Computer Methods in Applied Mechanics and Engineering最新文献

{"title":"Nonlinear projection-based model order reduction with machine learning regression for closure error modeling in the latent space","authors":"S. Ares de Parga, Radek Tezaur, Carlos G. Hernández, Charbel Farhat","doi":"10.1016/j.cma.2025.118443","DOIUrl":"https://doi.org/10.1016/j.cma.2025.118443","url":null,"abstract":"A significant advancement in nonlinear projection-based model order reduction (PMOR) is presented through a highly effective methodology. This methodology employs Gaussian process regression (GPR) and radial basis function (RBF) interpolation for closure error modeling in the latent space, offering notable gains in efficiency and expanding the scope of PMOR. Moving beyond the limitations of deep artificial neural networks (ANNs), previously used for this task, this approach provides crucial advantages in terms of interpretability and a reduced demand for extensive training data. The capabilities of GPR and RBFs are showcased in two demanding applications: a two-dimensional parametric inviscid Burgers problem, featuring propagating shocks across the entire computational domain, and a complex three-dimensional turbulent flow simulation around an Ahmed body. The results demonstrate that this innovative approach preserves accuracy and achieves substantial improvements in efficiency and interpretability when contrasted with traditional PMOR and ANN-based closure modeling.","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"27 1","pages":""},"PeriodicalIF":7.2,"publicationDate":"2025-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145261870","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 Green’s function fast multipole method for computation of micromechanical fields in heterogeneous materials","authors":"Miroslav Zecevic","doi":"10.1016/j.cma.2025.118436","DOIUrl":"https://doi.org/10.1016/j.cma.2025.118436","url":null,"abstract":"Computation of micromechanical fields in heterogeneous materials is usually performed using either the finite element method or the Green’s function method based on FFTs. The finite element method allows for accurate discretization and for non-periodic boundary conditions but is computationally expensive. On the other hand, the FFT-based method is computationally efficient but requires discretization on a regular grid of hexahedral voxels. In this paper, a Green’s function method allowing for accurate discretization using tetrahedral elements and for non-periodic boundary conditions is proposed. The convolution is computed using the fast multipole method, which provides good accuracy even for low-order expansion due to the fast decay of interactions between elements. The proposed Green’s function fast multipole method is verified by comparison with analytical and FFT-based solutions. The computational time is analyzed and compared to the FFT-based method for non-periodic convolution. Finally, effective properties of an elastic polycrystalline microstructure containing thin intergranular cracks are computed and analyzed.","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"120 1","pages":""},"PeriodicalIF":7.2,"publicationDate":"2025-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145261871","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 mesh-based geometric deep learning framework for rapid response prediction of large-scale and multi-component mechanical structures in engineering","authors":"Gongxi Zhang, Ying Liu, Yi Quan, Junfei Yan","doi":"10.1016/j.cma.2025.118435","DOIUrl":"https://doi.org/10.1016/j.cma.2025.118435","url":null,"abstract":"Mesh-based finite element method (FEM) plays a critical role in simulating structural response. However, the analysis of complex physical processes, such as vehicle crashworthiness, is hindered by inherent high nonlinearities and large-scale meshes, leading to significant computational overhead and impeding rapid structure design. In recent years, the use of machine learning (ML) or deep learning (DL) methods to build surrogate models for simulations has gained much attention, which offers the potential to drastically reduce computational time while preserving accuracy. In this paper, we develop an end-to-end and mesh-based geometric DL framework that takes finite element (FE) solver files (such as.k file for LS-Dyna) containing mesh and material information as input, and quickly outputs response prediction of large-scale and multi-component mechanical structures in engineering, thus serving a promising alternative to FE solvers. We innovatively introduce the graph self-supervised learning (SSL) to transform FE data of structural component with varied material properties, complex geometric shapes and arbitrary number of unstructured meshes into low-dimensional embeddings, which are then employed to build an equivalent small-scale graph representation of the large-scale assembly, effectively alleviating the computational costs of subsequent prediction models. Then, we present GNN-FNN and GNN-Transformer models specifically designed for three different prediction tasks, including forecasting static and dynamic structural performance metrics, and constructing time-dependent physical fields. Using a large-scale industrial case of the electric vehicle (EV) under side pole impact, three regression tasks are carried out to assess the effectiveness of the proposed approach. Results reveal that the non-parametric model, free from the need for manually defined explicit parameters, excels in extracting implicit parameters for diverse structures, which support satisfactory prediction accuracy in each task with a considerable speedup than the simulation. Besides, it is surprising that our model is weakly sensitive to the moderate variation in the mesh resolution, which is valuable for practical engineering applications. The adaptability and scalability of our method are further verified on three additional industrial cases with varied structural simulation scenarios and progressively increasing FE model complexity. This work offers an effective surrogate model to accelerate the response evaluation of mechanical structures in engineering and shorten the design cycle requiring iterative optimization.","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"57 1","pages":""},"PeriodicalIF":7.2,"publicationDate":"2025-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145261873","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":"Stretch-based hyperelastic electromechanical constitutive metamodels via gradient enhanced Gaussian predictors using hierarchical structure discovery","authors":"Nathan Ellmer, Rogelio Ortigosa, Jesús Martínez-Frutos, Roman Poya, Johann Sienz, Antonio J. Gil","doi":"10.1016/j.cma.2025.118349","DOIUrl":"https://doi.org/10.1016/j.cma.2025.118349","url":null,"abstract":"This paper introduces a new approach to developing electromechanical constitutive metamodels via the use of Gradient Enhanced Gaussian Predictors (Kriging). The formulation uses principal stretches for the isotropic mechanics, invariants for the electrostatics and coupling terms, and accounts for anisotropy through the relevant inclusion of anisotropic invariants associated with a respective symmetry integrity basis. Three novelties are presented in this paper. The first is the use of orthogonal projections to identify the most appropriate set of inputs - related to material anisotropy - for use in the metamodel. By projecting the stress and electric field data into several derivative bases - defined for each anisotropic class - and then reconstructing the quantities, the errors in reconstruction can be assessed thus inferring the most appropriate class of anisotropy. Furthermore, the procedure forms a pre-processing stage and is particularly useful when an underlying model is completely unknown as seen when modelling Relative Volume Elements. The second novelty arises from the use of a hybrid formulation, namely the principal stretches for isotropic mechanics and the electromechanical anisotropic invariants. This is beneficial during the projection procedure in reducing the cases where the projection matrix becomes singular but requires careful development of the correlation function to maintain physical symmetry conditions. Thirdly, the electromechanical metamodels are calibrated upon the concentric styled data before being integrated within a Finite Element framework and tested upon a range of challenging simulations including bending actuators with induced torsion, frilling due to bending with selected electrode placement, as well as buckling plates tested with three rank-one laminate materials with increasing levels of anisotropy due to physical contrasts. The successful calibration and implementation of the metamodels can be witnessed amongst the wide range of presented numerical examples.","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"23 1","pages":""},"PeriodicalIF":7.2,"publicationDate":"2025-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145261907","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":"Improved accuracy of Dirichlet-like microscopic solutions on Representative Volume Elements","authors":"Louis Belgrand, Isabelle Ramière, Marc Josien, Frédéric Lebon","doi":"10.1016/j.cma.2025.118420","DOIUrl":"https://doi.org/10.1016/j.cma.2025.118420","url":null,"abstract":"This work focuses on the improvement of Dirichlet Boundary Value Finite Element solutions on Representative Volume Elements (RVE). For random microstructure Finite Element calculations, it is well-known that Periodic Boundary Conditions (PBC) applied on fixed size periodic RVE are much more precise than classical Dirichlet boundary conditions, so-called Uniform Strain Boundary Conditions (USBC), at the expense of additional efforts. The numerical experiments reported here clearly reveal that the inaccuracy of USBC is mainly due to boundary effects located around and in artificially cut inclusions because of the classical RVE cubic shape.","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"4 1","pages":""},"PeriodicalIF":7.2,"publicationDate":"2025-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145261875","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":"Dimension-reduced Chapman-Kolmogorov equation for high-dimensional stochastic dynamical systems","authors":"Jianbing Chen ,&nbsp;Meng-Ze Lyu ,&nbsp;Shenghan Zhang","doi":"10.1016/j.cma.2025.118433","DOIUrl":"10.1016/j.cma.2025.118433","url":null,"abstract":"<div><div>Random vibration analysis of high-dimensional dynamical systems is a fundamental problem in science and engineering, yet it remains challenging due to the curse of dimensionality. While dimension-reduced formulations have been developed for differential-type equations governing time-variant probability density, such as the Fokker-Planck equation, no equivalent formulation has been established for the integral-type Chapman-Kolmogorov (CK) equation, despite its theoretical importance and computational advantages. In this paper, a novel dimension-reduced Chapman-Kolmogorov (DRCK) equation is established governing the transient probability density function (PDF) of any quantity of interest in high-dimensional Markov systems. The derivation is conducted based on the projection of the full Chapman-Kolmogorov equation onto the dimension-reduced space. It is established that the intrinsic transition probability density (TPD) of the DRCK equation is the conditional expectation of the original TPD. Further, the short-time approximate intrinsic TPDs under both Gaussian and Poisson white noise excitations are derived analytically, enabling practical numerical implementation. The proposed DRCK equation provides a mathematically rigorous and computationally efficient framework for high-dimensional stochastic systems. Numerical examples are developed to demonstrate its accuracy and effectiveness. The DRCK equation thus provides a new tool for reliability assessment and uncertainty quantification in complex engineering applications.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"448 ","pages":"Article 118433"},"PeriodicalIF":7.3,"publicationDate":"2025-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145223345","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":"Physics- and data-driven active learning of neural network representations for free energy density functions of materials from statistical mechanics","authors":"J. Holber ,&nbsp;K. Garikipati","doi":"10.1016/j.cma.2025.118434","DOIUrl":"10.1016/j.cma.2025.118434","url":null,"abstract":"<div><div>Accurate free energy density representations are crucial for understanding phase dynamics in materials. We employ a scale-bridging approach to incorporate atomistic information into our free energy density model by training a neural network on DFT-informed Monte Carlo data. To optimize sampling in the high-dimensional Monte Carlo space, we present an active learning framework that integrates space-filling sampling, uncertainty-based sampling, and physics-informed sampling. Additionally, our approach includes methods such as hyperparameter tuning, dynamic sampling, and novelty enforcement. These strategies can be combined to reduce the mean squared error-either globally or in targeted regions of interest-while minimizing the number of required data points. The framework introduced here is broadly applicable to Monte Carlo sampling of a range of materials systems.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"448 ","pages":"Article 118434"},"PeriodicalIF":7.3,"publicationDate":"2025-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222631","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":"Mixed-dimensional analysis for coupling 2D elastodynamics and Timoshenko beam","authors":"Daniel Rabinovich ,&nbsp;Abimael F.D. Loula ,&nbsp;Dan Givoli","doi":"10.1016/j.cma.2025.118416","DOIUrl":"10.1016/j.cma.2025.118416","url":null,"abstract":"<div><div>Wave propagation is considered in a two-dimensional (2D) elastic structure, which includes a relatively small region whose behavior is fully 2D and a long and slender region whose bending behavior is like that of a Timoshenko beam. To save in computational effort, the latter region is reduced to a genuinely one-dimensional (1D) Timoshenko beam. The mathematical and computational problem posed then involves the coupling of the two regions, such that a well-posed, accurate, numerically stable and efficient hybrid 2D-elastic-Timoshenko-beam model is formed. The appropriate interface conditions are derived, and the well-posedness of the time-dependent problem is proved. A new computational coupling method is proposed, where the shape functions associated with the axial degrees of freedom on the interface of the elastic solid are modified in a special manner, to allow for the rotation continuity. The method results in a symmetric, positive and stable finite element formulation. Numerical examples are presented which demonstrate the performance of the scheme.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"448 ","pages":"Article 118416"},"PeriodicalIF":7.3,"publicationDate":"2025-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145223344","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":"Tensegrity structures and data-driven analysis for 3D cell mechanics","authors":"Ziran Zhou ,&nbsp;Jacinto Ulloa ,&nbsp;Guruswami Ravichandran ,&nbsp;José E. Andrade","doi":"10.1016/j.cma.2025.118406","DOIUrl":"10.1016/j.cma.2025.118406","url":null,"abstract":"<div><div>The cytoskeleton (CSK) plays an important role in many cell functions. Given the similarities between the mechanical behavior of tensegrity structures and the CSK, many studies have proposed different tensegrity-based models for simulating cell mechanics. However, the low symmetry of most tensegrity units has hindered the analysis of realistic 3D structures. As a result, tensegrity-based modeling in cell mechanics has been mainly focused on single cells or monolayers. In this paper, we propose a 3D tensegrity model based on the finite element method for simulating 3D cell mechanics. We show that the proposed model not only captures the nonlinearity of a single cell in an indentation test and a monolayer in stretch test but also the non-uniform stress distribution in multicellular spheroids upon non-uniform prestress design. Furthermore, we introduce a multiscale data-driven framework for cellular mechanics to optimize the computation, thus paving the way for modeling the mechanobiology of large cellular assemblies such as organs.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"448 ","pages":"Article 118406"},"PeriodicalIF":7.3,"publicationDate":"2025-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222636","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":"Personalized multiscale modeling of left atrial mechanics and blood flow","authors":"Lei Shi ,&nbsp;Boyang Gan ,&nbsp;Ian Y. Chen ,&nbsp;Vijay Vedula","doi":"10.1016/j.cma.2025.118412","DOIUrl":"10.1016/j.cma.2025.118412","url":null,"abstract":"<div><div>We present a personalized multiscale mechanics model of the left atrium (LA) to simulate its deformation throughout the cardiac cycle and drive blood flow. Our patient data-driven model tightly integrates 3D structural mechanics of the LA myocardium, incorporating both passive and active components, with a 0D closed-loop lumped parameter network (LPN)-based circulatory system model. A finite element (FE) model of LA tissue is constructed from the patient’s images, assuming uniform thickness and employing rule-based fiber directions. We then adopted a multi-step personalization approach, in which the LPN parameters with a surrogate LA model are first optimized to match cuff-based blood pressures and cardiac lumen volumes derived from time-resolved 3D gated computed tomography angiography (CTA) images. The surrogate LA pressure during passive expansion is used to estimate myocardial passive mechanics parameters and the reference unloaded configuration using an inverse finite element analysis (iFEA) framework. Finally, a robust multiscale coupling is applied between the iFEA-optimized FE model and the tuned 0D LPN model to characterize LA contraction. This effectively captures the physiological LA pressure-volume curve and reasonably aligns with the image-based cavity volumes and deformation. We then imposed the resulting simulation-predicted deformation as a moving-wall boundary condition to model atrial hemodynamics. We analyzed the model sensitivities to various simplifications to demonstrate its robustness and versatility and discussed potential future improvements. Overall, this comprehensive digital twinning platform could be applied to study LA biomechanics in health and disease and assist in devising personalized treatment plans.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"448 ","pages":"Article 118412"},"PeriodicalIF":7.3,"publicationDate":"2025-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222635","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}