Computer Methods in Applied Mechanics and Engineering最新文献

{"title":"Multi-domain topology optimization of connectable lattice structures with tunable transition patterns","authors":"Peng Wei ,&nbsp;Xinglong Chen ,&nbsp;Hui Liu","doi":"10.1016/j.cma.2025.117786","DOIUrl":"10.1016/j.cma.2025.117786","url":null,"abstract":"<div><div>The connectivity issue has always been a critical topic in multi-domain topology optimization of lattice structures. In this work, a novel multi-domain topology optimization approach is proposed, in which a set of transitional unit cells that follow a particular varying pattern is introduced between adjacent base microstructures to achieve optimized, multi-class, and well-connected multi-scale structures. Such smooth and tunable transition patterns are realized by interpolation of bar diameter, shape-morphing, and parameterized implicit functions, which exhibit superior adaptability to disconnected microstructures with intricate geometric configurations. To embed the varying transitional unit cells at the specified interface precisely, a graded interface model that extends from the erosion-based interface identification method is established utilizing a linear density filter. Additionally, a SIMP-based multi-domain interpolation scheme considering both base microstructures and transitional unit cells is proposed, in which each piece of interface layer can be further separately defined to navigate situations with more than two lattice material phases. Several 2D and 3D numerical examples are presented to demonstrate the stability, effectiveness, and scalability of the proposed method.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"437 ","pages":"Article 117786"},"PeriodicalIF":6.9,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143100932","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":"Accelerating high-fidelity simulations of chemically reacting flows using reduced-order modeling with time-dependent bases","authors":"Ki Sung Jung ,&nbsp;Cristian E. Lacey ,&nbsp;Hessam Babaee ,&nbsp;Jacqueline H. Chen","doi":"10.1016/j.cma.2025.117758","DOIUrl":"10.1016/j.cma.2025.117758","url":null,"abstract":"<div><div>Direct numerical simulations (DNS) of chemically reacting flows are extraordinarily expensive due to the large number of partial differential equations representing the transport of chemical species and stringent resolution requirements imposed by turbulence and flame scales. The present study extends a novel <em>on-the-fly</em> reduced-order modeling strategy based on time-dependent bases and CUR factorization (TDB-CUR) (previously applied to systems of stochastic partial differential equations, Donello et al. <em>Proc. R. Soc. A</em> 479 (2023) 20230320) to significantly reduce computational cost as well as memory and storage requirements of deterministic turbulent reacting flow simulations. The species transport equations are reformulated as a matrix differential equation (MDE) to leverage the instantaneous low-rank structure of the resulting species mass fraction matrix, constraining the solution of the species MDE to the manifold of low-rank matrices and integrating it explicitly in its low-rank form. In this formulation, the rows represent the grid points and the columns correspond to the species mass fractions. The species matrix contains significantly more rows than columns and is found to be amenable to accurate low-rank approximations. A CUR algorithm is employed to construct the low-rank approximation of the species matrix by sampling only a dominant subset of its columns and rows, extracted <em>on-the-fly</em>. We develop a time-explicit integration algorithm for the CUR low-rank approximation, constraining the selected columns (species) to only include slow species. The selected rows (grid points that include the fast species) have significantly fewer entries and are sub-cycled with smaller effective time steps, yielding implicit-like time-stepping while maintaining explicit-like computational costs. The proposed methodology is validated across a hierarchy of combustion problems on massively parallel supercomputers, demonstrating up to two orders of magnitude reduction in computational cost without compromising accuracy or relying on training data.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"437 ","pages":"Article 117758"},"PeriodicalIF":6.9,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143100936","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":"Multiphysics simulation of crystal growth with moving boundaries in FEniCS","authors":"Arved Wintzer ,&nbsp;Bilen Emek Abali ,&nbsp;Kaspars Dadzis","doi":"10.1016/j.cma.2025.117783","DOIUrl":"10.1016/j.cma.2025.117783","url":null,"abstract":"<div><div>Crystal growth processes and the Czochralski process in particular involves various physical phenomena such as heat transfer, phase change or liquid flows and requires a coupled multiphysical model for realistic numerical simulations. In this work, a new and extendable model is developed using the open-source software FEniCS. Basic equations for electromagnetic induction, heat conduction and radiation as well as phase change are thoroughly derived up to a finite element form and discussed together with the assumed boundary conditions and approximations. Verification of the FEniCS model with an analytical case demonstrated an accuracy with an error below 1%. A comparison with experimental results and numerical data from a similar model achieved a good agreement and showed opportunities for further improvement of melt flow modeling in particular.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"437 ","pages":"Article 117783"},"PeriodicalIF":6.9,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143071612","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A coupled FEM-VEM approach for crack tracking in quasi-brittle materials","authors":"Antonino Spada ,&nbsp;Marianna Puccia ,&nbsp;Elio Sacco ,&nbsp;Giuseppe Giambanco","doi":"10.1016/j.cma.2025.117756","DOIUrl":"10.1016/j.cma.2025.117756","url":null,"abstract":"<div><div>The numerical simulation of crack propagation in quasi-brittle materials has historically been mainly faced by means of consolidated approaches in the framework of the finite element method (FEM). However, the very recently developed virtual element method (VEM) is a new promising technique whose strong point is the possibility to model polygonal meshes, characterized by any number of edges. This paper proposes a new approach, coupling FEM and VEM for crack tracking in quasi-brittle materials. In these materials, diffuse degradation is followed by high deformation bands localizing in certain regions of the structure. To best exploit the potentialities of FEM and VEM, in this work the structure is initially entirely modeled through a FEM mesh. Then, when a diffuse damage meets the requirements for a localized band formation, the involved finite elements are converted into virtual sub-elements among which a thin layer is introduced. The thin layer is modeled through interphase (IPH) elements, which are advanced mechanical devices with respect to the common interface elements since internal strains and stresses are added to the contact ones. The portion of the structure modeled using VEs and IPHs is called substructure. Structure and substructure are solved through two nested iterative procedures.</div><div>The proposed numerical and crack tracking strategy are illustrated in detail and the results on three benchmark examples show its applicability as an alternative strategy to the full FEM approach.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"437 ","pages":"Article 117756"},"PeriodicalIF":6.9,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143071652","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A NURBS-based level set method for the manufacturing-oriented thermal buckling optimization of curvilinear fiber composite panels with cut-outs","authors":"Haoqing Ding ,&nbsp;Ruqi Sun ,&nbsp;Haocheng Tian ,&nbsp;Yutao Hu ,&nbsp;Xin Zhang ,&nbsp;Bin Xu","doi":"10.1016/j.cma.2025.117789","DOIUrl":"10.1016/j.cma.2025.117789","url":null,"abstract":"<div><div>Laminate composite panels with arbitrary cut-outs in a thermal environment may suffer buckling failure because of thermal stress. To address this issue, a manufacturing-oriented thermal-buckling optimization model is proposed for the design of curvilinear fiber paths. Furthermore, instead of using the traditional finite element method (FEM) with high computational costs, a cut non-uniform rational basis spline (NURBS) element method was developed for the thermal buckling analysis of laminate composite panels with arbitrary cut-outs. In this method, a level-set function, segmented density interpolation formulas, and an artificial shear correction factor were developed to describe arbitrary cut-outs, to overcome localized eigenmodes, and to avoid shear locking. Furthermore, a NURBS-based level-set method was proposed to illustrate the curvilinear fiber paths. The norm of the gradient vector of the NURBS-based level-set function was used to express the gap/overlap constraint. Subsequently, a thermal buckling optimization framework with compliance and manufacturing constraints was formulated. The effectiveness of the proposed optimization framework was verified numerically.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"437 ","pages":"Article 117789"},"PeriodicalIF":6.9,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143071610","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":"Generative reduced basis method","authors":"Ngoc Cuong Nguyen","doi":"10.1016/j.cma.2025.117754","DOIUrl":"10.1016/j.cma.2025.117754","url":null,"abstract":"<div><div>We present a generative reduced basis (RB) approach for the rapid and reliable solution of parametrized linear partial differential equations. Central to this approach is the construction of generative RB spaces that provide rapidly convergent approximations of the solution manifold. We propose a generative snapshot method to generate significantly larger sets of snapshots from a small initial set of solution snapshots. This method leverages multivariate nonlinear transformations to enrich the RB spaces, thereby enabling a more accurate approximation of the solution manifold than commonly used dimensionality reduction techniques such as proper orthogonal decomposition and greedy sampling. We employ the generative RB spaces to construct reduced order models and compute <em>a posteriori</em> error estimates. The error estimates allow us to efficiently explore the parameter space and select parameter points that improve the efficiency and accuracy of the reduced order model. Through numerical experiments, we demonstrate that the generative RB method not only improves the accuracy of the reduced order model but also provides tight error estimates.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"437 ","pages":"Article 117754"},"PeriodicalIF":6.9,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143071654","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 semi-implicit exactly fully well-balanced relaxation scheme for the Shallow Water Linearized Moment Equations","authors":"C. Caballero-Cárdenas ,&nbsp;I. Gómez-Bueno ,&nbsp;A. Del Grosso ,&nbsp;J. Koellermeier ,&nbsp;T. Morales de Luna","doi":"10.1016/j.cma.2025.117788","DOIUrl":"10.1016/j.cma.2025.117788","url":null,"abstract":"<div><div>When dealing with shallow water simulations, the velocity profile is often assumed to be constant along the vertical axis. However, since in many applications this is not the case, modeling errors can be significant. Hence, in this work, we deal with the Shallow Water Linearized Moment Equations (SWLME), in which the velocity is no longer constant in the vertical direction, where a polynomial expansion around the mean value is considered. The linearized version implies neglecting the non-linear terms of the basis coefficients in the higher order equations. As a result, the model is always hyperbolic and the stationary solutions can be more easily computed. Then, our objective is to propose an efficient, accurate and robust numerical scheme for the SWLME model, specially adapted for low Froude number situations. Hence, we describe a semi-implicit second order exactly fully well-balanced method. More specifically, a splitting is performed to separate acoustic and material phenomena. The acoustic waves are treated in an implicit manner to gain in efficiency when dealing with subsonic flow regimes, whereas the second order of accuracy is achieved thanks to a polynomial reconstruction and Strang-splitting method. We also exploit a reconstruction operator to achieve the fully well-balanced character of the method. Extensive numerical tests demonstrate the well-balanced properties and large speed-up compared to traditional methods.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"437 ","pages":"Article 117788"},"PeriodicalIF":6.9,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143071611","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":"Interval Isogeometric Analysis for coping with geometric uncertainty","authors":"Nataly A. Manque ,&nbsp;Jan Liedmann ,&nbsp;Franz-Joseph Barthold ,&nbsp;Marcos A. Valdebenito ,&nbsp;Matthias G.R. Faes","doi":"10.1016/j.cma.2025.117773","DOIUrl":"10.1016/j.cma.2025.117773","url":null,"abstract":"<div><div>Geometric uncertainty poses a significant challenge in many engineering sub-disciplines ranging from structural design to manufacturing processes, often attributed to the underlying manufacturing technology and operating conditions. When combined with geometric complexity, this phenomenon can result in substantial disparities between numerical predictions and the actual behavior of mechanical systems. One of the underlying causes lies in the initial design phase, where insufficient information impedes the development of robust numerical models due to epistemic uncertainty in system dimensions. In such cases, set-based methods, like intervals, prove useful for characterizing these uncertainties by employing lower and upper bounds to define uncertain input parameters. Nevertheless, employing interval methods for treating geometric uncertainties can become computationally demanding, especially when traditional methods like finite element analysis (FEA) are utilized to represent the system. This is due to the necessity of performing iterative analyses for different realizations of geometry within the bounds of uncertain parameters, requiring the repeated execution of the meshing process and thereby escalating the numerical effort. Moreover, the process of remeshing introduces a second challenge by disrupting the continuity of the underlying optimization problem inherent in interval analysis, further complicating the computational procedure. In this work, the potential of Isogeometric Analysis (IGA) for quantifying geometric uncertainties characterized by intervals is explored. IGA utilizes the same basis functions, Non-Uniform Rational B-Splines (NURBS), employed in Computer-Aided Design (CAD) to approximate solution fields in numerical analysis. This integration enhances the accurate description of complex shapes and interfaces while maintaining geometric fidelity throughout the simulation process. The primary advantage of employing IGA for uncertainty quantification lies in its ability to control the system’s geometry through the position of control points, which define the shape of NURBS. Consequently, alterations in the model’s geometry can be achieved by varying the position of these control points, thereby bypassing the numerical costs associated with remeshing when performing uncertainty quantification considering intervals. To propagate geometric uncertainties, a gradient-based optimization (GBO) algorithm is applied to determine the lower and upper bounds of the system response. The corresponding sensitivities are computed from the IGA model with a variational approach. Two case studies involving linear systems with uncertain geometric parameters demonstrate that the proposed strategy accurately estimates uncertain stress triaxiality.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"437 ","pages":"Article 117773"},"PeriodicalIF":6.9,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143071613","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Energy-based physics-informed neural network for frictionless contact problems under large deformation","authors":"Jinshuai Bai ,&nbsp;Zhongya Lin ,&nbsp;Yizheng Wang ,&nbsp;Jiancong Wen ,&nbsp;Yinghua Liu ,&nbsp;Timon Rabczuk ,&nbsp;YuanTong Gu ,&nbsp;Xi-Qiao Feng","doi":"10.1016/j.cma.2025.117787","DOIUrl":"10.1016/j.cma.2025.117787","url":null,"abstract":"<div><div>Numerical methods for contact mechanics are of great importance in engineering applications, enabling the prediction and analysis of complex surface interactions under various conditions. In this work, we propose an energy-based physics-informed neural network (PINN) framework for solving frictionless contact problems under large deformation. Inspired by microscopic Lennard-Jones potential, a surface contact energy is used to describe the contact phenomena. To ensure the robustness of the proposed PINN framework, relaxation, gradual loading and output scaling techniques are introduced. In the numerical examples, the well-known Hertz contact benchmark problem is conducted, demonstrating the effectiveness and robustness of the proposed PINN framework. Moreover, challenging contact problems with the consideration of geometrical and material nonlinearities are tested. It has been shown that the proposed PINN framework provides a reliable and powerful tool for nonlinear contact mechanics. More importantly, the proposed PINN framework exhibits competitive computational efficiency to the commercial FEM software when dealing with those complex contact problems. The codes used in this manuscript are available at <span><span>https://github.com/JinshuaiBai/energy_PINN_Contact</span><svg><path></path></svg></span>.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"437 ","pages":"Article 117787"},"PeriodicalIF":6.9,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143071653","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":"Godunov loss functions for modelling of hyperbolic conservation laws","authors":"Rami Cassia,&nbsp;Rich Kerswell","doi":"10.1016/j.cma.2025.117782","DOIUrl":"10.1016/j.cma.2025.117782","url":null,"abstract":"<div><div>Machine learning techniques are being used as an alternative to traditional numerical discretization methods for solving hyperbolic partial differential equations (PDEs) relevant to fluid flow. Whilst numerical methods are higher fidelity, they are computationally expensive. Machine learning methods on the other hand are lower fidelity but can provide significant speed-ups. The emergence of physics-informed neural networks (PINNs) in fluid dynamics has allowed scientists to directly use PDEs for evaluating loss functions. The downfall of this approach is that the differential form of systems is invalid at regions of shock inherent in hyperbolic PDEs such as the compressible Euler equations. To circumvent this problem we propose the Godunov loss function: a loss based on the finite volume method (FVM) that crucially incorporates the flux of Godunov-type methods. These Godunov-type methods are also known as approximate Riemann solvers and evaluate intercell fluxes in an entropy-satisfying and non-oscillatory manner, yielding more physically accurate shocks. Our approach leads to superior performance compared to standard PINNs that use regularized PDE-based losses as well as FVM-based losses, as tested on the 2D Riemann problem in the context of time-stepping and super-resolution reconstruction.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"437 ","pages":"Article 117782"},"PeriodicalIF":6.9,"publicationDate":"2025-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143071655","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}