Computer Methods in Applied Mechanics and Engineering最新文献

{"title":"An isogeometric assumed natural strain method to alleviate locking in solid beams","authors":"Alessia Patton ,&nbsp;Leonardo Leonetti ,&nbsp;Josef Kiendl","doi":"10.1016/j.cma.2025.118024","DOIUrl":"10.1016/j.cma.2025.118024","url":null,"abstract":"<div><div>This work proposes a novel Isogeometric Analysis (IGA) extension of the assumed natural strain (ANS) method to alleviate locking phenomena in solid beams, which are modeled as 3D elements accounting for displacement degrees of freedom solely and designed such that accurate analyses can be generally obtained using only one element to discretize the structure’s cross-section. ANS methods substitute covariant compatible strains that cause locking in solid beams, when, e.g., constrained to be thin, with a so-called assumed strain field. Namely, the compatible strains are interpolated at suitable locations, termed tying points, and the assumed strains are then derived using an <em>ad hoc</em> element-based extrapolation. This local operation involves, in principle, the inversion of extrapolation matrices; yet, these quantities can be computed at once and in closed form, using a linear extrapolation in the quadratic case, without needing any inversion operation. The introduced IGA ANS technique, specifically tailored to mitigate membrane and shear locking, given the superior geometric approximation provided by the adopted IGA framework, as well as the high regularity of the utilized computer-aided design basis functions, is also able to naturally alleviate thickness and curvature-thickness locking phenomena and its effectiveness is proven through extensive numerical testing.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"442 ","pages":"Article 118024"},"PeriodicalIF":6.9,"publicationDate":"2025-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143891334","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 Aggregated Material Point Method (AgMPM)","authors":"William M. Coombs,&nbsp;Robert E. Bird,&nbsp;Giuliano Pretti","doi":"10.1016/j.cma.2025.118012","DOIUrl":"10.1016/j.cma.2025.118012","url":null,"abstract":"<div><div>The Material Point Method (MPM) has been shown to be an effective approach for analysing large deformation processes across a range of physical problems. However, the method suffers from a number of spurious artefacts, such as a widely documented cell crossing instability, which can be mitigated by adopting basis functions with higher order continuity. The larger stencil of these basis functions exacerbate a less widely discussed issue - <em>small cuts</em>. The small cut issue is linked to the arbitrary interaction between the physical body and the background mesh that is used to assemble and solve the governing equations in the MPM. There is the potential for degrees of freedom near the boundary of the body to have very small contributions from material points, which causes two problems: (i) artificially large accelerations/displacements at the boundary and (ii) ill conditioning of the global linear system. This paper provides a new mesh Aggregated MPM, or AgMPM, that mitigates the small cut issue by forming aggregated elements, tying the ill-behaved degrees of freedom to well posed interior elements. Implicit quasi-static and explicit dynamic formulations are provided and demonstrated through a series of numerical examples. The approach does not introduce any new numerical parameters and can be applied to implementations that adopt a lumped mass matrix. Aggregation is shown to significantly improve the stability of implicit implementations of the MPM, often at a lower computational cost compared to standard, non-aggregated, implementations. The technique improves the energy conservation and the stress field of explicit dynamic MPMs.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"442 ","pages":"Article 118012"},"PeriodicalIF":6.9,"publicationDate":"2025-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143891275","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":"Asymptotic homogenization-based strain gradient elastodynamics: Governing equations, well-posedness and numerical examples","authors":"Quanzhang Li ,&nbsp;Yipeng Rao ,&nbsp;Zihao Yang ,&nbsp;Junzhi Cui ,&nbsp;Meizhen Xiang","doi":"10.1016/j.cma.2025.118010","DOIUrl":"10.1016/j.cma.2025.118010","url":null,"abstract":"<div><div>We develop a strain gradient elastodynamics model for heterogeneous materials based on the two-scale asymptotic homogenization theory. Utilizing only the first-order cell functions, the present model is more concise and more computationally efficient than previous works with high-order truncations. Furthermore, we rigorously prove that the coefficient tensors, including the homogenized elasticity tensor, the strain gradient stiffness tensor, and the micro-inertial tensor are symmetric positive definite, thereby establishing the well-posedness of the strain gradient elastodynamics model, i.e., the existence and uniqueness of solutions. Numerical simulations are performed to confirm the theoretical findings and illustrate the characteristics of the present model in comparison with classical elastodynamics model (without strain gradient terms) and strain gradient models with higher-order truncations. The results indicate that the strain gradient model derived based on the first-order truncation can achieve an optimal balance between accuracy and computational cost.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"442 ","pages":"Article 118010"},"PeriodicalIF":6.9,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143882308","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":"An efficient discrete physics-informed neural networks for geometrically nonlinear topology optimization","authors":"Jichao Yin ,&nbsp;Shuhao Li ,&nbsp;Yaya Zhang ,&nbsp;Hu Wang","doi":"10.1016/j.cma.2025.118043","DOIUrl":"10.1016/j.cma.2025.118043","url":null,"abstract":"<div><div>The application of geometrically nonlinear topology optimization (GNTO) poses a substantial challenge due to the extensive memory requirements and prohibitive computational demands involved. To tackle this challenge, a discrete physics-informed neural network (dPINN) is suggested as a promising approach to alleviate computational demands and enhance the applicability to large-scale problems. In comparison to collocation point-based PINNs, the most distinctive characteristic of dPINN is its mesh-based local interpolation for the evaluation of the system energy. This approach not only circumvents the issue of material mapping between elements and collocation points, but also provides improved robustness. Moreover, the partial differential equation (PDE) that corresponds to the adjoint equations lacks explicit expressions. The dPINN is capable of naturally evaluating equivalent energy through discrete expressions, a capability that collocation point-based PINNs lack. Furthermore, the activation state of sub-networks in series is determined in accordance with the density variation, thereby saving computational costs by dynamically incorporating each sub-network to reduce the trainable parameters in certain optimization steps, while conserving computational resources. The dPINN demonstrates exceptional accuracy and efficiency, along with enhanced resilience against mesh distortion compared to the finite element method (FEM), thereby enabling the application of larger loads. The dPINN-based GNTO is validated to be robust with regard to different geometries, loads, and volume fractions through several examples, and the outcomes are largely consistent with those of the FEM-based approach. Of greater significance is the fact that dPINN is capable of solving a million-DOFs 3D GNTO problem, which represents a notable advantage.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"442 ","pages":"Article 118043"},"PeriodicalIF":6.9,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143878823","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":"Transient dynamic robust topology optimization methodology for continuum structure under stochastic uncertainties","authors":"Zeng Meng ,&nbsp;Zixuan Tian ,&nbsp;Yongxin Gao ,&nbsp;Matthias G.R. Faes ,&nbsp;Quhao Li","doi":"10.1016/j.cma.2025.118019","DOIUrl":"10.1016/j.cma.2025.118019","url":null,"abstract":"<div><div>Time-variant uncertainties are omnipresent in engineering systems. These significantly impact the structural performance. The main challenge in this context is how to handle them in dynamic domain response topology optimization. To tackle this challenge, a new transient dynamic robust topology optimization (TDRTO) method is proposed to optimize the topology of continuous structures. This method comprehensively considers the uncertainties of material property, loading directions, and time-variant stochastic parameters of loading amplitudes. The time-variant performance function is transformed into a set of independent instantaneous performance functions, where the stochastic processes are discretized by using the optimal linear estimation method to simulate the correlations among various time nodes. The mean and standard deviation of the structural compliance are approximated through a Taylor expansion. Moreover, the Hilber-Hughes-Taylor <em>α</em> method is employed to address the structural dynamic problem. The design and stochastic sensitivities are derived by the “discretize-then-differentiate” and the adjoint methods, thereby improving the computational efficiency. Three illustrative cases are tested to validate the efficacy of TDRTO method, which shows its superiority over the traditional robust topology optimization method for dealing with time-variant stochastic uncertainties.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"442 ","pages":"Article 118019"},"PeriodicalIF":6.9,"publicationDate":"2025-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143876669","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":"Simultaneous topology and fiber path optimization for variable stiffness Double-Double laminates with strength control","authors":"Dan Wang ,&nbsp;Yucheng Zhong ,&nbsp;David W. Rosen ,&nbsp;Sridhar Narayanaswamy","doi":"10.1016/j.cma.2025.118021","DOIUrl":"10.1016/j.cma.2025.118021","url":null,"abstract":"<div><div>Variable stiffness laminates offer the advantage of tailoring structural performance by adjusting in-plane stiffness through curved fiber paths. Additionally, material distribution at the structural level can further fine-tune performance by varying the topology. If both the structural topology and curved fiber paths are optimized together, super-efficient composite laminates can be achieved. In this paper, a simultaneous topology and fiber path optimization method based on a coarse background mesh is proposed for variable stiffness Double-Double (DD) laminates with strength control. Firstly, elemental pseudo densities and nodal fiber orientations are selected as design variables to control topology and curved fiber paths, respectively. Due to the reduced design redundancy in DD laminates, only two independent fiber orientations are necessary for each node of a coarse background mesh. This ensures global fiber path continuity through interpolation of elemental values. Additionally, it helps decouple fiber path generation from the computationally expensive finite element analysis, significantly reducing the number of design variables and related constraints. Secondly, an optimization model is developed to maximize the laminate strength while satisfying weight and compliance constraints. The nested p-norm of Tsai-Hill failure indices is used to aggregate stresses across different elements and layers, enhancing the overall calculation efficiency. Additionally, minimum angle difference constraints are incorporated between the two groups of DD angles to ensure the laminate’s ability to resist secondary loads, thereby improving structural integrity. Notably, the proposed framework is the first to address the simultaneous optimization of both topology and curved fiber paths with strength considerations for multi-layer composite laminates. Sensitivities for both topology and fiber orientation design variables are efficiently calculated by solving a single adjoint problem, significantly improving computational efficiency. Finally, representative numerical examples demonstrate the effectiveness of the proposed method, achieving significant stress concentration reductions (over 40 %) compared to results from topology optimization alone. The optimized designs exhibit more compact topologies, improved load transfer, and enhanced resistance to secondary loading, validating the robustness of the proposed method.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"442 ","pages":"Article 118021"},"PeriodicalIF":6.9,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143875008","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":"An unconditionally stable variable time step scheme for two-phase ferrofluid flows","authors":"Aytura Keram ,&nbsp;Pengzhan Huang ,&nbsp;Yinnian He","doi":"10.1016/j.cma.2025.118018","DOIUrl":"10.1016/j.cma.2025.118018","url":null,"abstract":"<div><div>In this paper, a decoupled, linearized, unconditionally stable, and fully discrete numerical scheme is presented for simulating two-phase ferrofluid flows. This scheme is constructed by introducing two scalar auxiliary variables. It is based on the backward Euler scheme with variable time step and mixed finite element discretization. Nonlinear terms are treated explicitly to simplify the computational process. Meanwhile, without any restriction on time step, we show the stability of the proposed scheme. Finally, numerical examples are presented to check the accuracy and efficiency of the proposed scheme.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"442 ","pages":"Article 118018"},"PeriodicalIF":6.9,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143875009","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":"Overlapping Schwarz preconditioners for randomized neural networks with domain decomposition","authors":"Yong Shang ,&nbsp;Alexander Heinlein ,&nbsp;Siddhartha Mishra ,&nbsp;Fei Wang","doi":"10.1016/j.cma.2025.118011","DOIUrl":"10.1016/j.cma.2025.118011","url":null,"abstract":"<div><div>Randomized neural networks (RaNNs), characterized by fixed hidden layers after random initialization, offer a computationally efficient alternative to fully parameterized neural networks trained using stochastic gradient descent-type algorithms. In this paper, we integrate RaNNs with overlapping Schwarz domain decomposition in two primary ways: firstly, to formulate the least-squares problem with localized basis functions, and secondly, to construct effective overlapping Schwarz preconditioners for solving the resulting linear systems. Specifically, neural networks are randomly initialized in each subdomain following a uniform distribution, and these localized solutions are combined through a partition of unity, providing a global approximation to the solution of the partial differential equation. Boundary conditions are imposed via a constraining operator, eliminating the necessity for penalty methods. Furthermore, we apply principal component analysis (PCA) within each subdomain to reduce the number of basis functions, thereby significantly improving the conditioning of the resulting linear system. By constructing additive Schwarz (AS) and restricted AS preconditioners, we efficiently solve the least-squares problems using iterative solvers such as the Conjugate Gradient (CG) and generalized minimal residual methods. Numerical experiments clearly demonstrate that the proposed methodology substantially reduces computational time, particularly for multi-scale and time-dependent PDE problems. Additionally, we present a three-dimensional numerical example illustrating the superior efficiency of employing the CG method combined with an AS preconditioner over direct methods like QR decomposition for solving the associated least-squares system.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"442 ","pages":"Article 118011"},"PeriodicalIF":6.9,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143868378","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":"An optimal-transport finite-particle method for driven mass diffusion","authors":"A. Pandolfi ,&nbsp;I. Romero ,&nbsp;M. Ortiz","doi":"10.1016/j.cma.2025.118013","DOIUrl":"10.1016/j.cma.2025.118013","url":null,"abstract":"<div><div>We formulate a finite-particle method of mass transport that accounts for general mixed boundary conditions. The particle method couples a geometrically-exact treatment of advection; Wasserstein gradient-flow dynamics; and a Kullback–Leibler representation of the entropy. General boundary conditions are enforced by introducing an adsorption/depletion layer at the boundary wherein particles are added or removed as dictated by the boundary conditions. We demonstrate the range and scope of the method through a number of examples of application, including absorption of particles into a sphere and flow through pipes of square and circular cross section, with and without occlusions. In all cases, the solution is observed to converge weakly, or in the sense of local averages.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"442 ","pages":"Article 118013"},"PeriodicalIF":6.9,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143864541","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":"Parallel Algebraic Multigrid Solvers for Composite Discontinuous Galerkin Discretization of the Cardiac EMI Model in Heterogeneous Media","authors":"Edoardo Centofanti ,&nbsp;Ngoc Mai Monica Huynh ,&nbsp;Luca F. Pavarino ,&nbsp;Simone Scacchi","doi":"10.1016/j.cma.2025.118001","DOIUrl":"10.1016/j.cma.2025.118001","url":null,"abstract":"<div><div>In this paper, we develop and numerically study algebraic multigrid (AMG) preconditioners for the cardiac EMI (Extracellular space, cell Membrane, and Intracellular space) model, a recent and biophysically detailed framework for cardiac electrophysiology. The EMI model addresses the limitations of traditional homogenized cardiac models and leverages contemporary computational power to enable high-resolution simulations at the cellular scale. Using a composite Discontinuous Galerkin (DG) discretization, we introduce an AMG-EMI solver for the three dimensional EMI model. Our investigation includes the AMG-EMI scalability performance, both weak and strong, and evaluates its numerical robustness under ischemic conditions, addressing the challenges of heterogeneous media. Numerical tests exploit state-of-the-art pre-exascale supercomputers with hybrid CPU–GPU architectures. The results indicate better scalability performance of the AMG-EMI solver on CPUs compared to GPUs. However, the best solution times achieved using GPUs are up to 40x faster than those obtained on CPUs.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"442 ","pages":"Article 118001"},"PeriodicalIF":6.9,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143868380","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}