This paper presents a micromechanical model to predict the quasi-brittle behavior of Lightweight Aggregate Concrete (LWAC) under uniaxial and multiaxial loadings. The model integrates the incremental mean-field homogenization theory with continuum damage mechanics, focusing on LWAC filled with varying combinations of fine and coarse expanded clay (EC) aggregates. To simplify the modeling of EC aggregates with different densities, the concept of Fictitious Equivalent Inclusion (FEI) is introduced. Each LWAC sample is represented as a two-phase composite within a Representative Volume Element (RVE), consisting of a reference concrete matrix and a volume fraction of FEI. The incremental Mori–Tanaka model predicts stress and strain phase averages in the RVE, while the cementitious matrix follows Mazars’s -damage model coupled with fracture energy regularization. A confinement coefficient, accounting for triaxiality and porosity, enhances the model’s accuracy under multiaxial loadings. FEI, treated as softer than the matrix, exhibit elastic behavior. The model is validated against experimental data from literature, showing promising predictions for uniaxial, biaxial, and triaxial compression responses of LWC samples with various densities.
{"title":"Micromechanical modeling of the nonlinear behavior of lightweight aggregate concrete — Failure under multiaxial loading conditions","authors":"Slim Kammoun , Bilel Miled , Ali Ellouze , Karim Miled","doi":"10.1016/j.mechmat.2026.105628","DOIUrl":"10.1016/j.mechmat.2026.105628","url":null,"abstract":"<div><div>This paper presents a micromechanical model to predict the quasi-brittle behavior of Lightweight Aggregate Concrete (LWAC) under uniaxial and multiaxial loadings. The model integrates the incremental mean-field homogenization theory with continuum damage mechanics, focusing on LWAC filled with varying combinations of fine and coarse expanded clay (EC) aggregates. To simplify the modeling of EC aggregates with different densities, the concept of Fictitious Equivalent Inclusion (FEI) is introduced. Each LWAC sample is represented as a two-phase composite within a Representative Volume Element (RVE), consisting of a reference concrete matrix and a volume fraction of FEI. The incremental Mori–Tanaka model predicts stress and strain phase averages in the RVE, while the cementitious matrix follows Mazars’s <span><math><mi>μ</mi></math></span>-damage model coupled with fracture energy regularization. A confinement coefficient, accounting for triaxiality and porosity, enhances the model’s accuracy under multiaxial loadings. FEI, treated as softer than the matrix, exhibit elastic behavior. The model is validated against experimental data from literature, showing promising predictions for uniaxial, biaxial, and triaxial compression responses of LWC samples with various densities.</div></div>","PeriodicalId":18296,"journal":{"name":"Mechanics of Materials","volume":"215 ","pages":"Article 105628"},"PeriodicalIF":4.1,"publicationDate":"2026-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146078162","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-27DOI: 10.1016/j.mechmat.2026.105624
Nathan Perchikov , Jacob Aboudi , Konstantin Y. Volokh
The present paper treats the problem of dynamic propagation of damage in porous or composite materials with hyperelastic constituents subjected to rapid surface loading using a mechanistically derived constitutive theory, the High-Fidelity-Generalized-Method-of-Cells (HFGMC), specifically developed for the micromechanics of composites, and an explicit time-integration scheme. The constitutive theory includes a material density (damage) variable representing the mass fraction of intact material, associated with a homogenized stress, a momentum balance equation associated with a conserved mass of degrading matter and an evolution equation for the damage variable, based on local mass balance and a sharp energy threshold. Representative examples are solved, showing the emergence of spatial damage patterns of fractal character and associated power-law temporal dissipation correlations, both found to comply with experimental observations. The model can be used for material damage simulation in civil-engineering, biomechanical and geophysical applications. The paper complements previous studies on the application of the HFGMC to stress analysis in hyperelastic composites with fixed damage, quasistatic evolution of damage in hyperelastic composites and slow evolution of damage in viscoelastic composites.
{"title":"Self-organizing fractal damage patterns in dynamically-loaded heterogeneous materials","authors":"Nathan Perchikov , Jacob Aboudi , Konstantin Y. Volokh","doi":"10.1016/j.mechmat.2026.105624","DOIUrl":"10.1016/j.mechmat.2026.105624","url":null,"abstract":"<div><div>The present paper treats the problem of dynamic propagation of damage in porous or composite materials with hyperelastic constituents subjected to rapid surface loading using a mechanistically derived constitutive theory, the High-Fidelity-Generalized-Method-of-Cells (HFGMC), specifically developed for the micromechanics of composites, and an explicit time-integration scheme. The constitutive theory includes a material density (damage) variable representing the mass fraction of intact material, associated with a homogenized stress, a momentum balance equation associated with a conserved mass of degrading matter and an evolution equation for the damage variable, based on local mass balance and a sharp energy threshold. Representative examples are solved, showing the emergence of spatial damage patterns of fractal character and associated power-law temporal dissipation correlations, both found to comply with experimental observations. The model can be used for material damage simulation in civil-engineering, biomechanical and geophysical applications. The paper complements previous studies on the application of the HFGMC to stress analysis in hyperelastic composites with fixed damage, quasistatic evolution of damage in hyperelastic composites and slow evolution of damage in viscoelastic composites.</div></div>","PeriodicalId":18296,"journal":{"name":"Mechanics of Materials","volume":"216 ","pages":"Article 105624"},"PeriodicalIF":4.1,"publicationDate":"2026-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146096047","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-22DOI: 10.1016/j.mechmat.2026.105622
Runyan Du , John Orr , Zhenjun Yang , Zihua Zhang
Interfacial debonding between fibre-reinforced polymer (FRP) and concrete is one of the most common failure modes in externally bonded FRP (EB-FRP) strengthened concrete structures, typically occurring within a thin layer of concrete near the interface. This study uses the scaled boundary finite element method (SBFEM), a semi-analytical numerical approach, to model the interfacial debonding process between FRP and concrete. The quadtree meshing scheme is used to smooth the mesh transition near the interface, and high computational efficiency is achieved by exploiting the advantages of SBFEM. The Mazars damage model, which considers the tensile and compressive damage separately, is integrated with a nonlocal model to eliminate mesh sensitivity, thereby enabling the accurate prediction of damage evolution in the concrete substrate. Several benchmarks, including three-point bending notched beams (TPBNB), a double-notched tension beam (DNTB) and single shear FRP-concrete specimens, are simulated to confirm the effectiveness and reliability of the proposed method. The numerical results align closely with both the experimental data and finite element modelling. Furthermore, the effects of internal length, bond length, FRP stiffness, and concrete strength on the interfacial bonding performance are investigated. The existence of the effective bond length and its relation to the bond length are confirmed. The results also reveal that the failure mode of the interface is sensitive to the internal length and that the ultimate debonding load depends critically on both FRP stiffness and concrete strength.
{"title":"Modelling of interfacial debonding between FRP and concrete using the scaled boundary finite element method","authors":"Runyan Du , John Orr , Zhenjun Yang , Zihua Zhang","doi":"10.1016/j.mechmat.2026.105622","DOIUrl":"10.1016/j.mechmat.2026.105622","url":null,"abstract":"<div><div>Interfacial debonding between fibre-reinforced polymer (FRP) and concrete is one of the most common failure modes in externally bonded FRP (EB-FRP) strengthened concrete structures, typically occurring within a thin layer of concrete near the interface. This study uses the scaled boundary finite element method (SBFEM), a semi-analytical numerical approach, to model the interfacial debonding process between FRP and concrete. The quadtree meshing scheme is used to smooth the mesh transition near the interface, and high computational efficiency is achieved by exploiting the advantages of SBFEM. The Mazars damage model, which considers the tensile and compressive damage separately, is integrated with a nonlocal model to eliminate mesh sensitivity, thereby enabling the accurate prediction of damage evolution in the concrete substrate. Several benchmarks, including three-point bending notched beams (TPBNB), a double-notched tension beam (DNTB) and single shear FRP-concrete specimens, are simulated to confirm the effectiveness and reliability of the proposed method. The numerical results align closely with both the experimental data and finite element modelling. Furthermore, the effects of internal length, bond length, FRP stiffness, and concrete strength on the interfacial bonding performance are investigated. The existence of the effective bond length and its relation to the bond length are confirmed. The results also reveal that the failure mode of the interface is sensitive to the internal length and that the ultimate debonding load depends critically on both FRP stiffness and concrete strength.</div></div>","PeriodicalId":18296,"journal":{"name":"Mechanics of Materials","volume":"215 ","pages":"Article 105622"},"PeriodicalIF":4.1,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146078161","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-21DOI: 10.1016/j.mechmat.2026.105616
R. Vigneshwaran, A.A. Benzerga
The purpose of this work is to assess iterated variational homogenization estimates of the evolution of relative lengths and axes of ellipsoidal pores under unhomogeneous yielding. The latter is generally understood as the percolation of elastically unloaded zones in a porous material. To this end, the instantaneous average strain rate and rotation rate of the pores are calculated by requiring the overall strain rate to be congruent with unhomogeneous yielding. The predictions are then compared against numerically determined strain and rotation rates of the pores using finite element based limit-analysis. The two fundamental modes of unhomogeneous yielding are considered: opening/closure and sliding. We discuss in particular whether the predictions capture the extreme shearing of pores under sliding or the lateral bulging of pores under opening. For the opening mode, iterated variational homogenization performs well in predicting lateral bulging, except for nearly spherical pores. For sliding shear, the iterated variational homogenization estimates are qualitatively inaccurate and consistently underpredict the shearing and rotation rates of the pores. It is shown that simpler estimates from linear variational homogenization, augmented with ‘complementary’ concentration tensors, compare favorably with numerical results.
{"title":"Assessment of iterated variational homogenization for microstructure evolution in porous materials","authors":"R. Vigneshwaran, A.A. Benzerga","doi":"10.1016/j.mechmat.2026.105616","DOIUrl":"10.1016/j.mechmat.2026.105616","url":null,"abstract":"<div><div>The purpose of this work is to assess iterated variational homogenization estimates of the evolution of relative lengths and axes of ellipsoidal pores under unhomogeneous yielding. The latter is generally understood as the percolation of elastically unloaded zones in a porous material. To this end, the instantaneous average strain rate and rotation rate of the pores are calculated by requiring the overall strain rate to be congruent with unhomogeneous yielding. The predictions are then compared against numerically determined strain and rotation rates of the pores using finite element based limit-analysis. The two fundamental modes of unhomogeneous yielding are considered: opening/closure and sliding. We discuss in particular whether the predictions capture the extreme shearing of pores under sliding or the lateral bulging of pores under opening. For the opening mode, iterated variational homogenization performs well in predicting lateral bulging, except for nearly spherical pores. For sliding shear, the iterated variational homogenization estimates are qualitatively inaccurate and consistently underpredict the shearing and rotation rates of the pores. It is shown that simpler estimates from linear variational homogenization, augmented with ‘complementary’ concentration tensors, compare favorably with numerical results.</div></div>","PeriodicalId":18296,"journal":{"name":"Mechanics of Materials","volume":"215 ","pages":"Article 105616"},"PeriodicalIF":4.1,"publicationDate":"2026-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146078224","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-21DOI: 10.1016/j.mechmat.2026.105621
Yuanyuan Ma , Yueting Zhou , Shaonan Lu , Juan Yang , Xuefen Zhao , Shenghu Ding
The wave scattering caused by the quasicrystals (QCs) inclusion directly affects the overall wave behaviors of the QCs. Using the Gurtin-Murdoch (G-M) surface/interface theory and the complex function theory, this paper explores the scattering problem of SH wave by a cylindrical nano inclusion in the 1D hexagonal QCs. The scattered wave is expressed as a series of wave functions by applying the wave function expansion method. Then, the boundary conditions at the nanoscale, extrapolated from the generalized Young-Laplace equations, are used to establish an infinite system of algebraic equations for solving the scattered wave functions with unknown coefficients. The analytical stress field solutions are derived from the orthogonal characteristics of the trigonometric functions, which provide a new idea and solution for wave propagation problems in QCs. The effects of the surface effect parameters, the elastic constants, the coupling coefficients, and the wave numbers on the dimensionless hoop and radial stresses of the phonon and phason fields (DHRSPP) around the nano inclusion are analyzed in numerical examples. The results show that the dimensionless hoop stress (DHS) around the nano inclusion gradually decreases, and the dimensionless radial stress (DRS) increases with the increase of the surface effect parameters as well as the ratio of the phonon field's elastic constants. The distribution of dimensionless radial and hoop stress around the nano inclusion becomes more complex with the increase in wave number. The coupling coefficients have a considerably small effect on the DHRSPP around the nano inclusion. The research here contributes to the optimization and improvement of acoustic imaging, non-destructive testing, and material evaluation methods for QCs.
{"title":"Scattering of SH wave by a cylindrical nano inclusion in the 1D hexagonal quasicrystals","authors":"Yuanyuan Ma , Yueting Zhou , Shaonan Lu , Juan Yang , Xuefen Zhao , Shenghu Ding","doi":"10.1016/j.mechmat.2026.105621","DOIUrl":"10.1016/j.mechmat.2026.105621","url":null,"abstract":"<div><div>The wave scattering caused by the quasicrystals (QCs) inclusion directly affects the overall wave behaviors of the QCs. Using the Gurtin-Murdoch (G-M) surface/interface theory and the complex function theory, this paper explores the scattering problem of SH wave by a cylindrical nano inclusion in the 1D hexagonal QCs. The scattered wave is expressed as a series of wave functions by applying the wave function expansion method. Then, the boundary conditions at the nanoscale, extrapolated from the generalized Young-Laplace equations, are used to establish an infinite system of algebraic equations for solving the scattered wave functions with unknown coefficients. The analytical stress field solutions are derived from the orthogonal characteristics of the trigonometric functions, which provide a new idea and solution for wave propagation problems in QCs. The effects of the surface effect parameters, the elastic constants, the coupling coefficients, and the wave numbers on the dimensionless hoop and radial stresses of the phonon and phason fields (DHRSPP) around the nano inclusion are analyzed in numerical examples. The results show that the dimensionless hoop stress (DHS) around the nano inclusion gradually decreases, and the dimensionless radial stress (DRS) increases with the increase of the surface effect parameters as well as the ratio of the phonon field's elastic constants. The distribution of dimensionless radial and hoop stress around the nano inclusion becomes more complex with the increase in wave number. The coupling coefficients have a considerably small effect on the DHRSPP around the nano inclusion. The research here contributes to the optimization and improvement of acoustic imaging, non-destructive testing, and material evaluation methods for QCs.</div></div>","PeriodicalId":18296,"journal":{"name":"Mechanics of Materials","volume":"215 ","pages":"Article 105621"},"PeriodicalIF":4.1,"publicationDate":"2026-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146078225","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-15DOI: 10.1016/j.mechmat.2026.105620
Haoyuan Che , Zepu Liu , Fei Jia , Jian Sun , Yanju Liu
Soft materials with designed pore structures often exhibit superior properties, becoming increasingly important in advanced applications such as metamaterials and soft robotics. Quantitative characterization of the intrinsic mechanical properties of defect-containing soft materials is crucial for optimizing their performance. This study investigates spherical indentation for soft materials with cylindrical cavity defects. In contrast to the response of bulk materials, a critical load is identified from the load–displacement curve of the indentation test, at which the insertion-induced instability occurs. This is followed by a load decay and subsequent stabilization to in regions sufficiently remote from the cavity termini. By combining dimensional analysis with finite element method, the explicit expressions relating and to material parameters and friction coefficients are determined. An indentation method is subsequently developed to evaluate the shear modulus and friction coefficient simultaneously. Optimal parameter space of normalized cavity radius and is preliminarily determined to provide guidance for the indentation tests and avoid the absence of or the phenomenon of self-contact. The effectiveness of the proposed method is validated experimentally. By combining finite element analysis with theory of contact mechanics, we analyze the evolution of the load during indentation process. Experiments on specimens with multiple cavities show that the method remains reasonably effective for specimens containing multiple cavities. Through the incorporation of the Ogden hyperelastic model into finite element simulations, the method’s sensitivity to strain hardening is evaluated, confirming its robust performance for typical soft materials. Finally, an approximate expression for the stabilized load under low-friction conditions is derived, and the adhesive stress is further considered in the indentation method for cases involving low friction and relatively small adhesive stress.
{"title":"Characterization of soft materials with cylindrical cavity pores via indentation technique","authors":"Haoyuan Che , Zepu Liu , Fei Jia , Jian Sun , Yanju Liu","doi":"10.1016/j.mechmat.2026.105620","DOIUrl":"10.1016/j.mechmat.2026.105620","url":null,"abstract":"<div><div>Soft materials with designed pore structures often exhibit superior properties, becoming increasingly important in advanced applications such as metamaterials and soft robotics. Quantitative characterization of the intrinsic mechanical properties of defect-containing soft materials is crucial for optimizing their performance. This study investigates spherical indentation for soft materials with cylindrical cavity defects. In contrast to the response of bulk materials, a critical load <span><math><msub><mrow><mi>P</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> is identified from the load–displacement curve of the indentation test, at which the insertion-induced instability occurs. This is followed by a load decay and subsequent stabilization to <span><math><msub><mrow><mi>P</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> in regions sufficiently remote from the cavity termini. By combining dimensional analysis with finite element method, the explicit expressions relating <span><math><msub><mrow><mi>P</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>P</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> to material parameters and friction coefficients are determined. An indentation method is subsequently developed to evaluate the shear modulus <span><math><msub><mrow><mi>μ</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> and friction coefficient <span><math><mi>f</mi></math></span> simultaneously. Optimal parameter space of normalized cavity radius <span><math><msub><mrow><mover><mrow><mi>R</mi></mrow><mrow><mo>̄</mo></mrow></mover></mrow><mrow><mtext>h</mtext></mrow></msub></math></span> and <span><math><mi>f</mi></math></span> is preliminarily determined to provide guidance for the indentation tests and avoid the absence of <span><math><msub><mrow><mi>P</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> or the phenomenon of self-contact. The effectiveness of the proposed method is validated experimentally. By combining finite element analysis with theory of contact mechanics, we analyze the evolution of the load <span><math><mi>P</mi></math></span> during indentation process. Experiments on specimens with multiple cavities show that the method remains reasonably effective for specimens containing multiple cavities. Through the incorporation of the Ogden hyperelastic model into finite element simulations, the method’s sensitivity to strain hardening is evaluated, confirming its robust performance for typical soft materials. Finally, an approximate expression for the stabilized load <span><math><msub><mrow><mi>P</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> under low-friction conditions is derived, and the adhesive stress is further considered in the indentation method for cases involving low friction and relatively small adhesive stress.</div></div>","PeriodicalId":18296,"journal":{"name":"Mechanics of Materials","volume":"215 ","pages":"Article 105620"},"PeriodicalIF":4.1,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146024178","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-14DOI: 10.1016/j.mechmat.2026.105606
Eleonora Maggiorelli , Matteo Negri , Francesco Vicentini , Laura De Lorenzis
Reproducing the key features of fracture behavior under multiaxial stress states is essential for accurate modeling. Experimental evidence indicates that three intrinsic material properties govern fracture nucleation in elastic materials: elasticity, strength, and fracture toughness (or critical energy release rate). The flexibility in introducing these features in phase-field models poses significant challenges, especially under complex loading conditions. To attain this goal, recent work introduces a new energy functional within a cohesive phase-field framework. This model introduces an internal variable to describe the inelastic response. Notably, the strength is decoupled from the internal length, that is not interpreted as a material length scale, as often done in literature, but rather as a purely variational tool. The proposed functional allows for a rigorous variational framework, enabling the use of tools from the calculus of variations. We investigate the -convergence of the model to a sharp cohesive fracture energy in the one dimensional setting, using a finite element discrete formulation and exploiting the strong localization of the damage variable. Notably, unlike classical models where the elastic and fracture energies converge independently, this model exhibits a coupling of all energy terms. The limiting cohesive energy arises from the combined asymptotic behavior of the elastic energy (concentrated in a single element), the fracture energy, and the potential for the internal variable, while the remaining elastic energy converges separately. We highlight that the -convergence of the model can be extended to the two-dimensional (anti-plane) setting.
Finally, we present numerical simulations exploring the sensitivity of the model to mesh anisotropy, offering insight into both its theoretical robustness and its practical implementation.
{"title":"Γ-convergence for a phase-field cohesive energy","authors":"Eleonora Maggiorelli , Matteo Negri , Francesco Vicentini , Laura De Lorenzis","doi":"10.1016/j.mechmat.2026.105606","DOIUrl":"10.1016/j.mechmat.2026.105606","url":null,"abstract":"<div><div>Reproducing the key features of fracture behavior under multiaxial stress states is essential for accurate modeling. Experimental evidence indicates that three intrinsic material properties govern fracture nucleation in elastic materials: elasticity, strength, and fracture toughness (or critical energy release rate). The flexibility in introducing these features in phase-field models poses significant challenges, especially under complex loading conditions. To attain this goal, recent work introduces a new energy functional within a cohesive phase-field framework. This model introduces an internal variable to describe the inelastic response. Notably, the strength is decoupled from the internal length, that is not interpreted as a material length scale, as often done in literature, but rather as a purely variational tool. The proposed functional allows for a rigorous variational framework, enabling the use of tools from the calculus of variations. We investigate the <span><math><mi>Γ</mi></math></span>-convergence of the model to a sharp cohesive fracture energy in the one dimensional setting, using a finite element discrete formulation and exploiting the strong localization of the damage variable. Notably, unlike classical models where the elastic and fracture energies converge independently, this model exhibits a coupling of all energy terms. The limiting cohesive energy arises from the combined asymptotic behavior of the elastic energy (concentrated in a single element), the fracture energy, and the potential for the internal variable, while the remaining elastic energy converges separately. We highlight that the <span><math><mi>Γ</mi></math></span>-convergence of the model can be extended to the two-dimensional (anti-plane) setting.</div><div>Finally, we present numerical simulations exploring the sensitivity of the model to mesh anisotropy, offering insight into both its theoretical robustness and its practical implementation.</div></div>","PeriodicalId":18296,"journal":{"name":"Mechanics of Materials","volume":"215 ","pages":"Article 105606"},"PeriodicalIF":4.1,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979411","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-14DOI: 10.1016/j.mechmat.2025.105585
Hiroyuki Ono
In a previous paper, the author serendipitously identified that a simple discrete orientation distribution, which can represent two or three-dimensional random orientation states of isotropic ellipsoidal fillers, is closely related to the golden ratio. In particular, a three-dimensional random orientation state can be realized by assigning the same orientation angles to the fillers as those of the vertices of a regular dodecahedron or icosahedron, both of which are related to the golden ratio. This orientation method leads to isotropic macroscopic elastic constants and thermal expansion coefficients in the resulting material. In this study, we name this orientation method the regular polyhedron orientation method, and aim to extend this method to cases where the fillers have the same anisotropy as orthorhombic materials. By introducing a novel method that decomposes the anisotropic elastic constants into isotropic and anisotropic parts, and applying the Mori–Tanaka method, theoretical solutions for the macroscopic elastic constants and the thermal expansion coefficients are derived for both discrete and continuous random orientation states of fillers. Notably, the solution for the continuous two-dimensional random orientation can be obtained as a more general solution that also encompasses the solutions for both cases where fillers are aligned unidirectionally and oriented randomly in three dimensions. A comparison of the results from discrete and continuous orientation distributions reveals that the discrete orientation distributions that characterize the random orientation state are identical to those of the isotropic filler case. Therefore, the regular polyhedral orientation method is suggested to be effective regardless of the shape and physical properties of the fillers. Furthermore, it is also demonstrated that an approximate analysis using only the isotropic part of the fillers’ elastic constants may be valid with a certain degree of accuracy for analyzing three-dimensional random orientation states of fillers.
{"title":"A generalized discrete distribution model for random orientations of anisotropic fillers with orthorhombic properties: The regular polyhedron orientation method","authors":"Hiroyuki Ono","doi":"10.1016/j.mechmat.2025.105585","DOIUrl":"10.1016/j.mechmat.2025.105585","url":null,"abstract":"<div><div>In a previous paper, the author serendipitously identified that a simple discrete orientation distribution, which can represent two or three-dimensional random orientation states of isotropic ellipsoidal fillers, is closely related to the golden ratio. In particular, a three-dimensional random orientation state can be realized by assigning the same orientation angles to the fillers as those of the vertices of a regular dodecahedron or icosahedron, both of which are related to the golden ratio. This orientation method leads to isotropic macroscopic elastic constants and thermal expansion coefficients in the resulting material. In this study, we name this orientation method <em>the regular polyhedron orientation method</em>, and aim to extend this method to cases where the fillers have the same anisotropy as orthorhombic materials. By introducing a novel method that decomposes the anisotropic elastic constants into isotropic and anisotropic parts, and applying the Mori–Tanaka method, theoretical solutions for the macroscopic elastic constants and the thermal expansion coefficients are derived for both discrete and continuous random orientation states of fillers. Notably, the solution for the continuous two-dimensional random orientation can be obtained as a more general solution that also encompasses the solutions for both cases where fillers are aligned unidirectionally and oriented randomly in three dimensions. A comparison of the results from discrete and continuous orientation distributions reveals that the discrete orientation distributions that characterize the random orientation state are identical to those of the isotropic filler case. Therefore, the regular polyhedral orientation method is suggested to be effective regardless of the shape and physical properties of the fillers. Furthermore, it is also demonstrated that an approximate analysis using only the isotropic part of the fillers’ elastic constants may be valid with a certain degree of accuracy for analyzing three-dimensional random orientation states of fillers.</div></div>","PeriodicalId":18296,"journal":{"name":"Mechanics of Materials","volume":"215 ","pages":"Article 105585"},"PeriodicalIF":4.1,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146024179","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-13DOI: 10.1016/j.mechmat.2026.105604
Deepak B. Jadhav , Dhananjay Phansalkar , Kerstin Weinberg , Michael Ortiz , Sigrid Leyendecker
Phase field modeling of fracture is an effective approach for simulating crack propagation. However, the presence of a length scale parameter in the phase field model requires a uniformly fine mesh, leading to high computational costs, especially in dynamic simulations where the global time step is determined by the smallest spatial mesh element. A recently proposed asynchronous variational integrator (AVI) for the phase field modeling of dynamic fracture addresses this by allowing each spatial element to evolve with an independent time step. In this approach, mechanical fields are updated at every time step, while the phase field is updated only after the displacement update of the largest spatial mesh element, reducing the computational costs. We build upon this formulation by incorporating spatial adaptivity, refining the mesh based on a criterion guided by the phase field variable. This leads to a spatio-temporally adaptive AVI for the phase field model of dynamic fracture, with spatial adaptivity driven by the phase field evolution and temporal adaptivity inherently provided by the AVI. Benchmark studies show that the proposed method reduces computational costs while accurately capturing dynamic fracture behavior.
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Pub Date : 2026-01-13DOI: 10.1016/j.mechmat.2026.105607
Ruzhuan Wang , Weiguo Li
The high-temperature electrical breakdown strength is a critical indicator limiting the reliability of solid dielectric materials and their overall capacitor structure applications. Despite its crucial role, theoretical characterizing this high-temperature electrical breakdown strength is a challenging scientific issue that demands urgent attention. To address this gap, our work introduces a novel concept and model of temperature-dependent critical energy release rate corresponding to the electrical breakdown, which is based on the theory of energy storage limit. This concept, in turn, leads to the development of a temperature-dependent breakdown criterion that offers a more comprehensive understanding of the breakdown mechanisms at high temperature. Furthermore, we establish a temperature-dependent theoretical model and phase-field model for analyzing the electrical breakdown strength under the self-generated thermo-mechano-electrical coupling. This model takes into account temperature, electrically induced stress, the characteristic size of the electrical breakdown channel, and porosity. The developed breakdown criterion and theoretical model are verified by the remarkable agreements between the model predictions, phase-field simulation results and the experimental results from our work and the literature. The remarkable feature of the developed model is that, without any fitting, the quantitative characterization of coupling effects of temperature and microstructure evolution on the breakdown strength is realized. This work has developed a theory for high-temperature electrical breakdown, based on our research group's long-term work in the field of high-temperature fracture mechanics.
{"title":"Temperature-dependent electrical breakdown model of solid dielectric materials based on the high-temperature fracture mechanics","authors":"Ruzhuan Wang , Weiguo Li","doi":"10.1016/j.mechmat.2026.105607","DOIUrl":"10.1016/j.mechmat.2026.105607","url":null,"abstract":"<div><div>The high-temperature electrical breakdown strength is a critical indicator limiting the reliability of solid dielectric materials and their overall capacitor structure applications. Despite its crucial role, theoretical characterizing this high-temperature electrical breakdown strength is a challenging scientific issue that demands urgent attention. To address this gap, our work introduces a novel concept and model of temperature-dependent critical energy release rate corresponding to the electrical breakdown, which is based on the theory of energy storage limit. This concept, in turn, leads to the development of a temperature-dependent breakdown criterion that offers a more comprehensive understanding of the breakdown mechanisms at high temperature. Furthermore, we establish a temperature-dependent theoretical model and phase-field model for analyzing the electrical breakdown strength under the self-generated thermo-mechano-electrical coupling. This model takes into account temperature, electrically induced stress, the characteristic size of the electrical breakdown channel, and porosity. The developed breakdown criterion and theoretical model are verified by the remarkable agreements between the model predictions, phase-field simulation results and the experimental results from our work and the literature. The remarkable feature of the developed model is that, without any fitting, the quantitative characterization of coupling effects of temperature and microstructure evolution on the breakdown strength is realized. This work has developed a theory for high-temperature electrical breakdown, based on our research group's long-term work in the field of high-temperature fracture mechanics.</div></div>","PeriodicalId":18296,"journal":{"name":"Mechanics of Materials","volume":"215 ","pages":"Article 105607"},"PeriodicalIF":4.1,"publicationDate":"2026-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146024180","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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