/j.jmps.2025.106405
Haixiang Yu, Fengkai Liu, Jingda Tang
Soft collagenous tissues suffer fatigue damage with symptoms of reduced stiffness and residual deformation. Here we use bovine pericardium as a model tissue to study the fatigue damage and microstructure evolution through experiments and modeling. We propose an experimental method to characterize the fiber distribution during cyclic loading, and find that the evolution law satisfies an exponential function. We further establish the fatigue damage model by incorporating the evolution law of fiber dispersion degree, fiber stiffness and residual deformation into the constitutive model of soft tissues. The fatigue damage model can accurately predict the stress-stretch curves of bovine pericardium within 200,000 cycles. It is found that a larger stretch amplitude induces more fatigue damage with more severe fiber reorientation and stiffness reduction. The initial fiber orientation of tissues greatly influences fatigue damage, and microscopic observations are conducted to analyze the effect. This work incorporates the microstructural evolution into the phenomenological framework to quantify the fatigue damage behavior, and may help to understand the damage process of biological tissues.
{"title":"Fatigue damage and microstructure evolution of soft collagenous tissues","authors":"Haixiang Yu, Fengkai Liu, Jingda Tang","doi":"10.1016/j.jmps.2025.106405","DOIUrl":"10.1016/j.jmps.2025.106405","url":null,"abstract":"<div><div>Soft collagenous tissues suffer fatigue damage with symptoms of reduced stiffness and residual deformation. Here we use bovine pericardium as a model tissue to study the fatigue damage and microstructure evolution through experiments and modeling. We propose an experimental method to characterize the fiber distribution during cyclic loading, and find that the evolution law satisfies an exponential function. We further establish the fatigue damage model by incorporating the evolution law of fiber dispersion degree, fiber stiffness and residual deformation into the constitutive model of soft tissues. The fatigue damage model can accurately predict the stress-stretch curves of bovine pericardium within 200,000 cycles. It is found that a larger stretch amplitude induces more fatigue damage with more severe fiber reorientation and stiffness reduction. The initial fiber orientation of tissues greatly influences fatigue damage, and microscopic observations are conducted to analyze the effect. This work incorporates the microstructural evolution into the phenomenological framework to quantify the fatigue damage behavior, and may help to understand the damage process of biological tissues.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"206 ","pages":"Article 106405"},"PeriodicalIF":6.0,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145362832","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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