Pub Date : 2026-01-23DOI: 10.1016/j.compstruc.2026.108118
Xin Chen, Gabriele Milani, Yiwei Hua
This paper presents an efficient method for stochastic homogenized kinematic limit analysis of three quasi-periodic masonry bond patterns subjected to in-plane loading. The proposed methodology involves two key points. Firstly, simplified 2D rigid-plastic homogenization models for three bond patterns are proposed. The kinematic limit analysis problem, incorporating proposed homogenization models, is then formulated and solved by linear programming to obtain deterministic failure surfaces. Secondly, the block heights and lengths of representative element of volume are treated as random variables, and the probability density evolution method is employed to obtain the probability information (such as means and probability density functions) of failure surfaces. Three numerical examples are investigated. The results show that the proposed method can accurately derive the probabilistic information of failure surfaces and achieving a computational cost that is ten times lower than Monte Carlo simulation.
{"title":"Stochastic homogenized kinematic limit analysis for three quasi-periodic masonry bond patterns under in-plane loading via probability density evolution method","authors":"Xin Chen, Gabriele Milani, Yiwei Hua","doi":"10.1016/j.compstruc.2026.108118","DOIUrl":"10.1016/j.compstruc.2026.108118","url":null,"abstract":"<div><div>This paper presents an efficient method for stochastic homogenized kinematic limit analysis of three quasi-periodic masonry bond patterns subjected to in-plane loading. The proposed methodology involves two key points. Firstly, simplified 2D rigid-plastic homogenization models for three bond patterns are proposed. The kinematic limit analysis problem, incorporating proposed homogenization models, is then formulated and solved by linear programming to obtain deterministic failure surfaces. Secondly, the block heights and lengths of representative element of volume are treated as random variables, and the probability density evolution method is employed<!--> <!-->to obtain the probability information (such as means and probability density functions) of failure surfaces. Three numerical examples are investigated. The results show that the proposed method can accurately derive the probabilistic information of failure surfaces and achieving a computational cost that is ten times lower than Monte Carlo simulation.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"322 ","pages":"Article 108118"},"PeriodicalIF":4.8,"publicationDate":"2026-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146025718","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 : 2026-01-22DOI: 10.1016/j.compstruc.2025.108089
Eduard Rohan, Jan Heczko
The paper presents two-scale homogenization-based models of fluid-saturated porous elastic materials with self-contact interaction at the pore level. The periodic microstructures are constituted by a solid skeleton and fluid-filled pores. The unilateral frictionless contact interaction is considered on matching pore surfaces of the elastic skeleton, being coupled with the fluid-structure interaction. The periodic unfolding homogenization is employed to derive limit models for two types of periodic microstructures with disconnected and connected porosities. While in the first case the homogenized model is quite analogous to the one with void pores, in the latter case, the Stokes flow in deforming (possibly collapsible) porosity requires special treatment by a regularization to retain the pore connectivity. The macroscopic model attains the form of a nonlinear Biot continuum, whereby the Darcy flow model governs the fluid redistribution. To respect the dependence of the permeability on the deformation, an approximation based on the shape sensitivity analysis is proposed which enables to avoid resolving the microflow problems in severely deformed pores. Numerical examples of 2D deforming structures are presented to illustrate the influence of the pore fluid on the unilateral contact in the two types of porous structures.
{"title":"Homogenization-based modelling of self-contact and fluid-structure interaction in the microstructure of poroelastic materials","authors":"Eduard Rohan, Jan Heczko","doi":"10.1016/j.compstruc.2025.108089","DOIUrl":"10.1016/j.compstruc.2025.108089","url":null,"abstract":"<div><div>The paper presents two-scale homogenization-based models of fluid-saturated porous elastic materials with self-contact interaction at the pore level. The periodic microstructures are constituted by a solid skeleton and fluid-filled pores. The unilateral frictionless contact interaction is considered on matching pore surfaces of the elastic skeleton, being coupled with the fluid-structure interaction. The periodic unfolding homogenization is employed to derive limit models for two types of periodic microstructures with disconnected and connected porosities. While in the first case the homogenized model is quite analogous to the one with void pores, in the latter case, the Stokes flow in deforming (possibly collapsible) porosity requires special treatment by a regularization to retain the pore connectivity. The macroscopic model attains the form of a nonlinear Biot continuum, whereby the Darcy flow model governs the fluid redistribution. To respect the dependence of the permeability on the deformation, an approximation based on the shape sensitivity analysis is proposed which enables to avoid resolving the microflow problems in severely deformed pores. Numerical examples of 2D deforming structures are presented to illustrate the influence of the pore fluid on the unilateral contact in the two types of porous structures.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"322 ","pages":"Article 108089"},"PeriodicalIF":4.8,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146025719","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 : 2026-01-22DOI: 10.1016/j.compstruc.2026.108107
Haidong Wang , Feiqi Wang , Siqi Yin , She Li , Guidong Wang , Liming Wang , Xiangyang Cui
Generating high-quality quad-dominant mesh on complex geometric models remains a significant challenge in finite element pre-processing. Manually simplifying the small features of a geometric model increases the time cost for engineers. In this work, a series of automatic model edge suppression algorithms are proposed for geometric models. By utilizing the minimum allowed edge length and minimum allowed angle, these algorithms can automatically suppress geometric features such as short model edges, sharp tips, and narrow surfaces that may severely degrade mesh quality during meshing. A diffusion algorithm for geometric surfaces is employed to search for the sub-surfaces connected by the suppressed edge. Using virtual topological technology, these sub-surfaces are clustered to construct a virtual topological surface, which simplifies the model without altering its underlying topology. The virtual topological surface is globally parameterized via discrete harmonic mapping to ensure bidirectional mapping between the clustered surface and the parametric surface. Subsequently, an improved Q-Morph methodology was implemented for quad-dominant hybrid mesh generation on virtual topological surfaces, demonstrating effective preservation of mesh-boundary alignment characteristics.
{"title":"High-quality quad-dominant mesh generation aided by the virtual topological model generated after automatic suppression of small geometric features","authors":"Haidong Wang , Feiqi Wang , Siqi Yin , She Li , Guidong Wang , Liming Wang , Xiangyang Cui","doi":"10.1016/j.compstruc.2026.108107","DOIUrl":"10.1016/j.compstruc.2026.108107","url":null,"abstract":"<div><div>Generating high-quality quad-dominant mesh on complex geometric models remains a significant challenge in finite element pre-processing. Manually simplifying the small features of a geometric model increases the time cost for engineers. In this work, a series of automatic model edge suppression algorithms are proposed for geometric models. By utilizing the minimum allowed edge length and minimum allowed angle, these algorithms can automatically suppress geometric features such as short model edges, sharp tips, and narrow surfaces that may severely degrade mesh quality during meshing. A diffusion algorithm for geometric surfaces is employed to search for the sub-surfaces connected by the suppressed edge. Using virtual topological technology, these sub-surfaces are clustered to construct a virtual topological surface, which simplifies the model without altering its underlying topology. The virtual topological surface is globally parameterized via discrete harmonic mapping to ensure bidirectional mapping between the clustered surface and the parametric surface. Subsequently, an improved Q-Morph methodology was implemented for quad-dominant hybrid mesh generation on virtual topological surfaces, demonstrating effective preservation of mesh-boundary alignment characteristics.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"322 ","pages":"Article 108107"},"PeriodicalIF":4.8,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146006529","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 : 2026-01-21DOI: 10.1016/j.compstruc.2026.108111
Haoyu Wang , Zongliang Du , Yue Mei , Xiudong Li , Shan Tang
Data-driven generative design methods have emerged as a powerful paradigm for material and structural design. However, most existing approaches are limited to regular design domains and depend on structured meshes as design variables, which restrict their applicability in more complex scenarios. To overcome these constraints, this study introduces a novel unstructured generative design framework capable of handling irregular design domains. A centroidal Voronoi tessellation-based polygonal mesh is employed to discretize the irregular design space, improving geometric adaptability, enhancing mesh isotropy and uniformity, and eliminating the single-node connectivity issues commonly encountered in triangular meshes. To address the challenges of processing unstructured data arising from unstructured meshes, a Diffusion Transformer-based network is adopted to efficiently learn the reverse process of the diffusion model and to capture the conditional probabilistic distribution under specified mechanical constraints. The results demonstrate that the proposed method can rapidly generate metamaterials that meet the target properties, while also producing designs that differ significantly from those in the training dataset, thereby showcasing its creativity. This approach overcomes the limitations of existing generative design methods in handling irregular design domains, accelerates the design process, and advances the application of data-driven generative design in real-world engineering.
{"title":"Unstructured diffusion generative design of metamaterials for irregular design domains","authors":"Haoyu Wang , Zongliang Du , Yue Mei , Xiudong Li , Shan Tang","doi":"10.1016/j.compstruc.2026.108111","DOIUrl":"10.1016/j.compstruc.2026.108111","url":null,"abstract":"<div><div>Data-driven generative design methods have emerged as a powerful paradigm for material and structural design. However, most existing approaches are limited to regular design domains and depend on structured meshes as design variables, which restrict their applicability in more complex scenarios. To overcome these constraints, this study introduces a novel unstructured generative design framework capable of handling irregular design domains. A centroidal Voronoi tessellation-based polygonal mesh is employed to discretize the irregular design space, improving geometric adaptability, enhancing mesh isotropy and uniformity, and eliminating the single-node connectivity issues commonly encountered in triangular meshes. To address the challenges of processing unstructured data arising from unstructured meshes, a Diffusion Transformer-based network is adopted to efficiently learn the reverse process of the diffusion model and to capture the conditional probabilistic distribution under specified mechanical constraints. The results demonstrate that the proposed method can rapidly generate metamaterials that meet the target properties, while also producing designs that differ significantly from those in the training dataset, thereby showcasing its creativity. This approach overcomes the limitations of existing generative design methods in handling irregular design domains, accelerates the design process, and advances the application of data-driven generative design in real-world engineering.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"322 ","pages":"Article 108111"},"PeriodicalIF":4.8,"publicationDate":"2026-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146006528","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 : 2026-01-15DOI: 10.1016/j.compstruc.2026.108101
Marcel May , Atul Anantheswar , Ventseslav Yordanov , Elaheh Derakhi , Felix Hartung , Ines Wollny , Lutz Eckstein , Michael Kaliske
During braking, acceleration, and steering maneuvers in road traffic, dynamic vertical and horizontal loads act on the pavement structure. The resulting macroscopic multiaxial stress states arise not only from these highly time- and space-dependent loads but also from the anisotropic mechanical responses imprinted by material microstructural geometry.
In this work, a novel, dynamic multiscale-ALE method is introduced for the first time. By extending two numerically efficient concepts – the dynamic ALE approach and the microlayer framework – and integrating them into a unified scheme, it enables the consistent characterization of the mechanical response within layered roadway systems. Numerical efficiency and physical representativeness are achieved through the use of finite viscoelastic–elastoplastic constitutive models for the microstructural constituents, embedded in the microlayer framework – a thermodynamically derived multiscale formulation that avoids the computational cost of a conventional FE2 scheme. This framework provides an analytically computable microscale representation composed of simple geometric bodies, of which microstructural properties are homogenized to the macroscale. The numerical efficiency is further enhanced by the dynamic ALE, in which the load application region remains fixed on the pavement surface, while the pavement structure flows underneath it. Consequently, only a small longitudinal portion of the road structure must be explicitly discretized for FEM. During this ALE-induced material flow, the microscale configuration is updated consistently with the material motion before homogenization, ensuring that the anisotropic mechanical response induced by the microstructural geometry is fully preserved.
To experimentally determine the loads generated by a tire during a steering maneuver, a single-wheel test rig is used, in which, the side slip angle is systematically varied. The measured data is then used to generate time- and space-resolved footprints, which serve as realistic boundary conditions for simulating tire pavement interaction. A numerical study investigates the response of a standard pavement construction to the load induced by a tire, which rolls 700 m along the pavement under dynamic conditions including acceleration, braking and cornering. The example demonstrates the applicability of the approach.
{"title":"Incorporation of a viscoelastic-elastoplastic material model for asphalt based on the multiscale microlayer model into an ALE formulation for pavement structures considering dynamic tire loadings","authors":"Marcel May , Atul Anantheswar , Ventseslav Yordanov , Elaheh Derakhi , Felix Hartung , Ines Wollny , Lutz Eckstein , Michael Kaliske","doi":"10.1016/j.compstruc.2026.108101","DOIUrl":"10.1016/j.compstruc.2026.108101","url":null,"abstract":"<div><div>During braking, acceleration, and steering maneuvers in road traffic, dynamic vertical and horizontal loads act on the pavement structure. The resulting macroscopic multiaxial stress states arise not only from these highly time- and space-dependent loads but also from the anisotropic mechanical responses imprinted by material microstructural geometry.</div><div>In this work, a novel, dynamic multiscale-ALE method is introduced for the first time. By extending two numerically efficient concepts – the dynamic ALE approach and the microlayer framework – and integrating them into a unified scheme, it enables the consistent characterization of the mechanical response within layered roadway systems. Numerical efficiency and physical representativeness are achieved through the use of finite viscoelastic–elastoplastic constitutive models for the microstructural constituents, embedded in the microlayer framework – a thermodynamically derived multiscale formulation that avoids the computational cost of a conventional FE<sup>2</sup> scheme. This framework provides an analytically computable microscale representation composed of simple geometric bodies, of which microstructural properties are homogenized to the macroscale. The numerical efficiency is further enhanced by the dynamic ALE, in which the load application region remains fixed on the pavement surface, while the pavement structure flows underneath it. Consequently, only a small longitudinal portion of the road structure must be explicitly discretized for FEM. During this ALE-induced material flow, the microscale configuration is updated consistently with the material motion before homogenization, ensuring that the anisotropic mechanical response induced by the microstructural geometry is fully preserved.</div><div>To experimentally determine the loads generated by a tire during a steering maneuver, a single-wheel test rig is used, in which, the side slip angle is systematically varied. The measured data is then used to generate time- and space-resolved footprints, which serve as realistic boundary conditions for simulating tire pavement interaction. A numerical study investigates the response of a standard pavement construction to the load induced by a tire, which rolls 700 m along the pavement under dynamic conditions including acceleration, braking and cornering. The example demonstrates the applicability of the approach.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"321 ","pages":"Article 108101"},"PeriodicalIF":4.8,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145962593","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 : 2026-01-15DOI: 10.1016/j.compstruc.2026.108108
D. von Burg, R. Baumann
This paper presents a novel layerwise plate finite element formulation for the modelling of adhesively bonded multilayer structures subjected to thermal loading. Each structural layer is represented as a Reissner–Mindlin plate, while interlayer coupling is achieved through adhesive shear layers with defined thickness and shear stiffness. This approach enables the direct representation of adhesive compliance, which is often simplified or neglected in layerwise plate formulations. The formulation is derived via the principle of virtual work and incorporates mixed interpolation of tensorial components to prevent shear locking. Numerical examples demonstrate the accuracy and computational efficiency of the proposed element. Comparisons with three-dimensional solid finite element reference models show good agreement with the computed deflections, while requiring substantially fewer degrees of freedom. The resulting computational efficiency makes the approach particularly attractive for iterative analyses such as process simulations and parametric studies involving thermally induced deformations. Since the adhesive shear modulus enters the formulation only as a parameter, time- or temperature-dependent behaviour can be incorporated through constitutive modelling without modification of the element formulation.
{"title":"A layerwise plate element formulation with adhesive interface compliance and thermal loads for bonded multilayer structures","authors":"D. von Burg, R. Baumann","doi":"10.1016/j.compstruc.2026.108108","DOIUrl":"10.1016/j.compstruc.2026.108108","url":null,"abstract":"<div><div>This paper presents a novel layerwise plate finite element formulation for the modelling of adhesively bonded multilayer structures subjected to thermal loading. Each structural layer is represented as a Reissner–Mindlin plate, while interlayer coupling is achieved through adhesive shear layers with defined thickness and shear stiffness. This approach enables the direct representation of adhesive compliance, which is often simplified or neglected in layerwise plate formulations. The formulation is derived via the principle of virtual work and incorporates mixed interpolation of tensorial components to prevent shear locking. Numerical examples demonstrate the accuracy and computational efficiency of the proposed element. Comparisons with three-dimensional solid finite element reference models show good agreement with the computed deflections, while requiring substantially fewer degrees of freedom. The resulting computational efficiency makes the approach particularly attractive for iterative analyses such as process simulations and parametric studies involving thermally induced deformations. Since the adhesive shear modulus enters the formulation only as a parameter, time- or temperature-dependent behaviour can be incorporated through constitutive modelling without modification of the element formulation.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"321 ","pages":"Article 108108"},"PeriodicalIF":4.8,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145962600","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 : 2026-01-15DOI: 10.1016/j.compstruc.2026.108110
Yi-Cheng Sun , Yong Jiang , Chun-Yan Ling , Min Wang , Shun-Qi Zhang
As a typical variable-section structure, the flexible wing has attracted considerable attention in the aerospace field due to its advantages in load-bearing capacity, stiffness distribution and mass optimization. However, the variation in geometric and physical properties along the structural length significantly increases the complexity of dynamic modeling, consequently leading to pronounced changes in the mode shapes. To address this challenge, the paper establishes linear dynamic equations of flexible wings based on the Euler–Bernoulli beam theory and Lagrange’s principle. Building on this foundation, a dimensionless variable transformation is applied to normalize the geometric and physical parameters in the governing equations, thereby simplifying the coupling among different variables. Subsequently, a special function expansion method is employed to formalize the mode shapes as a linear combination of Bessel and Meijer-G functions, ensuring the satisfaction of boundary conditions and effectively capturing the influence of cross-sectional variations on modal characteristics. On this basis, an improved mode shape function for variable cross-section cantilever beams is developed. This method enables rapid determination of natural frequencies and mode shape functions without iterative procedures or approximate truncation, significantly improving computational efficiency while maintaining high accuracy, thus making it well-suited for efficient dynamic analysis of complex structures. The results indicate that the natural frequencies and mode shape curves obtained by this method are in good agreement with the ANSYS results, the existing literature, and the experimental tests, thereby verifying the rationality and effectiveness of the proposed method.
{"title":"Analytical model of variable cross-section flexible wings based on improved mode shape functions","authors":"Yi-Cheng Sun , Yong Jiang , Chun-Yan Ling , Min Wang , Shun-Qi Zhang","doi":"10.1016/j.compstruc.2026.108110","DOIUrl":"10.1016/j.compstruc.2026.108110","url":null,"abstract":"<div><div>As a typical variable-section structure, the flexible wing has attracted considerable attention in the aerospace field due to its advantages in load-bearing capacity, stiffness distribution and mass optimization. However, the variation in geometric and physical properties along the structural length significantly increases the complexity of dynamic modeling, consequently leading to pronounced changes in the mode shapes. To address this challenge, the paper establishes linear dynamic equations of flexible wings based on the Euler–Bernoulli beam theory and Lagrange’s principle. Building on this foundation, a dimensionless variable transformation is applied to normalize the geometric and physical parameters in the governing equations, thereby simplifying the coupling among different variables. Subsequently, a special function expansion method is employed to formalize the mode shapes as a linear combination of Bessel and Meijer-G functions, ensuring the satisfaction of boundary conditions and effectively capturing the influence of cross-sectional variations on modal characteristics. On this basis, an improved mode shape function for variable cross-section cantilever beams is developed. This method enables rapid determination of natural frequencies and mode shape functions without iterative procedures or approximate truncation, significantly improving computational efficiency while maintaining high accuracy, thus making it well-suited for efficient dynamic analysis of complex structures. The results indicate that the natural frequencies and mode shape curves obtained by this method are in good agreement with the ANSYS results, the existing literature, and the experimental tests, thereby verifying the rationality and effectiveness of the proposed method.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"321 ","pages":"Article 108110"},"PeriodicalIF":4.8,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145962152","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 : 2026-01-15DOI: 10.1016/j.compstruc.2026.108106
Dingyu Li , Wei He , Xiang Ao , Peidong Li
In this study, a phase-field model for hydraulic fracturing is developed, wherein the unified strength theory formulated by Maohong Yu is incorporated into the phase-field model framework to establish a novel phase-field driving energy, thereby enhancing the accuracy of mixed-mode fracture prediction. Comprehensive governing equations describing the mechanical, damage, and fluid transport fields are mathematically derived, alongside detailed finite element discretization schemes for the coupled multi-field variables. To validate the proposed model, multiple two-dimensional and three-dimensional numerical examples are conducted, demonstrating its robustness, precision, and the ability to simulate intricate hydraulic fracturing processes in rocks subjected to various loading conditions. Comparative analyses reveal an excellent agreement between the numerical results and the Khristianovic-Geertsma-de Klerk analytical model, as well as experimental data from true triaxial hydraulic fracturing tests. The results demonstrate that the proposed model effectively captures the processes of crack nucleation, propagation, and deflection. Consequently, this model stands as a robust computational tool for analyzing complex fracture mechanisms in hydraulic fracturing engineering.
{"title":"Phase-field model of hydraulic fracturing based on the unified strength theory","authors":"Dingyu Li , Wei He , Xiang Ao , Peidong Li","doi":"10.1016/j.compstruc.2026.108106","DOIUrl":"10.1016/j.compstruc.2026.108106","url":null,"abstract":"<div><div>In this study, a phase-field model for hydraulic fracturing is developed, wherein the unified strength theory formulated by Maohong Yu is incorporated into the phase-field model framework to establish a novel phase-field driving energy, thereby enhancing the accuracy of mixed-mode fracture prediction. Comprehensive governing equations describing the mechanical, damage, and fluid transport fields are mathematically derived, alongside detailed finite element discretization schemes for the coupled multi-field variables. To validate the proposed model, multiple two-dimensional and three-dimensional numerical examples are conducted, demonstrating its robustness, precision, and the ability to simulate intricate hydraulic fracturing processes in rocks subjected to various loading conditions. Comparative analyses reveal an excellent agreement between the numerical results and the Khristianovic-Geertsma-de Klerk analytical model, as well as experimental data from true triaxial hydraulic fracturing tests. The results demonstrate that the proposed model effectively captures the processes of crack nucleation, propagation, and deflection. Consequently, this model stands as a robust computational tool for analyzing complex fracture mechanisms in hydraulic fracturing engineering.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"321 ","pages":"Article 108106"},"PeriodicalIF":4.8,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145976683","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 : 2026-01-15DOI: 10.1016/j.compstruc.2026.108099
Insu Jeong, Minchul Yu, Gunwoo Noh
The direct inverse mass matrix (DI) approach can substantially reduce computational costs by eliminating the need to invert the global mass matrix in explicit time integration schemes. However, in the method of finite spheres (MFS), where multiple degrees of freedom are associated with a single node, an appropriate mass modification is required for the successful application of the DI. In this study, we propose a generalized formulation for such mass modification and determine its optimal parameters using a metaheuristic optimization algorithm. The accuracy and computational efficiency of the proposed approach are examined through benchmark problems, demonstrating its effectiveness and performance advantages.
{"title":"A generalized direct inverse mass matrix for the method of finite spheres in transient explicit wave propagation analysis","authors":"Insu Jeong, Minchul Yu, Gunwoo Noh","doi":"10.1016/j.compstruc.2026.108099","DOIUrl":"10.1016/j.compstruc.2026.108099","url":null,"abstract":"<div><div>The direct inverse mass matrix (DI) approach can substantially reduce computational costs by eliminating the need to invert the global mass matrix in explicit time integration schemes. However, in the method of finite spheres (MFS), where multiple degrees of freedom are associated with a single node, an appropriate mass modification is required for the successful application of the DI. In this study, we propose a generalized formulation for such mass modification and determine its optimal parameters using a metaheuristic optimization algorithm. The accuracy and computational efficiency of the proposed approach are examined through benchmark problems, demonstrating its effectiveness and performance advantages.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"321 ","pages":"Article 108099"},"PeriodicalIF":4.8,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145976684","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 : 2026-01-15DOI: 10.1016/j.compstruc.2026.108103
J.Ramesh Babu, Pranav M. Karve, Sankaran Mahadevan
This study presents a Bayesian framework for calibrating cellular automata (CA) models of pitting corrosion. A high-fidelity two-dimensional CA model is used to simulate pit morphology evolution under coupled electrochemical and mass transport processes, incorporating eight uncertain model parameters related to metal dissolution, hydrolysis, diffusion, and sedimentation. Key geometric indicators—maximum pit depth and pit aspect ratio—are extracted from the simulation outputs and reduced to interpretable scalar features using power-law fitting. Correlation analysis is conducted to assess linear relationships between model parameters and power-law coefficients. Gaussian Process Regression (GPR) surrogate models are constructed using Latin Hypercube Sampling (LHS) to emulate the high-fidelity CA model. Global sensitivity analysis (GSA) using Sobol’ indices is performed by utilizing the trained surrogate models; it identifies sedimentation and ionic diffusion as the dominant contributors to output feature variability, with significant nonlinear interactions. The trained surrogates are integrated into a Bayesian inference framework using Metropolis-Hastings Markov Chain Monte Carlo (MH-MCMC) sampling to infer posterior distributions of the uncertain model parameters. The posterior samples are further propagated through the surrogates to quantify the output uncertainty, and the prediction is evaluated using a distance-based probabilistic model validation metric. Two numerical examples related to API-5L X65 steel pipelines are presented, demonstrating that incorporating multiple geometric features—both pit depth and aspect ratio—improves predictive accuracy. The proposed framework supports uncertainty-aware modeling and decision-making for structural health assessment and maintenance planning in corrosion-critical infrastructure.
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