Computer Methods in Applied Mechanics and Engineering最新文献

{"title":"Handling geometrical variability in nonlinear reduced order modeling through Continuous Geometry-Aware DL-ROMs","authors":"Simone Brivio,&nbsp;Stefania Fresca,&nbsp;Andrea Manzoni","doi":"10.1016/j.cma.2025.117989","DOIUrl":"10.1016/j.cma.2025.117989","url":null,"abstract":"<div><div>Deep Learning-based Reduced Order Models (DL-ROMs) provide nowadays a well-established class of accurate surrogate models for complex physical systems described by parameterised PDEs, by nonlinearly compressing the solution manifold into a handful of latent coordinates. Until now, design and application of DL-ROMs mainly focused on physically parameterised problems. Within this work, we provide a novel extension of these architectures to problems featuring geometrical variability and parameterised domains, namely, we propose Continuous Geometry-Aware DL-ROMs (CGA-DL-ROMs). In particular, the space-continuous nature of the proposed architecture matches the need to deal with <em>multi-resolution</em> datasets, which are quite common in the case of geometrically parameterised problems. Moreover, CGA-DL-ROMs are endowed with a strong inductive bias that makes them aware of geometrical parametrizations, thus enhancing both the compression capability and the overall performance of the architecture. Within this work, we justify our findings through a thorough theoretical analysis, and we practically validate our claims by means of a series of numerical tests encompassing physically-and-geometrically parameterised PDEs, ranging from the unsteady Navier–Stokes equations for fluid dynamics to advection–diffusion–reaction equations for mathematical biology.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"442 ","pages":"Article 117989"},"PeriodicalIF":6.9,"publicationDate":"2025-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143851645","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":"Direct coupling of continuum and shell elements in large deformation problems","authors":"Astrid Pechstein ,&nbsp;Michael Neunteufel","doi":"10.1016/j.cma.2025.118002","DOIUrl":"10.1016/j.cma.2025.118002","url":null,"abstract":"<div><div>In many applications, thin shell-like structures are integrated within or attached to volumetric bodies. This includes reinforcements placed in soft matrix material in lightweight structure design, or hollow structures that are partially or completely filled. Finite element simulations of such setups are highly challenging. A brute force discretization of structural as well as volumetric parts using well-shaped three-dimensional elements may be accurate, but leads to problems of enormous computational complexity even for simple models. One desired alternative is the use of shell elements for thin-walled parts, as such a discretization greatly alleviates size restrictions on the underlying finite element mesh. However, the coupling of different formulations within a single framework is often not straightforward and may lead to locking if not done carefully. Neunteufel and Schöberl proposed a mixed shell element where, apart from displacements of the center surface, bending moments are used as independent unknowns. These elements were not only shown to be locking free and highly accurate in large-deformation regime, but also do not require differentiability of the shell surface and can handle kinked and branched shell structures. They can directly be coupled to classical volume elements of arbitrary order by sharing displacement degrees of freedom at the center surface, thus achieving the desired coupled discretization. As the elements can be used on unstructured meshes, adaptive mesh refinement based on local stress and bending moments can be used. We present computational results that confirm exceptional accuracy for problems where thin-walled structures are embedded as reinforcements within soft matrix material.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"442 ","pages":"Article 118002"},"PeriodicalIF":6.9,"publicationDate":"2025-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143855910","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":"Minimum-residual a posteriori error estimates for HDG discretizations of the Helmholtz equation","authors":"Liliana Camargo ,&nbsp;Sergio Rojas ,&nbsp;Patrick Vega","doi":"10.1016/j.cma.2025.117981","DOIUrl":"10.1016/j.cma.2025.117981","url":null,"abstract":"<div><div>We propose and analyze two a posteriori error indicators for hybridizable discontinuous Galerkin (HDG) discretizations of the Helmholtz equation. These indicators are built to minimize the residual associated with a local superconvergent postprocessing scheme for the primal variable, measured in a dual norm of an enlarged discrete test space. The residual minimization is reformulated into equivalent local saddle-point problems, yielding a superconvergent postprocessed approximation of the primal variable in the asymptotic regime for sufficiently regular exact solutions and a built-in residual representation with minimal computational effort. Both error indicators are based on frequency-dependent postprocessing schemes and verify reliability and efficiency estimates for a frequency-weighted <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-error for the scalar unknown and the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-error for the flux. We illustrate our theoretical findings through ad-hoc numerical experiments.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"441 ","pages":"Article 117981"},"PeriodicalIF":6.9,"publicationDate":"2025-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143847674","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":"Predicting crack nucleation and propagation in brittle materials using Deep Operator Networks with diverse trunk architectures","authors":"Elham Kiyani ,&nbsp;Manav Manav ,&nbsp;Nikhil Kadivar ,&nbsp;Laura De Lorenzis ,&nbsp;George Em Karniadakis","doi":"10.1016/j.cma.2025.117984","DOIUrl":"10.1016/j.cma.2025.117984","url":null,"abstract":"<div><div>Phase-field modeling reformulates fracture problems as energy minimization problems and enables a comprehensive characterization of the fracture process, including crack nucleation, propagation, merging and branching, without relying on ad-hoc assumptions. However, the numerical solution of phase-field fracture problems is characterized by a high computational cost. To address this challenge, in this paper, we employ a deep neural operator (DeepONet) consisting of a branch network and a trunk network to solve brittle fracture problems. We explore three distinct approaches that vary in their trunk network configurations. In the first approach, we demonstrate the effectiveness of a two-step DeepONet, which results in a simplification of the learning task. In the second approach, we employ a physics-informed DeepONet, whereby the mathematical expression of the energy is integrated into the trunk network’s loss to enforce physical consistency. The integration of physics also results in a substantially smaller data size needed for training. In the third approach, we replace the neural network in the trunk with a Kolmogorov–Arnold Network and train it without the physics loss. Using these methods, we model crack nucleation in a one-dimensional homogeneous bar under prescribed end displacements, as well as crack propagation and branching in single edge-notched specimens with varying notch lengths subjected to tensile and shear loading. We show that the networks predict the solution fields accurately and the error in the predicted fields is localized near the crack.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"441 ","pages":"Article 117984"},"PeriodicalIF":6.9,"publicationDate":"2025-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143850176","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":"Floating projection topology optimization framework for efficient design of bi-connected 3D acoustic metamaterials","authors":"Gengwang Yan ,&nbsp;Yingli Li ,&nbsp;Weibai Li ,&nbsp;Jiahui Yan ,&nbsp;Song Yao ,&nbsp;Xiaodong Huang","doi":"10.1016/j.cma.2025.118020","DOIUrl":"10.1016/j.cma.2025.118020","url":null,"abstract":"<div><div>Phononic crystals (PnCs) and acoustic metamaterials (AMs) are advanced functional materials engineered to achieve broad bandgaps for wave manipulation through optimized spatial distribution. Despite significant progress, the efficient design of three-dimensional AMs with bi-connected topologies remains a major challenge using conventional topology optimization methods. The novel floating projection topology optimization (FPTO) framework integrated with the Method of Moving Asymptotes (MMA) solver is developed to create and maximize bandgaps between specific dispersion curves. A key innovation of our approach is the incorporation of effective permeability constraints derived from homogenization theory, which ensures sufficient bi-connectivity of air/solid domains essential for practical applications. The optimized topologies exhibiting various-order bandgaps correlate with the equivalent number of air cavities, as revealed through eigenmode analysis and complex band structures. We thoroughly examined the optimization process across various mesh resolutions and permeability constraints to establish robust design guidelines. Both numerical calculations and experimental measurements of sound transmission loss (STL) validate the effectiveness of the optimized topologies for sound attenuation. Additionally, specific wave propagation paths can be engineered by introducing strategic defect features into the perfect lattices. This FPTO framework provides a robust platform for bandgap optimization and inverse design of PnCs and AMs, enabling the development of sophisticated acoustic devices.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"441 ","pages":"Article 118020"},"PeriodicalIF":6.9,"publicationDate":"2025-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143844966","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":"Stochastic deep material networks as efficient surrogates for stochastic homogenisation of non-linear heterogeneous materials","authors":"Ling Wu,&nbsp;Ludovic Noels","doi":"10.1016/j.cma.2025.117994","DOIUrl":"10.1016/j.cma.2025.117994","url":null,"abstract":"<div><div>The Interaction-Based Deep Material Network (IB-DMN) is reformulated to decouple the phase volume fraction from the topological parameters of the IB-DMN. Since the phase volume fraction is no longer influenced by the topological parameters, on the one hand the stochastic IB-DMN can predict the response of arbitrary phase volume fraction, and on the other hand the stochastic IB-DMN can be constructed by introducing uncertainties to the topological parameters of a reference IB-DMN, which is trained using data obtained from full-field linear elastic homogenisation, allowing to capture the variability resulting from the micro-structure organisation such as a phase clustering.</div><div>The non-linear predictions of the proposed stochastic IB-DMN are compared to those from Direct Numerical Simulation (DNS) on 2D Stochastic Volume Elements (SVEs) of unidirectional fibre-reinforced matrix composites in a finite-strain setting. The results from in-plane uni-axial stress and shear tests show that the proposed stochastic IB-DMN is capable of reproducing random non-linear responses with the same stochastic characteristics as the predictions of the DNS conducted on SVE realisations.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"441 ","pages":"Article 117994"},"PeriodicalIF":6.9,"publicationDate":"2025-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143844965","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":"Ellipsoidal soft micro-particles suspended in dilute viscous flow","authors":"Jana Wedel ,&nbsp;Matjaž Hriberšek ,&nbsp;Jure Ravnik ,&nbsp;Paul Steinmann","doi":"10.1016/j.cma.2025.117973","DOIUrl":"10.1016/j.cma.2025.117973","url":null,"abstract":"<div><div>Soft particles in viscous flows are prevalent both in nature and in various industrial applications. Notable examples include biological cells such as blood cells and bacteria as well as hydrogels and vesicles. To model these intriguing particles, we present an extension of our recent, efficient, and versatile pseudo-rigid body approach, originally developed for initially spherical soft particles suspended in arbitrary macroscale viscous flows. The novel extension allows modeling the barycenter and shape dynamics of soft initially non-spherical, i.e. ellipsoidal particles by introducing a novel shape and orientation tensor. We consider soft, micrometer-sized, ellipsoidal particles deforming affinely. To this end, we combine affine deformations (as inherent to a pseudo-rigid body) and the Jeffery-Roscoe model to analytically determine the traction exerted on a soft ellipsoidal particle suspended locally in a creeping flow at the particle scale. Without loss of generality, we assume nonlinear hyperelastic material behavior for the particles considered. The novel extension of our recent numerical approach for soft particles demonstrates that the deformation and motion of the particles can be accurately reproduced also for ellipsoidal particles and captures results from the literature, however, at drastically reduced computational costs. Furthermore, we identify both the tumbling and trembling dynamic regime for soft ellipsoidal particles suspended in simple shear flow again capturing results from the literature. Our extended approach is first validated using experimental and numerical studies from the literature for quasi-rigid as well as soft particles, followed by a comparison of the effects of particle deformability for some well-known fluid flow cases, such as laminar pipe flow, lid-driven cavity flow, and a simplified bifurcation. We find that taking particle deformability into account leads to notable deviations in the particle trajectory compared to rigid particles, with increased deviations for higher initial particle aspect ratio. Furthermore, we demonstrate that our approach can track a statistically relevant number of soft particles in complex flow situations.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"441 ","pages":"Article 117973"},"PeriodicalIF":6.9,"publicationDate":"2025-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143844967","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":"Mechanical state estimation with a Polynomial-Chaos-Based Statistical Finite Element Method","authors":"Vahab Narouie ,&nbsp;Henning Wessels ,&nbsp;Fehmi Cirak ,&nbsp;Ulrich Römer","doi":"10.1016/j.cma.2025.117970","DOIUrl":"10.1016/j.cma.2025.117970","url":null,"abstract":"<div><div>The Statistical Finite Element Method (statFEM) offers a Bayesian framework for integrating computational models with observational data, thus providing improved predictions for structural health monitoring and digital twinning. This paper presents a sampling-free statFEM tailored for non-conjugate, non-Gaussian prior probability densities. We assume that constitutive parameters, modeled as weakly stationary random fields, are the primary source of uncertainty and approximate them using the Karhunen–Loève (KL) expansion. The resulting stochastic solution field, i.e., the displacement field, is a non-stationary, non-Gaussian random field, which we approximate via the Polynomial Chaos (PC) expansion. The PC coefficients are determined through projection using Smolyak sparse grids. Additionally, we model the measurement noise as a stationary Gaussian random field and the model misspecification as a mean-free, non-stationary Gaussian random field, which is also approximated using the KL expansion and where the coefficients are treated as hyperparameters. The PC coefficients of the stochastic posterior displacement field are computed using the Gauss–Markov–Kálmán filter, while the hyperparameters are determined by maximizing the marginal likelihood. We demonstrate the efficiency and convergence of the proposed method through one- and two-dimensional elastostatic problems.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"441 ","pages":"Article 117970"},"PeriodicalIF":6.9,"publicationDate":"2025-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143838578","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":"Enforcing physics onto PINNs for more accurate inhomogeneous material identification","authors":"B. van der Heijden ,&nbsp;X. Li ,&nbsp;G. Lubineau ,&nbsp;E. Florentin","doi":"10.1016/j.cma.2025.117993","DOIUrl":"10.1016/j.cma.2025.117993","url":null,"abstract":"<div><div>Physics-Informed Neural Networks (PINNs) are computationally efficient tools for addressing inverse problems in solid mechanics, but often face accuracy limitations when compared to traditional methods. We introduce a refined PINN approach that rigorously enforces certain physics constraints, improving accuracy while retaining the computational benefits of PINNs. Unlike conventional PINNs, which are trained to approximate (differential) equations, this method incorporates classical techniques, such as stress potentials, to satisfy certain physical laws. The result is a physics-enforced PINN that combines the precision of the Constitutive Equation Gap Method (CEGM) with the automatic differentiation and optimization frameworks characteristic of PINNs. Numerical comparisons reveal that the enforced PINN approach indeed achieves near-CEGM accuracy while preserving the efficiency advantages of PINNs. Validation through real experimental data demonstrates the ability of the method to accurately identify material properties and inclusion geometries in inhomogeneous samples.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"441 ","pages":"Article 117993"},"PeriodicalIF":6.9,"publicationDate":"2025-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143844964","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 novel improved edge-based smoothed particle finite element method for elastoplastic contact analysis using second order cone programming","authors":"Xi-Wen ZHOU ,&nbsp;Yin-Fu JIN ,&nbsp;Zhen-Yu YIN ,&nbsp;Feng-Tao LIU ,&nbsp;Xiangsheng CHEN","doi":"10.1016/j.cma.2025.118016","DOIUrl":"10.1016/j.cma.2025.118016","url":null,"abstract":"<div><div>Contact problems are of paramount importance in engineering but present significant challenges for numerical solutions due to their highly nonlinear nature. Recognizing that contact problems can be formulated as optimization problems with inequality constraints has paved the way for advanced techniques such as the Interior Point (IP) method. This study presents an Improved Edge-based Smoothed Particle Finite Element Method (IES-PFEM) with novel contact scheme for elastoplastic analysis involving large deformation using Second-Order Cone Programming (SOCP). Within the proposed framework, classical node-to-surface (NTS) and surface-to-surface (STS) contact discretization schemes in SOCP form are rigorously achieved. The governing equations of elastoplastic boundary value problems are formulated as a min-max problem via the mixed variation principle, and by applying the primal-dual theory of convex optimization, the problem is transformed into a dual formulation with stresses as optimization variables. The Mohr-Coulomb plastic yield criterion and the Coulomb friction law are naturally expressed as second-order cone constraints. A fixed-point iteration scheme is developed to address unphysical normal expansion arising from the natural derivation of an associated friction model within the SOCP formulation. Furthermore, the volumetric locking problem in nearly incompressible materials is alleviated by IES-PFEM formulation without requiring additional stabilization techniques. The proposed method is validated through a series of benchmark examples involving contact and elastoplastic deformations. Numerical results confirm the capability of the proposed approach to handle both contact and elastoplastic nonlinearities effectively, without the need for convergence control, highlighting the superiority of the proposed method.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"441 ","pages":"Article 118016"},"PeriodicalIF":6.9,"publicationDate":"2025-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143834454","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}