Finite Elements in Analysis and Design最新文献

{"title":"An implicit coupled method of scaled boundary finite element and peridynamics for fracture analysis","authors":"Wei Yu ,&nbsp;Jun Liu ,&nbsp;Haibo Wang ,&nbsp;Lei Qin ,&nbsp;Lei Gan ,&nbsp;Quansheng Zang ,&nbsp;Wenbin Ye","doi":"10.1016/j.finel.2025.104453","DOIUrl":"10.1016/j.finel.2025.104453","url":null,"abstract":"<div><div>In this paper, firstly, an innovative multi-scale coupled method based on scaled boundary finite element (SBFEM) and peridynamics (PD) is proposed for predicting fracture propagation of elastic bodies in static/quasi-static problems. The coupled process in this method is established not by transition regions (overlapping regions), but by force equilibrium conditions at common points, which greatly reduces the complexity of modeling. The SBFEM is introduced to model the non-cracked domain and the PD is applied to model the cracked domain in this method. This reduces a great deal of computational time compared to the PD method. Moreover, the limitations of surface effects and troublesome load conditions for the PD calculation can be eliminated or mitigated. The SBFEM is different from FEM in that only the boundary of elastic bodies is discretized. Therefore, the computational efficiency is further improved compared with the coupled method of the FEM and PD. The SBFEM is also different from BEM in that it does not need to provide the fundamental solution and compute the singular integrals. Hence, the method is more convenient for solving complex problems compared with the coupled method of the BEM and PD. The accuracy of this coupled method is demonstrated by one example of accuracy analysis for single coupled and multiple coupled interfaces, and three examples of fracture propagation analysis (two pre-determined cracks and one spontaneous crack). The results show that the coupled method has a high accuracy. Furthermore, it is recommended that the spacing of the common points be set equal to the spacing of the PD material points so that the accuracy of the coupled method can be maximized. Finally, the cracking forms of a square plate with different shaped holes are explored. It shows that the proposed coupled method has potential for engineering applications.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"252 ","pages":"Article 104453"},"PeriodicalIF":3.5,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097372","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}

{"title":"Mesoscale FEM model of concrete: Statistical assessment of inherent stress concentrations in dependence on phase heterogeneity","authors":"Jan Mašek,&nbsp;Petr Miarka","doi":"10.1016/j.finel.2025.104442","DOIUrl":"10.1016/j.finel.2025.104442","url":null,"abstract":"<div><div>Concrete heterogeneity originates from its production process, which involves bonding aggregates with a binder matrix. This study presents a mesoscale finite element model (MFEM) that offers detailed insights into the fracture process at the aggregate–cement matrix interface, focusing on one of concrete’s key properties: its mechanical response. Unlike discrete models, which often average out critical stress concentrations within the mesostructure, the MFEM approach captures detailed stress distributions, revealing localized effects crucial for understanding damage evolution. Although computationally more demanding, the MFEM leverages modern high-performance computing (HPC) to provide a detailed description of the stress field and material damage across different phases and interfaces. The proposed modeling framework integrates a collision-checked aggregate generation procedure, Voronoi-based mesostructure construction, and adaptive 3D meshing, forming a reusable methodology for stress analysis in heterogeneous composites. This approach offers transparent, physically interpretable parameterization of phase properties in contrast to black-box discrete models. Another methodological contribution is the statistical post-processing of stress data using histogram-based analysis across cross-sectional planes. This enables quantitative evaluation of stress concentration distributions, providing valuable insights into the mesoscale mechanical response and serving as a useful visualization tool for researchers working on heterogeneous material modeling. Various matrix-to-aggregate stiffness ratios are considered to evaluate the influence of material heterogeneity on the stress field. The results are based on a statistical evaluation of stress concentrations arising from variations in material stiffness. The model is applied to investigate the impact of using recycled crushed bricks as aggregates in concrete, with particular emphasis on the stiffness mismatch between the matrix and aggregates. The study examines how this stiffness contrast affects stress distribution and ultimately influences the composite’s failure mechanisms. Beyond this application, the MFEM framework provides a foundation for further investigations into nonlinear fracture processes, fatigue analysis, and mechanical optimization of alternative aggregate-matrix systems.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"252 ","pages":"Article 104442"},"PeriodicalIF":3.5,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145050584","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}

{"title":"The polytopal composite element method for finite strain hyperelastic problems","authors":"Y. Li ,&nbsp;B.W. Wang ,&nbsp;Z.Q. Feng","doi":"10.1016/j.finel.2025.104436","DOIUrl":"10.1016/j.finel.2025.104436","url":null,"abstract":"<div><div>Polygonal elements have emerged as a cutting-edge discretization paradigm in computational solid mechanics, demonstrating significant potential for linear elasticity analyses. This work pioneers a robust computational framework extending polytopal composite elements to finite-strain hyperelasticity. The key idea by constructing a polynomial projection using least squares approximation for linear-compatible strain fields, followed by extending the derived linear operator to large deformation cases involving nonlinear strain. The computational framework of this method is fundamentally consistent with finite elements, allowing it to adapt and extend to various nonlinear problems. Through several numerical investigation we show that this approach maintains the excellent accuracy, convergence and stability, and is potentially offering new insights and references for polygonal elements in future nonlinear problems.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"252 ","pages":"Article 104436"},"PeriodicalIF":3.5,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097376","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}

{"title":"Uzawa methods for the coupling of free flow and porous medium flow","authors":"Qingzhou Wang,&nbsp;Guangzhi Du","doi":"10.1016/j.finel.2025.104460","DOIUrl":"10.1016/j.finel.2025.104460","url":null,"abstract":"<div><div>In this paper, two kinds of Uzawa algorithms are proposed and investigated to solve the coupling of free flow and porous medium flow, which is modeled by the mixed Stokes-Darcy problem with the Beavers-Joseph-Saffman interface condition. The first Uzawa method as an iterative method can avoid solving the saddle point problem at each iteration step. The second method aims to optimize the first one by combining the two-grid strategy. Rigorously theoretical analysis is established for these two algorithms. Some numerical experiments are carried out to verify the theoretical findings.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"252 ","pages":"Article 104460"},"PeriodicalIF":3.5,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097377","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}

{"title":"An expandable local and parallel two-grid finite element scheme for Stokes problem","authors":"Hongwei Song ,&nbsp;Jianping Zhao ,&nbsp;Yanren Hou","doi":"10.1016/j.finel.2025.104375","DOIUrl":"10.1016/j.finel.2025.104375","url":null,"abstract":"<div><div>A novel locally parallel finite element algorithm for addressing the Stokes problem has been developed, leveraging the two-grid method and the unit splitting technique. This innovative algorithm boasts several key advantages: (1) it operates independently of the hyperapproximation property, enhancing its applicability across various scenarios; (2) the decomposition of regions is solely dependent on the unit splitting technique, simplifying the computational process; and (3) by incorporating constraints on local corrections, the algorithm employs the penalized form of the Stokes problem. This strategic choice facilitates the exclusive resolution of the velocity field function under specific assumptions, thereby streamlining the solution process and potentially reducing computational complexity.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"252 ","pages":"Article 104375"},"PeriodicalIF":3.5,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145027842","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}

{"title":"The neural approximated virtual element method for elasticity problems","authors":"Stefano Berrone ,&nbsp;Moreno Pintore ,&nbsp;Gioana Teora","doi":"10.1016/j.finel.2025.104467","DOIUrl":"10.1016/j.finel.2025.104467","url":null,"abstract":"<div><div>We present the Neural Approximated Virtual Element Method to numerically solve elasticity problems. This hybrid technique combines classical concepts from the Finite Element Method and the Virtual Element Method with recent advances in deep neural networks. Specifically, it is a polygonal method where the virtual basis functions are element-wise approximated by a neural network, eliminating the need for stabilization or projection operators typically required in the standard Virtual Element Method. We present the discrete formulation of the problem together with theoretical results, and we provide numerical tests on both linear and non-linear elasticity problems, demonstrating the advantages of a simple discretization, particularly in handling non-linearities.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"252 ","pages":"Article 104467"},"PeriodicalIF":3.5,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145268251","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}

{"title":"A simplified gradient-enhanced damage model based on energy limiters for crack propagation under time-dependent loading","authors":"Hung Thanh Tran","doi":"10.1016/j.finel.2025.104443","DOIUrl":"10.1016/j.finel.2025.104443","url":null,"abstract":"<div><div>This paper presents the development and investigation of a simplified energy limiter-based nonlocal damage model for dynamic crack propagation in brittle media. The key idea underlying the proposed model is that crack growth under impact loading is primarily influenced by the tensile component of the strain tensor. Consequently, the energy-based damage-driving term is simplified to a strain-based counterpart, which is integrated using the first principal strain. This simplification leads to a model that is not only easier to implement but also more effective in capturing dynamic crack propagation compared to the original theory. In addition, the computational framework incorporates an energy limiter-based gradient damage formulation with a damage threshold, enabling natural crack initiation and propagation while significantly reducing spurious damage. One of the distinctive features of the proposed approach is the treatment of the nonlocal crack field as a primary unknown, alongside displacements. This allows the use of identical shape functions for both fields within the finite element analysis, enhancing consistency and computational efficiency. Consistent with classical continuum damage mechanics, the model can accurately simulate arbitrary and complex multiple crack paths, including three-dimensional (3D) crack propagation. Furthermore, to provide a more efficient numerical framework under time-dependent loading conditions with complex crack patterns, an explicit dynamic fracture algorithm is employed. This algorithm utilizes the central difference method, the row-sum technique for mass lumping, and a consistent procedure for updating the kinematic and damage-related terms. The advantages and modeling capabilities of the proposed strain-based gradient-enhanced damage formulation are demonstrated through representative numerical examples of dynamic fracture under shear, tension, and compression loading scenarios.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"252 ","pages":"Article 104443"},"PeriodicalIF":3.5,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145050052","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}

{"title":"POD-RBF hyper-reduction method for fast finite element analysis of nonlinear dynamic problems","authors":"Lam Vu-Tuong Nguyen,&nbsp;Hyun-Gyu Kim","doi":"10.1016/j.finel.2025.104455","DOIUrl":"10.1016/j.finel.2025.104455","url":null,"abstract":"<div><div>This paper proposes a new hyper-reduction method for fast finite element analysis of nonlinear dynamic problems using proper orthogonal decomposition (POD) and radial basis function (RBF) interpolation. In the offline stage, displacement and internal force snapshots are collected from full-order FE simulations of nonlinear dynamic problems with training load cases. POD basis vectors are extracted from the displacement snapshots using the singular value decomposition (SVD). RBF coefficients for the internal force snapshots are also computed in the offline stage. The proposed POD-RBF hyper-reduction method efficiently estimates the reduced internal force vectors and the reduced tangent stiffness matrices using RBF interpolation with respect to reduced generalized coordinates. A snapshot selection strategy combining K-means clustering and greedy sampling algorithms is used to reduce the size of solution snapshots, which further enhances the efficiency of the present method. Numerical results show that the POD-RBF hyper-reduction method can be efficiently and effectively used to quickly solve nonlinear dynamic problems in a reduced-order space.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"252 ","pages":"Article 104455"},"PeriodicalIF":3.5,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145050583","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}

{"title":"A novel interpolation scheme using partition-of-unity mapping for multi-material topology optimizations with compliance-based and stress-based designs","authors":"Tinh Quoc Bui,&nbsp;Minh Ngoc Nguyen","doi":"10.1016/j.finel.2025.104470","DOIUrl":"10.1016/j.finel.2025.104470","url":null,"abstract":"<div><div>This paper presents an enhanced computational framework for multi-material topology optimization using a novel interpolation scheme with the partition-of-unity (PU) mapping. Inspired by the recent <span><math><mi>p</mi></math></span>-norm mapping scheme by Yi et al., (2023) the developed scheme inherits the easy-to-implement property, as the interpolation is written in a SIMP-like manner, and the sensitivity with respect to each material phase takes the same form. More importantly, the current scheme addresses the lack of PU property of the <span><math><mi>p</mi></math></span>-norm scheme, that is, the sum of volume fraction of all material phases within each element must be equal to one. In the <span><math><mi>p</mi></math></span>-norm scheme setting, the case when the physical densities of the materials are all equal to one is theoretically possible. This phenomenon means the duplication of the element volume. In the developed scheme, the mapping functions are computed in rational form, explicitly satisfying the PU property. The performance of the present method is investigated through six numerical examples: the first three are for the compliance-based designs and the other three are for the stress-based designs including the design of periodic meta-material with high bulk modulus. It is demonstrated in the numerical examples that although the lack of PU property in <span><math><mi>p</mi></math></span>-norm scheme does not seem to cause problematic issue in compliance-based design with only fixed load, erroneous patterns may appear in more complicated problems, e.g., in compliance-based design with consideration of self-weight load, and in stress-based design. The issue is successfully removed in the proposed PU mapping scheme.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"252 ","pages":"Article 104470"},"PeriodicalIF":3.5,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145363530","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}

{"title":"Analysis of the stability of frames composed of thin-walled beams with open cross-section using a High Order Continuation Method","authors":"Zaenab Bakhach ,&nbsp;Bouazza Braikat ,&nbsp;Abdellah Hamdaoui ,&nbsp;Noureddine Damil","doi":"10.1016/j.finel.2025.104437","DOIUrl":"10.1016/j.finel.2025.104437","url":null,"abstract":"<div><div>This study presents the numerical modeling of frames composed of thin-walled beams with open cross-section subjected to large torsions by a High Order Continuation Method (HOCM), based on Asymptotic Numerical Method (ANM) techniques. The theoretical model is developed using <span><math><mrow><mn>3</mn><mi>D</mi></mrow></math></span> beam kinematics, which accounts for flexion-torsion coupling and large rotations. The connection between beams is ensured by joints (stiffening plates) to avoid local deformations, mathematically modeled by compatibility conditions applied to the connection nodes. The equilibrium equations are established using the minimization of the Lagrangian. Discretization is performed with a two-node beam element having seven degrees of freedom per node. The transformation from local to global reference frames is done using Euler angles for the first six degrees of freedom, while the transformation of the seventh degree of freedom is related to the transmission of warping between elements. The equilibrium equations are solved using a HOCM. Tested examples of frames of thin-walled beams with open cross-section subjected to different loadings and boundary conditions are investigated. The obtained results are compared with those calculated by the commercial software ABAQUS and with those from the literature.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"251 ","pages":"Article 104437"},"PeriodicalIF":3.5,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144932278","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}