Pub Date : 2026-03-01Epub Date: 2025-12-01DOI: 10.1016/j.ijsolstr.2025.113799
Zhaoyang Hu , Rui Li
This work introduces novel analytical solutions for the buckling of non-Lévy-type plate assemblies with line hinges and line supports, overcoming the constraints of current methods that concentrate primarily on Lévy-type cases. By utilizing the domain partitioning, we effectively divide plate assemblies into subplates free of internal discontinuities, facilitating the application of the symplectic superposition to derive analytical solutions with satisfactory convergence. Comparisons with the finite element method and the Ritz method confirm the reliability of the obtained buckling solutions. Comprehensive parametric studies reveal the significant effects of the hinge/support positions and the aspect ratios on the critical buckling loads. Moreover, the analytical framework developed in this paper is versatile enough to accommodate mixed boundary conditions and can be extended to thermal buckling. This research not only fills a gap in the existing literature but also deepens the understanding of buckling phenomena in line-hinged and line-supported plate assemblies.
{"title":"New buckling analysis of plate assemblies: Analytical solutions","authors":"Zhaoyang Hu , Rui Li","doi":"10.1016/j.ijsolstr.2025.113799","DOIUrl":"10.1016/j.ijsolstr.2025.113799","url":null,"abstract":"<div><div>This work introduces novel analytical solutions for the buckling of non-Lévy-type plate assemblies with line hinges and line supports, overcoming the constraints of current methods that concentrate primarily on Lévy-type cases. By utilizing the domain partitioning, we effectively divide plate assemblies into subplates free of internal discontinuities, facilitating the application of the symplectic superposition to derive analytical solutions with satisfactory convergence. Comparisons with the finite element method and the Ritz method confirm the reliability of the obtained buckling solutions. Comprehensive parametric studies reveal the significant effects of the hinge/support positions and the aspect ratios on the critical buckling loads. Moreover, the analytical framework developed in this paper is versatile enough to accommodate mixed boundary conditions and can be extended to thermal buckling. This research not only fills a gap in the existing literature but also deepens the understanding of buckling phenomena in line-hinged and line-supported plate assemblies.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"327 ","pages":"Article 113799"},"PeriodicalIF":3.8,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145692251","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2026-03-01Epub Date: 2025-12-08DOI: 10.1016/j.ijsolstr.2025.113806
Qingxian Li, Canhui Yang
Stretchable ionic conductors such as ionic hydrogels are the key functional materials for emerging applications, yet they are susceptible to composition fluctuation caused by swelling, which adversely alters their mechanical and electrical properties and limits their utility. Encapsulation with an elastomeric coating offers an effective means to suppress excessive swelling, however, the absence of quantitative mechanics analysis has significantly hindered rational designs and broader applications. Herein, we develop a theoretical model for the constrained swelling of an encapsulated structure comprising a cylindrical ionic conductor core and a non-absorbing elastomeric coating. We analyze the mechanics at equilibrium, providing quantitative insights into the deformation and stress fields, osmotic pressure, and solvent concentration distribution. The influence of key parameters—such as the modulus and thickness of the coating, the modulus and solvent-polymer affinity of the ionic conductor, environmental chemical potential and externally applied loads—on equilibrium solvent uptake is systematically evaluated. The proposed model elucidates the fundamental principles underlying compliantly constrained swelling in stretchable ionic conductors, thereby offering a robust theoretical foundation for the design and application of encapsulated ionic devices.
{"title":"Constrained swelling of stretchable ionic conductors with compliant encapsulations","authors":"Qingxian Li, Canhui Yang","doi":"10.1016/j.ijsolstr.2025.113806","DOIUrl":"10.1016/j.ijsolstr.2025.113806","url":null,"abstract":"<div><div>Stretchable ionic conductors such as ionic hydrogels are the key functional materials for emerging applications, yet they are susceptible to composition fluctuation caused by swelling, which adversely alters their mechanical and electrical properties and limits their utility. Encapsulation with an elastomeric coating offers an effective means to suppress excessive swelling, however, the absence of quantitative mechanics analysis has significantly hindered rational designs and broader applications. Herein, we develop a theoretical model for the constrained swelling of an encapsulated structure comprising a cylindrical ionic conductor core and a non-absorbing elastomeric coating. We analyze the mechanics at equilibrium, providing quantitative insights into the deformation and stress fields, osmotic pressure, and solvent concentration distribution. The influence of key parameters—such as the modulus and thickness of the coating, the modulus and solvent-polymer affinity of the ionic conductor, environmental chemical potential and externally applied loads—on equilibrium solvent uptake is systematically evaluated. The proposed model elucidates the fundamental principles underlying compliantly constrained swelling in stretchable ionic conductors, thereby offering a robust theoretical foundation for the design and application of encapsulated ionic devices.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"327 ","pages":"Article 113806"},"PeriodicalIF":3.8,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145836735","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2026-03-01Epub Date: 2025-12-05DOI: 10.1016/j.ijsolstr.2025.113803
Xuebo Yuan
Film–substrate systems are ubiquitous in biological adhesion, multi-chip packaging, flexible electronics, and nanomaterials, with peeling behavior directly influencing structural stability and functionality. However, the peeling mechanics of films with adhesive heterogeneity are not yet fully understood. In this work, the peeling behavior of elastic films with spatially varying adhesion under a vertical peeling force, bonded to a rigid substrate, is investigated. Based on the principle of minimum potential energy, a large-deformation mechanics model for peeling heterogeneous films is developed within finite deflection and validated using molecular dynamics simulations. The results show that adhesive heterogeneity can markedly influence the evolution of the peeling force. When the peeling front traverses segments with different adhesion toughness, the resulting increase or decrease in peeling force depends on the segment adhesion, segment length, and overall geometrical proportions. Periodically heterogeneous films exhibit oscillatory peeling forces, with amplitudes regulated by the period length and adhesive distribution, which can be approximated by a homogeneous film with equivalent adhesion toughness. The variations in peeling force primarily result from the redistribution of bending energy within the film and the work required to overcome interfacial interactions. The findings provide a theoretical foundation for tuning the peeling behavior of film–substrate systems.
{"title":"Finite-deflection peeling of elastic films with adhesive heterogeneity","authors":"Xuebo Yuan","doi":"10.1016/j.ijsolstr.2025.113803","DOIUrl":"10.1016/j.ijsolstr.2025.113803","url":null,"abstract":"<div><div>Film–substrate systems are ubiquitous in biological adhesion, multi-chip packaging, flexible electronics, and nanomaterials, with peeling behavior directly influencing structural stability and functionality. However, the peeling mechanics of films with adhesive heterogeneity are not yet fully understood. In this work, the peeling behavior of elastic films with spatially varying adhesion under a vertical peeling force, bonded to a rigid substrate, is investigated. Based on the principle of minimum potential energy, a large-deformation mechanics model for peeling heterogeneous films is developed within finite deflection and validated using molecular dynamics simulations. The results show that adhesive heterogeneity can markedly influence the evolution of the peeling force. When the peeling front traverses segments with different adhesion toughness, the resulting increase or decrease in peeling force depends on the segment adhesion, segment length, and overall geometrical proportions. Periodically heterogeneous films exhibit oscillatory peeling forces, with amplitudes regulated by the period length and adhesive distribution, which can be approximated by a homogeneous film with equivalent adhesion toughness. The variations in peeling force primarily result from the redistribution of bending energy within the film and the work required to overcome interfacial interactions. The findings provide a theoretical foundation for tuning the peeling behavior of film–substrate systems.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"327 ","pages":"Article 113803"},"PeriodicalIF":3.8,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145749211","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2026-03-01Epub Date: 2025-12-24DOI: 10.1016/j.ijsolstr.2025.113816
Linlong Mu , Tao Zhou , Yimin Lu , Maosong Huang
Understanding the vertical dynamic impedance of rigid foundations on saturated soils is critical for offshore and marine infrastructure design but remains challenging due to coupled solid–fluid interactions and complex boundary conditions. While previous studies often assume interface conditions − either fully permeable or fully impermeable, practical scenarios like suction bucket involve mixed-permeability boundaries, a problem rarely addressed rigorously under high-frequency excitation. This study presents a semi-analytical solution for the high-frequency vertical vibration of a rigid impermeable circular disk resting on a saturated poroelastic half-space. The governing equations, derived from Biot’s theory, are solved using displacement potential functions and Hankel integral transforms, fully incorporating the compressibility of both the soil skeleton and pore fluid. A dual integral equation describing the mixed boundary conditions at the impermeable disk interface is established and transformed into a numerically solvable second-kind Fredholm integral equation. The solution is validated against time-domain finite element simulations and classical results, showing excellent agreement across a wide frequency range. Parametric studies reveal that Poisson’s ratio and porosity significantly influence dynamic compliance in the high-frequency regime, while the compressibility of the solid and fluid phases plays a minor role. Interface permeability is shown to substantially affect the dynamic response in highly permeable soils, but has negligible impact in low-permeability conditions. These findings enhance the theoretical framework for soil-structure interaction in saturated media and provide a robust tool for designing dynamically loaded seabed-mounted foundations.
{"title":"High-frequency vertical vibration of a rigid impermeable disk on a saturated poroelastic half-space","authors":"Linlong Mu , Tao Zhou , Yimin Lu , Maosong Huang","doi":"10.1016/j.ijsolstr.2025.113816","DOIUrl":"10.1016/j.ijsolstr.2025.113816","url":null,"abstract":"<div><div>Understanding the vertical dynamic impedance of rigid foundations on saturated soils is critical for offshore and marine infrastructure design but remains challenging due to coupled solid–fluid interactions and complex boundary conditions. While previous studies often assume interface conditions − either fully permeable or fully impermeable, practical scenarios like suction bucket involve mixed-permeability boundaries, a problem rarely addressed rigorously under high-frequency excitation. This study presents a semi-analytical solution for the high-frequency vertical vibration of a rigid impermeable circular disk resting on a saturated poroelastic half-space. The governing equations, derived from Biot’s theory, are solved using displacement potential functions and Hankel integral transforms, fully incorporating the compressibility of both the soil skeleton and pore fluid. A dual integral equation describing the mixed boundary conditions at the impermeable disk interface is established and transformed into a numerically solvable second-kind Fredholm integral equation. The solution is validated against time-domain finite element simulations and classical results, showing excellent agreement across a wide frequency range. Parametric studies reveal that Poisson’s ratio and porosity significantly influence dynamic compliance in the high-frequency regime, while the compressibility of the solid and fluid phases plays a minor role. Interface permeability is shown to substantially affect the dynamic response in highly permeable soils, but has negligible impact in low-permeability conditions. These findings enhance the theoretical framework for soil-structure interaction in saturated media and provide a robust tool for designing dynamically loaded seabed-mounted foundations.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"327 ","pages":"Article 113816"},"PeriodicalIF":3.8,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145837207","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2026-03-01Epub Date: 2025-12-19DOI: 10.1016/j.ijsolstr.2025.113810
Enzhao Xiao , Hao Wang , Jibin Ding , Xueyuan Tang , Bo Sun , Zhenxuan Yin , Tong Han , Yihe Wang
As one of the most fundamental mechanical properties of snow, the elastic modulus is necessary for diverse applications including avalanche modelling as well as designs and constructions of snow infrastructures. Against the backdrop that snow densities are insufficient to fully parameterize snow elastic moduli, relating mesoscale parameters beyond density to snow elastic moduli is a critical and longstanding problem which hinders accurate parameterizations of snow elastic moduli. However, as an important step towards solving this problem, the mesoscale mechanical responses corresponding to snow elastic moduli have rarely been quantitatively analyzed. In this study we investigate the mesoscale mechanical responses corresponding to the elastic moduli of compacted Antarctic snow near Zhongshan Station. Firstly, the P wave propagation experiments are employed to quantify the effects of density and sintering time on the elastic modulus, and microstructures of compacted Antarctic snow are obtained from X-ray tomography images. Afterwards the finite element method based mesoscale simulations are validated against the measured elastic modulus from the P wave propagation experiments. Finally, the mesoscale mechanical responses for uniaxial compressions are quantitatively analyzed based on the mesoscale simulation results. It is found that for the considered densities and sintering times, the volume ratio of tensile stresses in the loading direction range from 3.25% to 9.46%, and the volume ratio of compressive stresses larger than the nominal compressive stress in the loading direction range from 38.66% to 44.22%. Bending moments in the cross sections perpendicular to the loading direction exist and are uncorrelated to the statical moment of area, yet the average bending moments depend on the average statical moment of area among cross sections perpendicular to the loading direction. By scrutinizing the stress distributions within the microstructures, the connected local force transmitting channel throughout the microstructure in the loading direction is identified as a necessary condition for load-bearing force chains. Additionally, the potential of the directional connectivity and the structure thickness to parameterize snow elastic moduli are discussed.
{"title":"Mesoscale mechanical responses corresponding to the elastic moduli of compacted Antarctic snow near Zhongshan Station","authors":"Enzhao Xiao , Hao Wang , Jibin Ding , Xueyuan Tang , Bo Sun , Zhenxuan Yin , Tong Han , Yihe Wang","doi":"10.1016/j.ijsolstr.2025.113810","DOIUrl":"10.1016/j.ijsolstr.2025.113810","url":null,"abstract":"<div><div>As one of the most fundamental mechanical properties of snow, the elastic modulus is necessary for diverse applications including avalanche modelling as well as designs and constructions of snow infrastructures. Against the backdrop that snow densities are insufficient to fully parameterize snow elastic moduli, relating mesoscale parameters beyond density to snow elastic moduli is a critical and longstanding problem which hinders accurate parameterizations of snow elastic moduli. However, as an important step towards solving this problem, the mesoscale mechanical responses corresponding to snow elastic moduli have rarely been quantitatively analyzed. In this study we investigate the mesoscale mechanical responses corresponding to the elastic moduli of compacted Antarctic snow near Zhongshan Station. Firstly, the P wave propagation experiments are employed to quantify the effects of density and sintering time on the elastic modulus, and microstructures of compacted Antarctic snow are obtained from X-ray tomography images. Afterwards the finite element method based mesoscale simulations are validated against the measured elastic modulus from the P wave propagation experiments. Finally, the mesoscale mechanical responses for uniaxial compressions are quantitatively analyzed based on the mesoscale simulation results. It is found that for the considered densities and sintering times, the volume ratio of tensile stresses in the loading direction range from 3.25% to 9.46%, and the volume ratio of compressive stresses larger than the nominal compressive stress in the loading direction range from 38.66% to 44.22%. Bending moments in the cross sections perpendicular to the loading direction exist and are uncorrelated to the statical moment of area, yet the average bending moments depend on the average statical moment of area among cross sections perpendicular to the loading direction. By scrutinizing the stress distributions within the microstructures, the connected local force transmitting channel throughout the microstructure in the loading direction is identified as a necessary condition for load-bearing force chains. Additionally, the potential of the directional connectivity and the structure thickness to parameterize snow elastic moduli are discussed.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"327 ","pages":"Article 113810"},"PeriodicalIF":3.8,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145836737","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This study proposes a coupling method that integrates local and nonlocal continuum mechanics to predict brittle fractures in functionally graded materials (FGMs). The main advantage of this approach is its ability to combine the strengths of classical continuum mechanics (CCM) and bond-based peridynamics (BPD), enabling accurate and efficient fracture simulations in FGMs. By establishing a pointwise equivalence of deformation energy density, an equivalent continuum mechanics model is derived from the bond-based peridynamic framework for FGMs and the relationship between the equivalent stiffness tensors and the micromodulus of the BPD model is formulated. These two models are then coupled into a unified system of equations, with a transition region introduced to ensure a smooth connection between them. The nonlocal BPD model is applied specifically to the fracture region, while the local CCM is employed in areas undergoing continuous deformation, thereby significantly reducing the computational cost of FGM fracture simulations. The convergence of the coupling model to CCM is demonstrated through rigorous mathematical analysis. Finally, the accuracy and efficiency of the coupling method are verified through two- and three-dimensional numerical examples.
{"title":"A energy-based coupling approach of peridynamic and classical continuum mechanics for FGM brittle fractures","authors":"Shaoqi Zheng , Yanfu Chen , Jiwei Zhang , Jieqiong Zhang , Zihao Yang","doi":"10.1016/j.ijsolstr.2025.113802","DOIUrl":"10.1016/j.ijsolstr.2025.113802","url":null,"abstract":"<div><div>This study proposes a coupling method that integrates local and nonlocal continuum mechanics to predict brittle fractures in functionally graded materials (FGMs). The main advantage of this approach is its ability to combine the strengths of classical continuum mechanics (CCM) and bond-based peridynamics (BPD), enabling accurate and efficient fracture simulations in FGMs. By establishing a pointwise equivalence of deformation energy density, an equivalent continuum mechanics model is derived from the bond-based peridynamic framework for FGMs and the relationship between the equivalent stiffness tensors and the micromodulus of the BPD model is formulated. These two models are then coupled into a unified system of equations, with a transition region introduced to ensure a smooth connection between them. The nonlocal BPD model is applied specifically to the fracture region, while the local CCM is employed in areas undergoing continuous deformation, thereby significantly reducing the computational cost of FGM fracture simulations. The convergence of the coupling model to CCM is demonstrated through rigorous mathematical analysis. Finally, the accuracy and efficiency of the coupling method are verified through two- and three-dimensional numerical examples.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"327 ","pages":"Article 113802"},"PeriodicalIF":3.8,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145749205","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 2025-11-18DOI: 10.1016/j.ijsolstr.2025.113767
I. Doghri , M. Haddad , G. Tsilimidos , Y. Ru , M. Lackner , Z. Major
High cycle fatigue (HCF) of solids and structures made of thermoplastic polymers is predicted with a new time and space multiscale formulation. The microstructure is viewed as being made of a viscoelastic (VE) matrix phase with small concentrations of process-induced pores and viscoelastic–viscoplastic (VEVP) damaging weak spots, which have almost no visible influence on the structural response but are responsible eventually for fatigue failure. The structure is first computed as being VE, using a Laplace-Carson based formulation enabling to compute accurate histories of strain and stress fields at a very reduced cost, which is also independent of the number of cycles. Next, the full VEVP solution for any heterogeneous representative volume element (RVE) is computed by coupling time homogenization with space homogenization. The former theory uses fast and slow time scales and asymptotic time expansions, while the latter is based on mean-field homogenization via the incremental-secant model. Coupled time and space homogenization enables to compute complete RVE solution histories at extremely limited cost. The number of cycles to failure at the macroscale is predicted when microscale damage in the weak spots reaches a critical value. The numerical accuracy of the new formulation is verified against reference solutions, and its predictions compared against experimental S-N curves for additively manufactured hollow and notched cylindrical specimens of TPU material, under displacement or force controlled HCF.
{"title":"Time and space multiscale modeling of the high cycle fatigue of polymer solids and structures","authors":"I. Doghri , M. Haddad , G. Tsilimidos , Y. Ru , M. Lackner , Z. Major","doi":"10.1016/j.ijsolstr.2025.113767","DOIUrl":"10.1016/j.ijsolstr.2025.113767","url":null,"abstract":"<div><div>High cycle fatigue (HCF) of solids and structures made of thermoplastic polymers is predicted with a new time and space multiscale formulation. The microstructure is viewed as being made of a viscoelastic (VE) matrix phase with small concentrations of process-induced pores and viscoelastic–viscoplastic (VEVP) damaging weak spots, which have almost no visible influence on the structural response but are responsible eventually for fatigue failure. The structure is first computed as being VE, using a Laplace-Carson based formulation enabling to compute accurate histories of strain and stress fields at a very reduced cost, which is also independent of the number of cycles. Next, the full VEVP solution for any heterogeneous representative volume element (RVE) is computed by coupling time homogenization with space homogenization. The former theory uses fast and slow time scales and asymptotic time expansions, while the latter is based on mean-field homogenization via the incremental-secant model. Coupled time and space homogenization enables to compute complete RVE solution histories at extremely limited cost. The number of cycles to failure at the macroscale is predicted when microscale damage in the weak spots reaches a critical value. The numerical accuracy of the new formulation is verified against reference solutions, and its predictions compared against experimental S-N curves for additively manufactured hollow and notched cylindrical specimens of TPU material, under displacement or force controlled HCF.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"326 ","pages":"Article 113767"},"PeriodicalIF":3.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145569772","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 2025-11-07DOI: 10.1016/j.ijsolstr.2025.113745
Yiwei Hua, Gabriele Milani
This paper proposes two alternatives for the polygon discretization in the finite element limit analysis. The construction of the upper bound limit analysis for the constant-strain polygon element is first presented. However, when implementing it to analyze the strip footing problems, a severe locking effect is observed in the results, which stems from the constant-strain assumption. Further sensitivity analysis demonstrates that such a locking issue becomes significant when using polygons with complex or concave shapes. The volumetric incompressible effect will also appear in both polygon and triangular meshes in the zero-friction case, and this is more remarkable in the polygon case because of the severe interlocking among the elements. The corresponding optimization problem will become unsolvable. An approximated solution can still be obtained by including spurious interfacial friction though. Finally, to theoretically resolve the locking problem, another type of polygon element with piecewise-constant strain is developed. Reproducing the previously considered strip footing problems through the new element, the results indicate that the polygon locking is largely released after introducing the strain variation in the elements. The analysis gives an accurate load prediction within an acceptable computational cost, presenting a great edge in precision and robustness against the established triangular elements. Nonetheless, the constant-strain polygon can remain employed in some scenarios where the locking effect is not obvious, taking merit from its great efficiency.
{"title":"New deformable element with arbitrary polygon shape for continuous modeling of limit analysis","authors":"Yiwei Hua, Gabriele Milani","doi":"10.1016/j.ijsolstr.2025.113745","DOIUrl":"10.1016/j.ijsolstr.2025.113745","url":null,"abstract":"<div><div>This paper proposes two alternatives for the polygon discretization in the finite element limit analysis. The construction of the upper bound limit analysis for the constant-strain polygon element is first presented. However, when implementing it to analyze the strip footing problems, a severe locking effect is observed in the results, which stems from the constant-strain assumption. Further sensitivity analysis demonstrates that such a locking issue becomes significant when using polygons with complex or concave shapes. The volumetric incompressible effect will also appear in both polygon and triangular meshes in the zero-friction case, and this is more remarkable in the polygon case because of the severe interlocking among the elements. The corresponding optimization problem will become unsolvable. An approximated solution can still be obtained by including spurious interfacial friction though. Finally, to theoretically resolve the locking problem, another type of polygon element with piecewise-constant strain is developed. Reproducing the previously considered strip footing problems through the new element, the results indicate that the polygon locking is largely released after introducing the strain variation in the elements. The analysis gives an accurate load prediction within an acceptable computational cost, presenting a great edge in precision and robustness against the established triangular elements. Nonetheless, the constant-strain polygon can remain employed in some scenarios where the locking effect is not obvious, taking merit from its great efficiency.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"326 ","pages":"Article 113745"},"PeriodicalIF":3.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145518001","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 2025-11-21DOI: 10.1016/j.ijsolstr.2025.113783
Romain Quey
Closed-form expressions of the size of the representative volume element are determined for computing the elastic moduli of polycrystalline materials with cubic and hexagonal crystal symmetries. The size of the representative volume element corresponds to the number of grains needed in a polycrystal, , to compute a property of the material (an elastic modulus) with a given error, . The elastic moduli are computed using periodic polycrystals and finite element simulations. A typical, experimental grain-growth microstructure is considered as a reference case, and the microstructure properties are then modified. This allows us to determine the effect of the different microstructural properties on the error (). The relationship between the error () and the size of the representative volume element () is shown to be , where depends on both the crystal anisotropy of the material and the variability of the effective orientation distribution of the microstructure. This variability in turn arises from the cumulative effects of two main sources: the random sampling of the orientation distribution and the grain size distribution. Then, general expressions of applying to all cubic and hexagonal-symmetry materials are determined. It is demonstrated that reducing the microstructural variability does not affect the computed elastic modulus values, thereby enabling the use of polycrystals with significantly fewer grains. For copper, the error in the computed shear modulus () can be reduced by a factor of 9.4 (for a given number of grains in a polycrystal, ), or equivalently, the number of grains needed in a polycrystal () can be reduced by a factor of about 90 (for a given error, ). Similar results are obtained for (hexagonal-symmetry) titanium and zinc, for which can be reduced by factors of 140 and 45, respectively. The results also indicate that the size of the representative volume element () is smaller for hexagonal-symmetry materials than for cubic-symmetry materials, and smaller for the bulk modulus than for the shear modulus.
{"title":"Microstructural dependence and reduction of the size of the representative volume element in polycrystals: Case of cubic and hexagonal elasticity","authors":"Romain Quey","doi":"10.1016/j.ijsolstr.2025.113783","DOIUrl":"10.1016/j.ijsolstr.2025.113783","url":null,"abstract":"<div><div>Closed-form expressions of the size of the representative volume element are determined for computing the elastic moduli of polycrystalline materials with cubic and hexagonal crystal symmetries. The size of the representative volume element corresponds to the number of grains needed in a polycrystal, <span><math><mi>N</mi></math></span>, to compute a property of the material (an elastic modulus) with a given error, <span><math><mi>e</mi></math></span>. The elastic moduli are computed using periodic polycrystals and finite element simulations. A typical, experimental grain-growth microstructure is considered as a reference case, and the microstructure properties are then modified. This allows us to determine the effect of the different microstructural properties on the error (<span><math><mi>e</mi></math></span>). The relationship between the error (<span><math><mi>e</mi></math></span>) and the size of the representative volume element (<span><math><mi>N</mi></math></span>) is shown to be <span><math><mrow><mi>e</mi><mo>=</mo><mi>a</mi><mo>/</mo><msqrt><mrow><mi>N</mi></mrow></msqrt></mrow></math></span>, where <span><math><mi>a</mi></math></span> depends on both the crystal anisotropy of the material and the variability of the effective orientation distribution of the microstructure. This variability in turn arises from the cumulative effects of two main sources: the random sampling of the orientation distribution and the grain size distribution. Then, general expressions of <span><math><mi>a</mi></math></span> applying to all cubic and hexagonal-symmetry materials are determined. It is demonstrated that reducing the microstructural variability does not affect the computed elastic modulus values, thereby enabling the use of polycrystals with significantly fewer grains. For copper, the error in the computed shear modulus (<span><math><mi>e</mi></math></span>) can be reduced by a factor of 9.4 (for a given number of grains in a polycrystal, <span><math><mi>N</mi></math></span>), or equivalently, the number of grains needed in a polycrystal (<span><math><mi>N</mi></math></span>) can be reduced by a factor of about 90 (for a given error, <span><math><mi>e</mi></math></span>). Similar results are obtained for (hexagonal-symmetry) titanium and zinc, for which <span><math><mi>N</mi></math></span> can be reduced by factors of 140 and 45, respectively. The results also indicate that the size of the representative volume element (<span><math><mi>N</mi></math></span>) is smaller for hexagonal-symmetry materials than for cubic-symmetry materials, and smaller for the bulk modulus than for the shear modulus.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"326 ","pages":"Article 113783"},"PeriodicalIF":3.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145615476","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This study systematically investigates the viscoelastic–plastic mechanical behavior of thermoplastic composite matrix PEEK-5600G under wide temperature range (23-180 °) and multi strain rate (0.00229-0.19361/s) conditions. Tensile and stress relaxation experiments under large strain conditions and temperature-dependent viscoelastic parameters were conducted to obtain true stress responses. A novel physics-informed data-driven approach was proposed, where an Artificial Neural Network (ANN) architecture was developed for flow stress prediction. Through a comparative analysis methodology of multiple ANN configurations, the optimized model was acquired, demonstrating exceptional predictive capability characterized by a Pearson’s correlation coefficient of R=0.9998, Mean Squared Error , and Average Absolute Relative Error %. Building upon experimental data and the optimized ANN framework, an incremental VK-ANN viscoelastic–plastic constitutive model was established by integrating Voigt–Kelvin viscoelastic theory with ANN-based flow rules. The corresponding VUMAT subroutine was implemented in the Abaqus/Explicit finite element code, with numerical simulations of tensile loading tests validating the model’s superior predictive accuracy.
{"title":"A viscoelastic-plastic constitutive model for PEEK resin based on the physical model and artificial neural network","authors":"FeiYang Zhao, Jinzhao Huang, Shangyang Yu, Jikai Yu, Licheng Guo","doi":"10.1016/j.ijsolstr.2025.113738","DOIUrl":"10.1016/j.ijsolstr.2025.113738","url":null,"abstract":"<div><div>This study systematically investigates the viscoelastic–plastic mechanical behavior of thermoplastic composite matrix PEEK-5600G under wide temperature range (23-180 °<span><math><mi>C</mi></math></span>) and multi strain rate (0.00229-0.19361/s) conditions. Tensile and stress relaxation experiments under large strain conditions and temperature-dependent viscoelastic parameters were conducted to obtain true stress responses. A novel physics-informed data-driven approach was proposed, where an Artificial Neural Network (ANN) architecture was developed for flow stress prediction. Through a comparative analysis methodology of multiple ANN configurations, the optimized model was acquired, demonstrating exceptional predictive capability characterized by a Pearson’s correlation coefficient of R=0.9998, Mean Squared Error <span><math><mrow><msub><mrow><mi>E</mi></mrow><mrow><mi>MSE</mi></mrow></msub><mo>=</mo><mn>1</mn><mo>.</mo><mn>12</mn><mi>E</mi><mo>−</mo><mn>5</mn></mrow></math></span>, and Average Absolute Relative Error <span><math><mrow><msub><mrow><mi>E</mi></mrow><mrow><mi>AAR</mi></mrow></msub><mo>=</mo><mn>3</mn><mo>.</mo><mn>42</mn></mrow></math></span>%. Building upon experimental data and the optimized ANN framework, an incremental VK-ANN viscoelastic–plastic constitutive model was established by integrating Voigt–Kelvin viscoelastic theory with ANN-based flow rules. The corresponding VUMAT subroutine was implemented in the Abaqus/Explicit finite element code, with numerical simulations of tensile loading tests validating the model’s superior predictive accuracy.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"326 ","pages":"Article 113738"},"PeriodicalIF":3.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145464476","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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