Pub Date : 2026-01-05DOI: 10.1016/j.compstruc.2025.108095
Zhiyuan Tong, Mauricio Ponga
We present a novel meshfree method for accurate and efficient solutions to solid mechanics problems involving large deviatoric deformation, fracture, and fragmentation. Central to the approach is a newly developed meshfree shape function that satisfies the Kronecker delta property, exhibits first-order consistency, is non-negative, and achieves smoothness. The formulation employs nodal integration which is desirable for problems with large topological changes. The combination of nodal integration and the Kronecker delta property leads to a naturally diagonal explicit equilibrium equation even in the presence of complex boundary and contact conditions. A key innovation is the introduction of shadow nodes, which, in conjunction with a local triangle removal strategy, enables the seamless handling of complex geometries and evolving discontinuities without explicit boundary representations. The method demonstrates excellent convergence and high accuracy across a range of linear and nonlinear benchmark problems. Its robustness and versatility are further illustrated through challenging simulations involving extreme fracture and fragmentation.
{"title":"A new meshfree method for accurate and efficient solutions to solid mechanics problems involving large deviatoric deformation, fracture, and fragmentation","authors":"Zhiyuan Tong, Mauricio Ponga","doi":"10.1016/j.compstruc.2025.108095","DOIUrl":"10.1016/j.compstruc.2025.108095","url":null,"abstract":"<div><div>We present a novel meshfree method for accurate and efficient solutions to solid mechanics problems involving large deviatoric deformation, fracture, and fragmentation. Central to the approach is a newly developed meshfree shape function that satisfies the Kronecker delta property, exhibits first-order consistency, is non-negative, and achieves <span><math><msup><mrow><mi>C</mi></mrow><mn>1</mn></msup></math></span> smoothness. The formulation employs nodal integration which is desirable for problems with large topological changes. The combination of nodal integration and the Kronecker delta property leads to a naturally diagonal explicit equilibrium equation even in the presence of complex boundary and contact conditions. A key innovation is the introduction of shadow nodes, which, in conjunction with a local triangle removal strategy, enables the seamless handling of complex geometries and evolving discontinuities without explicit boundary representations. The method demonstrates excellent convergence and high accuracy across a range of linear and nonlinear benchmark problems. Its robustness and versatility are further illustrated through challenging simulations involving extreme fracture and fragmentation.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"321 ","pages":"Article 108095"},"PeriodicalIF":4.8,"publicationDate":"2026-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145902509","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-02DOI: 10.1016/j.compstruc.2025.108086
Nasrin Talebi, Knut Andreas Meyer, Magnus Ekh
Simulation of many loading cycles with traditional time-domain material models, requiring discretization of each cycle with several time steps, can result in high computational cost. One effective approach to speed up cyclic simulations is employing cycle-domain material models. Finite element simulations of rails subjected to many wheel passages are a relevant application of such models. Proposing a per-cycle evolution equation for plastic strains in cycle-domain models is, however, a challenge. To address this, we investigate the feasibility and accuracy of using machine learning models as tools for formulating such an equation. Specifically, we enforce our knowledge from constitutive modeling for elasticity and formulate the evolution law by employing feed-forward neural networks with different inputs, as well as symbolic regression to discover an interpretable expression. Training, validation, and test data have been generated using a cyclic time-domain plasticity model considering pulsating uniaxial stress loadings with constant and variable strain ranges. The obtained results demonstrate the potential of cycle-domain plasticity modeling using both uninterpretable and interpretable data-driven machine learning as an alternative to time-domain material modeling. Furthermore, both approaches have revealed reasonably good extrapolation performance beyond the training regime.
{"title":"Cycle-domain plasticity modeling using neural networks and symbolic regression","authors":"Nasrin Talebi, Knut Andreas Meyer, Magnus Ekh","doi":"10.1016/j.compstruc.2025.108086","DOIUrl":"10.1016/j.compstruc.2025.108086","url":null,"abstract":"<div><div>Simulation of many loading cycles with traditional time-domain material models, requiring discretization of each cycle with several time steps, can result in high computational cost. One effective approach to speed up cyclic simulations is employing cycle-domain material models. Finite element simulations of rails subjected to many wheel passages are a relevant application of such models. Proposing a per-cycle evolution equation for plastic strains in cycle-domain models is, however, a challenge. To address this, we investigate the feasibility and accuracy of using machine learning models as tools for formulating such an equation. Specifically, we enforce our knowledge from constitutive modeling for elasticity and formulate the evolution law by employing feed-forward neural networks with different inputs, as well as symbolic regression to discover an interpretable expression. Training, validation, and test data have been generated using a cyclic time-domain plasticity model considering pulsating uniaxial stress loadings with constant and variable strain ranges. The obtained results demonstrate the potential of cycle-domain plasticity modeling using both uninterpretable and interpretable data-driven machine learning as an alternative to time-domain material modeling. Furthermore, both approaches have revealed reasonably good extrapolation performance beyond the training regime.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"321 ","pages":"Article 108086"},"PeriodicalIF":4.8,"publicationDate":"2026-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884327","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-02DOI: 10.1016/j.compstruc.2025.108094
Yopi P. Oktiovan , Francesco Messali , Bora Pulatsu , Satyadhrik Sharma , José V. Lemos , Jan G. Rots
This paper presents a cyclic joint constitutive model within a Distinct Element Method framework to simulate the in-plane response of unreinforced masonry structures. The model combines multi-surface failure criteria, including tensile cut-off, Coulomb friction, and an elliptical compression cap. It incorporates exponential softening, a unified damage scalar for stiffness degradation, and a hardening–softening law for compression. Shear-induced dilatancy is captured via an uplift-correction mechanism with an exponential dilatancy-decay law, while stiffness degradation governs energy dissipation. The model is validated at both material and structural scales. Material-level simulations of cyclic compression and shear tests show close agreement with experimental data. Structural-scale validation on full-height calcium-silicate walls under combined compression and cyclic lateral loading demonstrates the ability to reproduce rocking-dominated, shear-dominated, and hybrid failure mechanisms. The model successfully replicated global hysteretic force–drift loops, capturing stiffness decay and energy dissipation, as well as local failures like cracking, sliding, and toe crushing. The model also reproduced the drift-dependent transition from rocking to friction-controlled sliding, a key mechanism for earthquake assessment. By integrating these features into a single, efficient framework, the proposed constitutive model provides a robust tool for evaluating seismic performance and conserving heritage.
{"title":"Cyclic constitutive model for masonry joint damage and energy dissipation using the distinct element method","authors":"Yopi P. Oktiovan , Francesco Messali , Bora Pulatsu , Satyadhrik Sharma , José V. Lemos , Jan G. Rots","doi":"10.1016/j.compstruc.2025.108094","DOIUrl":"10.1016/j.compstruc.2025.108094","url":null,"abstract":"<div><div>This paper presents a cyclic joint constitutive model within a Distinct Element Method framework to simulate the in-plane response of unreinforced masonry structures. The model combines multi-surface failure criteria, including tensile cut-off, Coulomb friction, and an elliptical compression cap. It incorporates exponential softening, a unified damage scalar for stiffness degradation, and a hardening–softening law for compression. Shear-induced dilatancy is captured via an uplift-correction mechanism with an exponential dilatancy-decay law, while stiffness degradation governs energy dissipation. The model is validated at both material and structural scales. Material-level simulations of cyclic compression and shear tests show close agreement with experimental data. Structural-scale validation on full-height calcium-silicate walls under combined compression and cyclic lateral loading demonstrates the ability to reproduce rocking-dominated, shear-dominated, and hybrid failure mechanisms. The model successfully replicated global hysteretic force–drift loops, capturing stiffness decay and energy dissipation, as well as local failures like cracking, sliding, and toe crushing. The model also reproduced the drift-dependent transition from rocking to friction-controlled sliding, a key mechanism for earthquake assessment. By integrating these features into a single, efficient framework, the proposed constitutive model provides a robust tool for evaluating seismic performance and conserving heritage.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"321 ","pages":"Article 108094"},"PeriodicalIF":4.8,"publicationDate":"2026-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884457","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-02DOI: 10.1016/j.compstruc.2025.108093
Ziling Song , Smriti , Sundararajan Natarajan , Tiantang Yu
Structural shape optimization plays a crucial role in finding aesthetically pleasing shape designs with reasonable mechanical performance. Isogeometric analysis offers a promising approach for such optimization due to its advantage of unifying the design and analysis models. This paper presents a comprehensive shape optimization methodology for free-form surfaces within isogeometric analysis framework, addressing both compliance and buckling problems. The analytical solution of Kirchhoff-Love shell is derived to enable efficient gradient-based optimization. For complex free-form surfaces modeled with multiple non-uniform rational B-spline (NURBS) patches, a gradient-free optimization strategy is employed to ensure robustness. Continuity constraints across multi-patch interfaces are enforced through Nitsche’s method. The proposed method is validated through several numerical examples, demonstrating simultaneous improvement in structural compliance and buckling stability.
{"title":"Multi-patch isogeometric shape optimization of complex free-form surfaces with buckling constraints","authors":"Ziling Song , Smriti , Sundararajan Natarajan , Tiantang Yu","doi":"10.1016/j.compstruc.2025.108093","DOIUrl":"10.1016/j.compstruc.2025.108093","url":null,"abstract":"<div><div>Structural shape optimization plays a crucial role in finding aesthetically pleasing shape designs with reasonable mechanical performance. Isogeometric analysis offers a promising approach for such optimization due to its advantage of unifying the design and analysis models. This paper presents a comprehensive shape optimization methodology for free-form surfaces within isogeometric analysis framework, addressing both compliance and buckling problems. The analytical solution of Kirchhoff-Love shell is derived to enable efficient gradient-based optimization. For complex free-form surfaces modeled with multiple non-uniform rational B-spline (NURBS) patches, a gradient-free optimization strategy is employed to ensure robustness. Continuity constraints across multi-patch interfaces are enforced through Nitsche’s method. The proposed method is validated through several numerical examples, demonstrating simultaneous improvement in structural compliance and buckling stability.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"321 ","pages":"Article 108093"},"PeriodicalIF":4.8,"publicationDate":"2026-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884329","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 : 2025-12-30DOI: 10.1016/j.compstruc.2025.108092
Chunfa Wang , Libang Hu , Yudong Li , Hengxiao Lu , Yan Li , Han Hu , Zhiqiang Feng
Shell-like elastic structures—such as hemispherical shells and semi-cylinders—exhibit heightened susceptibility to buckling instability under axial compressive loading, a phenomenon particularly critical in confined assemblies, stacked components, or adhesive-bonded structures. In such practical engineering scenarios, frictional contact and adhesion interactions with adjacent objects emerge as pivotal factors influencing buckling behavior. These interfacial forces, stemming from localized contact pressures, confinement effects, or adhesive bonding, induce a complex coupling between contact mechanics and buckling phenomena, thereby fundamentally altering the structural response under compressive stress. To analyze these effects, we present a computational framework that integrates a point-to-segment (PTS) contact formulation and an exponential cohesive zone model for adhesion. This unified framework enables the simultaneous simulation of friction, adhesion, and buckling, including large deformations and sliding. Implemented on an in-house isogeometric analysis platform, the framework is rigorously validated against theoretical, experimental, and numerical benchmarks. Numerical experiments demonstrate its robustness under challenging conditions, revealing key bidirectional couplings: (1) friction and adhesion suppress buckling by resisting compressive stresses within the shell-like structures, thereby increasing the critical buckling load; (2) buckling-induced geometric nonlinearities dynamically alter contact areas and pressure distributions, which in turn modulate interfacial friction and adhesion strengths.
{"title":"Analysis of friction-adhesion-buckling interactions in shell-like elastic structures via an isogeometric point-to-segment contact formulation","authors":"Chunfa Wang , Libang Hu , Yudong Li , Hengxiao Lu , Yan Li , Han Hu , Zhiqiang Feng","doi":"10.1016/j.compstruc.2025.108092","DOIUrl":"10.1016/j.compstruc.2025.108092","url":null,"abstract":"<div><div>Shell-like elastic structures—such as hemispherical shells and semi-cylinders—exhibit heightened susceptibility to buckling instability under axial compressive loading, a phenomenon particularly critical in confined assemblies, stacked components, or adhesive-bonded structures. In such practical engineering scenarios, frictional contact and adhesion interactions with adjacent objects emerge as pivotal factors influencing buckling behavior. These interfacial forces, stemming from localized contact pressures, confinement effects, or adhesive bonding, induce a complex coupling between contact mechanics and buckling phenomena, thereby fundamentally altering the structural response under compressive stress. To analyze these effects, we present a computational framework that integrates a point-to-segment (PTS) contact formulation and an exponential cohesive zone model for adhesion. This unified framework enables the simultaneous simulation of friction, adhesion, and buckling, including large deformations and sliding. Implemented on an in-house isogeometric analysis platform, the framework is rigorously validated against theoretical, experimental, and numerical benchmarks. Numerical experiments demonstrate its robustness under challenging conditions, revealing key bidirectional couplings: (1) friction and adhesion suppress buckling by resisting compressive stresses within the shell-like structures, thereby increasing the critical buckling load; (2) buckling-induced geometric nonlinearities dynamically alter contact areas and pressure distributions, which in turn modulate interfacial friction and adhesion strengths.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"321 ","pages":"Article 108092"},"PeriodicalIF":4.8,"publicationDate":"2025-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884326","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 : 2025-12-30DOI: 10.1016/j.compstruc.2025.108088
A. Brisson , E. Perrey-Debain , J.D. Chazot , C. Guigou-Carter , C. Fillol , P. Jean
Mitigating noise and vibration nuisances in engineering design requires efficient and rapid simulation tools during the design and pre-project phases. In civil engineering, post-and-beam structures which consist of skeletal frameworks composed of slabs, beams, and posts, semi-analytical methods such as the popular Dynamic Stiffness Method can be employed. The method avoids heavy computational resources but it relies on certain restrictive modeling simplifications. In contrast, the 3D Finite Element Method allows for taking into account all geometrical details of the structure, resulting in precise and reliable outcomes. In this paper, we propose a hybrid approach that combines both methods to enhance the accuracy of the Dynamic Stiffness Method while maintaining fast computation times. Specifically, the connections between posts and beams are modeled precisely with the FEM while the rest of the building structure is modeled with the Dynamic Stiffness Method. An additional Craig-Bampton reduction step is also applied to the finite element domain to further decrease the problem size. This article details the development of the hybrid dynamic stiffness method, demonstrating its effectiveness in terms of accuracy and model size reduction through comparisons with a full finite element model. Finally, a real application case is presented to test the method on a full-scale building structure.
{"title":"Development of a hybrid dynamic stiffness method adapted to Framed structures","authors":"A. Brisson , E. Perrey-Debain , J.D. Chazot , C. Guigou-Carter , C. Fillol , P. Jean","doi":"10.1016/j.compstruc.2025.108088","DOIUrl":"10.1016/j.compstruc.2025.108088","url":null,"abstract":"<div><div>Mitigating noise and vibration nuisances in engineering design requires efficient and rapid simulation tools during the design and pre-project phases. In civil engineering, post-and-beam structures which consist of skeletal frameworks composed of slabs, beams, and posts, semi-analytical methods such as the popular Dynamic Stiffness Method can be employed. The method avoids heavy computational resources but it relies on certain restrictive modeling simplifications. In contrast, the 3D Finite Element Method allows for taking into account all geometrical details of the structure, resulting in precise and reliable outcomes. In this paper, we propose a hybrid approach that combines both methods to enhance the accuracy of the Dynamic Stiffness Method while maintaining fast computation times. Specifically, the connections between posts and beams are modeled precisely with the FEM while the rest of the building structure is modeled with the Dynamic Stiffness Method. An additional Craig-Bampton reduction step is also applied to the finite element domain to further decrease the problem size. This article details the development of the hybrid dynamic stiffness method, demonstrating its effectiveness in terms of accuracy and model size reduction through comparisons with a full finite element model. Finally, a real application case is presented to test the method on a full-scale building structure.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"321 ","pages":"Article 108088"},"PeriodicalIF":4.8,"publicationDate":"2025-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884461","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}
Reciprocating longitudinal motion of suspension bridge girders, caused by thermal, traffic, wind, and seismic loads, poses fatigue and safety risks. Accurate yet computationally efficient prediction of such responses is crucial for the design and optimization of longitudinal control systems. However, conventional full-bridge finite element models are computationally prohibitive, particularly in scenarios requiring extensive parametric studies. To address this limitation, a novel reduced-order modeling technique, called an enhanced variant of quasi-static compensation-based component mode synthesis, is proposed. The method builds on the quasi-static compensation framework and introduces a coupling-matrix-based mode selection strategy, significantly improving the accuracy of the reduced-order models compared to the quasi-static compensation-based component mode synthesis method while maintaining computational efficiency. By treating the bridge as a substructure, the enhanced variant of quasi-static compensation-based component mode synthesis method enables rapid construction of the reduced-order models that retain key dynamic features of full-order finite element models. The approach is validated using the Jiangyin Suspension Bridge, showing close agreement with the full-order models in modal properties and dynamic responses under seismic and operational excitations. The method also captures nonlinear boundary effects, such as bearing friction and fluid viscous dampers, supporting the control-oriented design and optimization of longitudinal damping systems.
{"title":"Efficient model reduction for longitudinal motion of stiffening girders in suspension bridges","authors":"Zhi Chen , Zhouquan Feng , Haokun Jing , Xugang Hua , Zhengqing Chen","doi":"10.1016/j.compstruc.2025.108090","DOIUrl":"10.1016/j.compstruc.2025.108090","url":null,"abstract":"<div><div>Reciprocating longitudinal motion of suspension bridge girders, caused by thermal, traffic, wind, and seismic loads, poses fatigue and safety risks. Accurate yet computationally efficient prediction of such responses is crucial for the design and optimization of longitudinal control systems. However, conventional full-bridge finite element models are computationally prohibitive, particularly in scenarios requiring extensive parametric studies. To address this limitation, a novel reduced-order modeling technique, called an enhanced variant of quasi-static compensation-based component mode synthesis, is proposed. The method builds on the quasi-static compensation framework and introduces a coupling-matrix-based mode selection strategy, significantly improving the accuracy of the reduced-order models compared to the quasi-static compensation-based component mode synthesis method while maintaining computational efficiency. By treating the bridge as a substructure, the enhanced variant of quasi-static compensation-based component mode synthesis method enables rapid construction of the reduced-order models that retain key dynamic features of full-order finite element models. The approach is validated using the Jiangyin Suspension Bridge, showing close agreement with the full-order models in modal properties and dynamic responses under seismic and operational excitations. The method also captures nonlinear boundary effects, such as bearing friction and fluid viscous dampers, supporting the control-oriented design and optimization of longitudinal damping systems.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"321 ","pages":"Article 108090"},"PeriodicalIF":4.8,"publicationDate":"2025-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884330","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}
A novel multi-material topology optimization framework based on element-free Galerkin method is developed for designing novel symmetric and chiral negative thermal expansion (NTE) metamaterial structures. A meshless multi-material interpolation model is established by using discrete material optimization to design multi-material NTE metamaterial structures and the equivalent properties of microstructures are evaluated by the numerical homogenization method. The framework is evaluated through numerical examples at both macroscopic and microscopic scales. The effective performance of the optimized structures is verified through simulation analysis and additive manufacturing. The effects of material volume fraction, thermal expansion ratio of the constituent materials and the number of materials on optimal NTE metamaterial structures are evaluated. The results indicate that when two materials are utilized, setting the ratio of the coefficients of thermal expansion between 1:30 and 1:10, along with maintaining the volume fraction ratio of the material with low coefficient of thermal expansion to the material with high coefficient of thermal expansion within the range of 1:1 to 2:1, structures with more excellent negative thermal expansion performance can be obtained. It is suggested that the number of materials constituting the NTE metamaterial structure be 2 or 3, which can balance the structural performance and manufacturability.
{"title":"Multi-material topology optimization of negative thermal expansion metamaterial structures based on element-free Galerkin method","authors":"Jianping Zhang, Jiahong Chen, Ruiyuan Gao, Yafei Yang, Wang Kuang, Shuying Wu, Zhiqiang Zhang, Zhijian Zuo","doi":"10.1016/j.compstruc.2025.108080","DOIUrl":"10.1016/j.compstruc.2025.108080","url":null,"abstract":"<div><div>A novel multi-material topology optimization framework based on element-free Galerkin method is developed for designing novel symmetric and chiral negative thermal expansion (NTE) metamaterial structures. A meshless multi-material interpolation model is established by using discrete material optimization to design multi-material NTE metamaterial structures and the equivalent properties of microstructures are evaluated by the numerical homogenization method. The framework is evaluated through numerical examples at both macroscopic and microscopic scales. The effective performance of the optimized structures is verified through simulation analysis and additive manufacturing. The effects of material volume fraction, thermal expansion ratio of the constituent materials and the number of materials on optimal NTE metamaterial structures are evaluated. The results indicate that when two materials are utilized, setting the ratio of the coefficients of thermal expansion between 1:30 and 1:10, along with maintaining the volume fraction ratio of the material with low coefficient of thermal expansion to the material with high coefficient of thermal expansion within the range of 1:1 to 2:1, structures with more excellent negative thermal expansion performance can be obtained. It is suggested that the number of materials constituting the NTE metamaterial structure be 2 or 3, which can balance the structural performance and manufacturability.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"321 ","pages":"Article 108080"},"PeriodicalIF":4.8,"publicationDate":"2025-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884328","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 : 2025-12-28DOI: 10.1016/j.compstruc.2025.108084
Cancan Su , Dechun Lu , Xiaoying Zhuang , Timon Rabczuk , Xin Zhou , Qin He , Xiuli Du
This study presents a thermo-mechanically coupled nonlocal damage model for brittle fracture that is practically implementable and extensible to multi-physics applications. The proposed damage formulation preserves thermodynamic consistency within a variational framework and employs an implicit gradient scheme for efficient regularization. A local damage variable is defined to represent different fracture modes, while a Helmholtz-type PDE is introduced to mitigate mesh dependence. The model is first verified through mechanical benchmark problems, which confirm reduced mesh sensitivity. Its predictive capability is then demonstrated in thermo-mechanical simulations involving diverse geometries, initial conditions, material properties, and spatial dimensions (2D and 3D). The results consistently indicate that the proposed approach delivers robust and accurate predictions of thermal fracture processes while maintaining high computational efficiency.
{"title":"An energy-limited gradient damage approach for 3D thermal fracture analysis","authors":"Cancan Su , Dechun Lu , Xiaoying Zhuang , Timon Rabczuk , Xin Zhou , Qin He , Xiuli Du","doi":"10.1016/j.compstruc.2025.108084","DOIUrl":"10.1016/j.compstruc.2025.108084","url":null,"abstract":"<div><div>This study presents a thermo-mechanically coupled nonlocal damage model for brittle fracture that is practically implementable and extensible to multi-physics applications. The proposed damage formulation preserves thermodynamic consistency within a variational framework and employs an implicit gradient scheme for efficient regularization. A local damage variable is defined to represent different fracture modes, while a Helmholtz-type PDE is introduced to mitigate mesh dependence. The model is first verified through mechanical benchmark problems, which confirm reduced mesh sensitivity. Its predictive capability is then demonstrated in thermo-mechanical simulations involving diverse geometries, initial conditions, material properties, and spatial dimensions (2D and 3D). The results consistently indicate that the proposed approach delivers robust and accurate predictions of thermal fracture processes while maintaining high computational efficiency.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"321 ","pages":"Article 108084"},"PeriodicalIF":4.8,"publicationDate":"2025-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884460","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 : 2025-12-27DOI: 10.1016/j.compstruc.2025.108091
Helu Yu , Xinyu Luo , Hong Zhang , Jianting Zhou , Bin Wang , Yongle Li
By introducing the spectral decomposition-based explicit time-domain method, this paper presents an innovative computational framework for analyzing the non-stationary random vibration problem in a three-dimensional train-bridge system involving multi-variate random track irregularities. First, the time-dependent train-bridge model is formulated by coupling the train and bridge dynamics via a spatial wheel-rail interaction model. Next, the random track irregularities are decomposed through the spectral representation technique, enabling their time-domain discrete characterization in terms of three orthogonal random vectors. Then, an explicit mapping between the system responses and the orthogonal random vectors is constructed by integrating the precise integration method with a finite difference approach, leading to a recursive formulation that facilitates efficient computation of the response coefficient matrices. The obtained explicit response formulation allows straightforward computation of time–frequency response statistics of the train-bridge system, eliminating the need for repetitive time-domain simulations or extensive numerical integrations commonly associated with conventional non-stationary random vibration techniques. Lastly, the pseudo-excitation method and Monte Carlo simulation are adopted to verify the applicability of the proposed method, a comprehensive parametric investigation is also conducted to examine the individual contributions from different track irregularity components on the stochastic dynamic behavior of the train-bridge system.
{"title":"Non-stationary random vibration analysis of a three-dimensional train-bridge system using spectral decomposition-based explicit time-domain method","authors":"Helu Yu , Xinyu Luo , Hong Zhang , Jianting Zhou , Bin Wang , Yongle Li","doi":"10.1016/j.compstruc.2025.108091","DOIUrl":"10.1016/j.compstruc.2025.108091","url":null,"abstract":"<div><div>By introducing the spectral decomposition-based explicit time-domain method, this paper presents an innovative computational framework for analyzing the non-stationary random vibration problem in a three-dimensional train-bridge system involving multi-variate random track irregularities. First, the time-dependent train-bridge model is formulated by coupling the train and bridge dynamics via a spatial wheel-rail interaction model. Next, the random track irregularities are decomposed through the spectral representation technique, enabling their time-domain discrete characterization in terms of three orthogonal random vectors. Then, an explicit mapping between the system responses and the orthogonal random vectors is constructed by integrating the precise integration method with a finite difference approach, leading to a recursive formulation that facilitates efficient computation of the response coefficient matrices. The obtained explicit response formulation allows straightforward computation of time–frequency response statistics of the train-bridge system, eliminating the need for repetitive time-domain simulations or extensive numerical integrations commonly associated with conventional non-stationary random vibration techniques. Lastly, the pseudo-excitation method and Monte Carlo simulation are adopted to verify the applicability of the proposed method, a comprehensive parametric investigation is also conducted to examine the individual contributions from different track irregularity components on the stochastic dynamic behavior of the train-bridge system.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"321 ","pages":"Article 108091"},"PeriodicalIF":4.8,"publicationDate":"2025-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145840387","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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