Computer Methods in Applied Mechanics and Engineering最新文献

{"title":"Simultaneous multi-objective optimization of tri-directional graded material and porosity distributions for multi-patch structures using adaptive isogeometric analysis and Nitsche’s method","authors":"Guangshuai Gu ,&nbsp;Pin Wen ,&nbsp;Jie Gao ,&nbsp;Fei Chen","doi":"10.1016/j.cma.2026.118758","DOIUrl":"10.1016/j.cma.2026.118758","url":null,"abstract":"<div><div>This study presents a unified framework for the simultaneous multi-objective optimization of material, porosity, and geometry with tri-directional functionally graded distributions in multi-patch complex structures. The elastodynamic governing equations are derived based on three-dimensional elasticity theory, with Nitsche’s method employed to accurately enforce coupling constraints across non-conforming interfaces in multi-patch geometries. PHT-based adaptive isogeometric analysis is introduced to substantially reduce computational cost through appropriate mesh refinement. This numerical methodology is deeply integrated with the non-dominated sorting genetic algorithm III, enabling an efficient exploration of the Pareto front within an extensive design space, aiming to enhance the fundamental frequency of free vibration and reduce structural mass. An independent hexahedral design domain is introduced to decouple the design mesh from the analysis mesh, enabling more flexible and generalizable design representation. Several numerical examples are presented to demonstrate the effectiveness of the proposed approach. The results indicate that increased design mesh resolution with more design variables yields superior optimization outcomes by generating more refined material and porosity distributions, albeit at the cost of reduced population diversity. Furthermore, compared to non-porous and uniform porosity configurations, the simultaneous optimization of material and porosity distributions achieves remarkable structural overall performance enhancement by substantially increasing fundamental frequency while effectively reducing structural mass.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"452 ","pages":"Article 118758"},"PeriodicalIF":7.3,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146023845","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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 locking-free SPH solid-shell formulation for modeling shell structures with general constitutive models","authors":"Yao Lu ,&nbsp;Wenhao Shen ,&nbsp;Moubin Liu","doi":"10.1016/j.cma.2026.118766","DOIUrl":"10.1016/j.cma.2026.118766","url":null,"abstract":"<div><div>Shell structures composed of diverse materials play a fundamental role in modern engineering, and their accurate numerical modeling is essential for predicting structural performance and failure. However, conventional shell formulations often involve assumptions such as straight normals, constant transverse shear strain, and plane-stress condition, and these assumptions limit their ability to capture realistic 3D deformation and general constitutive responses. To address these limitations, this study proposes a novel smoothed particle hydrodynamics (SPH) solid-shell formulation. In contrast to existing SPH shell models derived from classical shell theories, the proposed formulation explicitly resolves the through-thickness field by introducing displacement degrees of freedom on the top and bottom surfaces. This concept preserves full 3D kinematics and provides a unified interface for various constitutive models. Furthermore, an enhanced assumed strain (EAS) approach is incorporated into SPH for the first time by introducing an independent transverse normal strain at each particle. The enhancement effectively mitigates thickness locking while maintaining full compatibility with general constitutive models. The proposed formulation is validated through a series of benchmark tests covering elasticity, isotropic and anisotropic hyperelasticity, viscoelasticity, and elastoplasticity, demonstrating its rapid convergence, high accuracy, and strong robustness. It establishes a versatile and reliable framework for simulating shell structures exhibiting strong nonlinearity and complex material behavior.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"452 ","pages":"Article 118766"},"PeriodicalIF":7.3,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146006491","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Computing leaky waves in semi-analytical waveguide models by exponential residual relaxation","authors":"Hauke Gravenkamp ,&nbsp;Bor Plestenjak ,&nbsp;Daniel A. Kiefer","doi":"10.1016/j.cma.2026.118763","DOIUrl":"10.1016/j.cma.2026.118763","url":null,"abstract":"<div><div>Semi-analytical methods for modeling guided waves in structures of constant cross-section yield frequency-dependent polynomial eigenvalue problems for the wavenumbers and mode shapes. Solving these eigenvalue problems over a range of frequencies results in continuous eigencurves. Recent research has shown that eigencurves of differentiable parameter-dependent eigenvalue problems can alternatively be computed as solutions to a system of ordinary differential equations (ODEs) obtained by postulating an exponentially decaying residual of a modal solution. Starting from an approximate initial guess of the eigenvalue and eigenvector at a given frequency, the complete eigencurve is obtained using standard numerical ODE solvers. We exploit this idea to develop an efficient method for computing the dispersion curves of plate structures coupled to unbounded solid or fluid media. In these scenarios, the approach is particularly useful because the boundary conditions give rise to nonlinear terms that severely hinder the application of traditional solvers. We discuss suitable approximations of the nonlinearity for obtaining initial values, analyze computational costs and robustness of the proposed algorithm, and verify results by comparison against existing methods.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"452 ","pages":"Article 118763"},"PeriodicalIF":7.3,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146023843","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Training deep physics-informed Kolmogorov–Arnold networks","authors":"Spyros Rigas ,&nbsp;Fotios Anagnostopoulos ,&nbsp;Michalis Papachristou ,&nbsp;Georgios Alexandridis","doi":"10.1016/j.cma.2026.118761","DOIUrl":"10.1016/j.cma.2026.118761","url":null,"abstract":"<div><div>Since their introduction, Kolmogorov–Arnold Networks (KANs) have been successfully applied across several domains, with physics-informed machine learning (PIML) emerging as one of the areas where they have thrived. In the PIML setting, Chebyshev-based physics-informed KANs (cPIKANs) have become the standard due to their computational efficiency. However, like their multilayer perceptron-based counterparts, cPIKANs face significant challenges when scaled to depth, leading to training instabilities that limit their applicability to several PDE problems. To address this, we propose a basis-agnostic, Glorot-like initialization scheme that preserves activation variance and yields substantial improvements in stability and accuracy over the default initialization of cPIKANs. Inspired by the PirateNet architecture, we further introduce Residual-Gated Adaptive KANs (RGA KANs), designed to mitigate divergence in deep cPIKANs where initialization alone is not sufficient. Through empirical tests and information bottleneck analysis, we show that RGA KANs successfully traverse all training phases, unlike baseline cPIKANs, which stagnate in the diffusion phase in specific PDE settings. Evaluations on nine standard forward PDE benchmarks under a fixed training pipeline with adaptive components demonstrate that RGA KANs consistently outperform parameter-matched cPIKANs and PirateNets—often by several orders of magnitude—while remaining stable in settings where the others diverge.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"452 ","pages":"Article 118761"},"PeriodicalIF":7.3,"publicationDate":"2026-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146014551","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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 variational phase-field framework for multiphysics modeling of delayed hydride cracking in zirconium alloys","authors":"Wei Li ,&nbsp;Han Zhao ,&nbsp;Minghua Chi ,&nbsp;Vincent Beng Chye Tan","doi":"10.1016/j.cma.2026.118765","DOIUrl":"10.1016/j.cma.2026.118765","url":null,"abstract":"<div><div>Delayed hydride cracking (DHC) poses a significant integrity threat to zirconium nuclear cladding, arising from the cyclic interplay of hydrogen diffusion and hydride precipitation/dissolution, which leads to characteristic intermittent subcritical crack advance. This work develops a thermodynamically consistent variational phase-field framework that, in a unified formulation, couples hydrogen diffusion, stress- and temperature-regulated hydride evolution, thermo-elastoplasticity, and a ductile-to-brittle fracture transition. The model reproduces key experimental observations across temperatures—intermittent crack advance, DHC velocity, striation spacing, and incubation time—and quantifies how stress and temperature jointly govern hydride nucleation and cracking. Mechanistically, hydrostatic tension reduces the terminal solid solubility for precipitation/dissolution and concentrates hydrogen; ensuing precipitation relaxes and redistributes stresses, establishing a self-sustaining feedback loop that triggers hydride precipitation–fracture–dissolution–reprecipitation cycles. Parametric studies of pre-cracked cladding reveal a stress-dependent transition between diffusion-controlled and precipitation-controlled initiation. High applied stress induces pronounced thermal sensitivity via stress-assisted hydrogen accumulating, whereas low stress exhibits a weaker temperature response that manifests only above a critical hydride fraction. Beyond DHC, the framework is readily extensible to simulations of oxide–hydride synergistic delayed cracking under reactor-relevant conditions. It thus provides a physics-based foundation for mechanism identification, threshold assessment, and life prediction of zirconium cladding, and establishes a platform for future extensions to oxide–hydride interaction.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"452 ","pages":"Article 118765"},"PeriodicalIF":7.3,"publicationDate":"2026-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146014810","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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 coupling of mixed and primal finite element methods for the coupled body-plate problem","authors":"Jun Hu ,&nbsp;Zhen Liu ,&nbsp;Rui Ma","doi":"10.1016/j.cma.2026.118750","DOIUrl":"10.1016/j.cma.2026.118750","url":null,"abstract":"<div><div>This paper considers the coupled problem of a three-dimensional elastic body and a two-dimensional plate, which are rigidly connected at their interface. The plate consists of a plane elasticity model along the plane direction and a plate bending model with Kirchhoff assumptions along the transverse direction. The Hellinger-Reissner formulation is adopted for the body by introducing the stress as an auxiliary variable, while the primal formulation is employed for the plate. The well-posedness of the new mixed weak formulation is established. This approach enables direct stress approximations and allows for non-matching meshes at the interface since the continuity condition of the displacement acts as a natural boundary condition for the body. Under certain assumptions, discrete stability and error estimates are derived for both conforming and nonconforming finite element methods. Two specific pairs of conforming and nonconforming finite elements are shown to satisfy the required assumptions, respectively. Furthermore, the problem is reduced to an interface problem based on the domain decomposition, which can be solved effectively by a conjugate gradient iteration. Numerical experiments are conducted to validate the theoretical results.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"452 ","pages":"Article 118750"},"PeriodicalIF":7.3,"publicationDate":"2026-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146014552","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Interpretable and flexible non-intrusive reduced-order models using reproducing kernel Hilbert spaces","authors":"Alejandro N. Diaz ,&nbsp;Shane A. McQuarrie ,&nbsp;John T. Tencer ,&nbsp;Patrick J. Blonigan","doi":"10.1016/j.cma.2026.118734","DOIUrl":"10.1016/j.cma.2026.118734","url":null,"abstract":"<div><div>This paper develops an interpretable, non-intrusive reduced-order modeling technique using regularized kernel interpolation. Existing non-intrusive approaches approximate the dynamics of a reduced-order model (ROM) by solving a data-driven least-squares regression problem for low-dimensional matrix operators. Our approach instead leverages regularized kernel interpolation, which yields an optimal approximation of the ROM dynamics from a user-defined reproducing kernel Hilbert space. We show that our kernel-based approach can produce interpretable ROMs whose structure mirrors full-order model structure by embedding judiciously chosen feature maps into the kernel. The approach is flexible and allows a combination of informed structure through feature maps and closure terms via more general nonlinear terms in the kernel. We also derive a computable <em>a posteriori</em> error bound that combines standard error estimates for intrusive projection-based ROMs and kernel interpolants. The approach is demonstrated in several numerical experiments that include comparisons to operator inference using both proper orthogonal decomposition and quadratic manifold dimension reduction.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"452 ","pages":"Article 118734"},"PeriodicalIF":7.3,"publicationDate":"2026-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146014554","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Discontinuous Galerkin cohesive zone modeling of toughness-controlled failure","authors":"Daniel Pickard","doi":"10.1016/j.cma.2025.118616","DOIUrl":"10.1016/j.cma.2025.118616","url":null,"abstract":"<div><div>A fracture analysis methodology is developed from the discontinuous Galerkin formalism, a simple failure locus, and the simple assumption of brittle unloading to the origin. For positive fracture energy, the semi-discrete system is a continuous function of the finite element nodal coordinate array, which renders the semi-discrete problem well-posed. In the perfectly brittle limit, the formulation reduces to the well-established discontinuous Galerkin/cohesive zone modeling paradigm. The robustness of the method is shown to stem from the blunting of the numerical flux at propagating crack tips, while its versatility is demonstrated through a series of large-scale fracture propagation problems.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"452 ","pages":"Article 118616"},"PeriodicalIF":7.3,"publicationDate":"2026-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146014556","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Graph neural networks with hybrid local-global attention for effective prediction of mechanical response in structures","authors":"Luca Patrignani,&nbsp;Silvestre T Pinho","doi":"10.1016/j.cma.2026.118753","DOIUrl":"10.1016/j.cma.2026.118753","url":null,"abstract":"<div><div>Graph Neural Networks (GNNs) are emerging as a transformative approach for predicting mechanical response in structures by naturally encoding unstructured finite element meshes as graphs. While traditional finite element analysis (FEA) provides trusted solutions for mechanics problems, it encounters significant computational and scalability bottlenecks. Existing machine learning approaches using regular grids fail to capture the irregular nature of real-world meshes, whereas standard GNNs suffer from over-smoothing and limited long-range information propagation that compromise accuracy. To overcome these limitations, we present a Graph Transformer methodology that implements an encoder-processor-decoder framework augmented with a frequency-controlled hybrid local-global attention mechanism, which systematically bridges local mesh connectivity with global information awareness across the computational domain. Our approach integrates seamlessly with real-world FEA workflows through an automated FEM-to-GNN pipeline that converts FE simulations to graph representations and generates training datasets directly from commercial solvers, enabling rapid deployment across various engineering applications without manual preprocessing bottlenecks. We validate our approach on open holes Carbon Fibre Reinforced Polymer (CFRP) laminate plates under various loading conditions and geometric configurations, and extend validation to nonlinear woven composites exhibiting plasticity and progressive damage under shear-dominated loadings, employing systematic hyperparameter optimisation with Tree-structured Parzen Estimator (TPE) sampling and mesh convergence studies. The linear case demonstrates excellent predictive accuracy (<span><math><mrow><msup><mi>R</mi><mn>2</mn></msup><mo>=</mo><mn>0.98</mn></mrow></math></span>, <span><math><mrow><mi>R</mi><mi>M</mi><mi>S</mi><mi>E</mi><mo>=</mo><mn>0.00028</mn></mrow></math></span>) with 70 ×  speedup over equivalent-accuracy FEA and <span><math><mrow><mn>58</mn><mo>−</mo><mn>64</mn><mo>%</mo></mrow></math></span> reduction in training and validation loss compared to standard message-passing GNN architectures without attention mechanisms, while the nonlinear case achieves <span><math><mrow><msup><mi>R</mi><mn>2</mn></msup><mo>=</mo><mn>0.97</mn></mrow></math></span> (<span><math><mrow><mi>R</mi><mi>M</mi><mi>S</mi><mi>E</mi><mo>=</mo><mn>0.0013</mn></mrow></math></span>) with 660 ×  speedup.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"452 ","pages":"Article 118753"},"PeriodicalIF":7.3,"publicationDate":"2026-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146000569","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Discovering neural cohesive zone laws from displacement fields","authors":"Georgios Barkoulis Gavris,&nbsp;WaiChing Sun","doi":"10.1016/j.cma.2026.118733","DOIUrl":"10.1016/j.cma.2026.118733","url":null,"abstract":"<div><div>Conventional inverse problems for cohesive zones often utilize homogenized responses of the effective media to identify a fixed set of material parameters prescribed <em>a priori</em>. However, the mixed-mode loading conditions of composites or natural materials may exhibit interfacial relations that are difficult to anticipate. This article presents a model-discovery framework for directly identifying cohesive zone models inferred from displacement fields across the interface, without fixing on a specific form of equations. We develop a differentiable version of the Material Point Method (MPM) with interface elements formulated to capture the traction-separation law at a pre-existing crack or bonded interface. Ensuring the differentiability of the MPM solver enables us to backpropagate the mismatch between simulated and measured (e.g., DIC/DVC) displacement fields through the time integrator and interface physics. Using only kinematics and equilibrium as constraints, numerical experiments suggest that the method may recover (i) a Mode-I traction-separation curve in a double-cantilever-beam test and (ii) a mixed-mode law for a circular interface shear test. These numerical results demonstrate that displacement-only experiments, combined with a differentiable solver, offer a promising pathway for identifying rich and potentially nonparametric cohesive laws.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"452 ","pages":"Article 118733"},"PeriodicalIF":7.3,"publicationDate":"2026-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145980090","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}