Computer Methods in Applied Mechanics and Engineering最新文献

{"title":"Information entropy regularization method for structural identification with large-scale damaged parameters","authors":"Yifei Wang,&nbsp;Xiaojun Wang,&nbsp;Geyong Cao","doi":"10.1016/j.cma.2025.117947","DOIUrl":"10.1016/j.cma.2025.117947","url":null,"abstract":"<div><div>With the advancement of structural health monitoring technology, the increasing precision in modeling, scalability of model parameters, and complexity of external environments have introduced significant challenges to damage identification. Notably, the ill-posed nature of large-scale parameter identification from refined models has become a critical technical challenge. Regularization methods are widely employed to mitigate ill-posedness and control the complexity of identification problems. Traditional regularization methods often penalize imbalances in damage parameters, leading to errors and suboptimal convergence, failing to accurately reflect actual damage conditions. To address these challenges, an information entropy regularization term is introduced to capture the distribution of structural damage location and severity. By integrating regularization term with an adjoint sensitivity optimization algorithm, a refined iterative approach is developed to manage large-scale damage parameter identification from detailed finite element models. Numerical analyses on a 2D stress plate and a 3D wing, along with experimental validation on impact damage of clamped plates, demonstrate the accuracy and effectiveness of the proposed method.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"440 ","pages":"Article 117947"},"PeriodicalIF":6.9,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143705339","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":"Populating cellular metamaterials on the extrema of attainable elasticity through neuroevolution","authors":"Maohua Yan,&nbsp;Ruicheng Wang,&nbsp;Ke Liu","doi":"10.1016/j.cma.2025.117950","DOIUrl":"10.1016/j.cma.2025.117950","url":null,"abstract":"<div><div>The trade-offs between different mechanical properties of materials pose fundamental challenges in engineering material design, such as balancing stiffness versus toughness, weight versus energy-absorbing capacity, and among the various elastic coefficients. Although gradient-based topology optimization approaches have been effective in finding specific designs and properties, they are not efficient tools for surveying the vast design space of metamaterials, and thus unable to reveal the attainable bound of interdependent material properties. Other common methods, such as parametric design or data-driven approaches, are limited by either the lack of diversity in geometry or the difficulty to extrapolate from known data, respectively. In this work, we formulate the simultaneous exploration of multiple competing material properties as a multi-objective optimization (MOO) problem and employ a neuroevolution algorithm to efficiently solve it. The Compositional Pattern-Producing Networks (CPPNs) is used as the generative model for unit cell designs, which provide very compact yet lossless encoding of geometry. A modified Neuroevolution of Augmenting Topologies (NEAT) algorithm is employed to evolve the CPPNs such that they create metamaterial designs on the Pareto front of the MOO problem, revealing empirical bounds of different combinations of elastic properties. Looking ahead, our method serves as a universal framework for the computational discovery of diverse metamaterials across a range of fields, including robotics, biomedicine, thermal engineering, and photonics.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"440 ","pages":"Article 117950"},"PeriodicalIF":6.9,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143715428","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":"Frictional contact between solids: A fully Eulerian phase-field approach","authors":"Flavio Lorez,&nbsp;Mohit Pundir","doi":"10.1016/j.cma.2025.117929","DOIUrl":"10.1016/j.cma.2025.117929","url":null,"abstract":"<div><div>Recent advancements have demonstrated that fully Eulerian methods can effectively model frictionless contact between deformable solids. Unlike traditional Lagrangian approaches, which require contact detection and resolution algorithms, the Eulerian framework utilizes a single, fixed spatial mesh combined with a diffuse interface phase-field approach, simplifying contact resolution significantly. Moreover, the Eulerian method is well-suited for developing a unified framework to handle multiphysical systems involving growing bodies that interact with a constraining medium. In this work, we extend our previous methodology to incorporate frictional contact. By leveraging the intersection of the phase fields of multiple bodies, we define normal and tangential penalty force fields, which are incorporated into the linear momentum equations to capture frictional interactions. This formulation allows independent motion of each body using distinct velocity fields, coupled solely through interfacial forces arising from contact and friction. We thoroughly validate the proposed approach through several numerical examples. The method is shown to handle large sliding effortlessly, accurately capture the stick–slip transition, and preserve history-dependent energy dissipation, offering a solution for modeling frictional contact in Eulerian models.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"440 ","pages":"Article 117929"},"PeriodicalIF":6.9,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143705338","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":"Key conditional quotient of random finite element model under measurement conditions","authors":"Yuelin Zhao,&nbsp;Feng Wu","doi":"10.1016/j.cma.2025.117943","DOIUrl":"10.1016/j.cma.2025.117943","url":null,"abstract":"<div><div>Uncertainty and nonlinearity in real-world structures like complex connections and composite materials often impede the establishment of accurate finite element models, requiring measurement assistance to estimate the actual structural response. However, accurately and efficiently estimating the structural response in the face of random measurement errors, structural uncertainty, and nonlinear effects remains a challenge. In this study, a novel key conditional quotient (KCQ) theory has been presented to tackle this challenge. By extracting key conditions from measurement data and applying the principle of probability conservation, the KCQ theory provides an precise quotient-form expression, i.e., KCQ, for estimating the structural response considering random measurement errors, structural uncertainty, and nonlinearity. To effectively extract key measurement conditions, this study also proposes two innovative methods: the strong correlation measurement points method, and the covariance matrix of measurement errors method. To accurately and efficiently estimating the KCQ, a numerical method by combining the generalized quasi-Monte Carlo method based on the generalized center discrepancy and an offline-online coupling computational strategy is proposed. Five numerical examples are provided to verify the precision, efficiency, and robustness against measurement errors of the proposed KCQ theory and numerical method.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"440 ","pages":"Article 117943"},"PeriodicalIF":6.9,"publicationDate":"2025-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143705336","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 competitive baseline for deep learning enhanced data assimilation using conditional Gaussian ensemble Kalman filtering","authors":"Zachariah Malik ,&nbsp;Romit Maulik","doi":"10.1016/j.cma.2025.117931","DOIUrl":"10.1016/j.cma.2025.117931","url":null,"abstract":"<div><div>Ensemble Kalman Filtering (EnKF) is a popular technique for data assimilation, with far ranging applications. However, the vanilla EnKF framework is not well-defined when perturbations are nonlinear. We study two non-linear extensions of the vanilla EnKF – dubbed the conditional-Gaussian EnKF (CG-EnKF) and the normal score EnKF (NS-EnKF) – which sidestep assumptions of linearity by constructing the Kalman gain matrix with the ‘conditional Gaussian’ update formula in place of the traditional one. We then compare these models against a state-of-the-art deep learning based particle filter called the score filter (SF). This model uses an expensive score diffusion model for estimating densities and also requires a strong assumption on the perturbation operator for validity. In our comparison, we find that CG-EnKF and NS-EnKF dramatically outperform SF for two canonical systems in data assimilation: the Lorenz-96 system and a double well potential system. Our analysis also demonstrates that the CG-EnKF and NS-EnKF can handle highly non-Gaussian additive noise perturbations, with the latter typically outperforming the former.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"440 ","pages":"Article 117931"},"PeriodicalIF":6.9,"publicationDate":"2025-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143704055","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":"Data-driven elastoplastic constitutive modelling with physics-informed RNNs using the Virtual Fields Method for indirect training","authors":"Rúben Lourenço ,&nbsp;Petia Georgieva ,&nbsp;A. Andrade-Campos","doi":"10.1016/j.cma.2025.117935","DOIUrl":"10.1016/j.cma.2025.117935","url":null,"abstract":"<div><div>The increasing demand for accurate material behaviour data in engineering simulations has exposed the limitations of traditional constitutive models. Although recent advances in full-field measurement techniques provide more detailed material characterization, conventional approaches still heavily rely on explicit assumptions and labour-intensive experimentation. This paper revisits the indirect training methodology introduced by the authors <span><span>[1]</span></span>, which integrates Recurrent Neural Networks (RNNs) with Gated-Recurrent Units (GRUs) and the Virtual Fields Method (VFM) to model material behaviour without labelled data. The earlier study demonstrated the feasibility of training a GRU-based RNN using only global force and strain data through the VFM. Building on those findings, this work presents a more robust approach featuring an improved network architecture, with residual connections to enhance gradient flow and training stability, while also incorporating physics-based constraints. Extensive hyperparameter tuning was conducted to optimize the model and a sensitivity analysis was performed to assess the impact of the virtual fields on the accuracy and training dynamics. The models were validated using additional heterogeneous mechanical tests and the Reconstructed Axial Force Ratio (RAFR), as a key performance indicator, to further assess the physical correctness. The results show enhanced predictive accuracy and improved force reconstruction when larger sets of virtual fields are employed. Additionally, normalizing the VFM loss contributed to more consistent predictions and force reconstruction across all time stages. Stress contour plots further confirm the model’s ability to accurately predict stress distributions, which are in good agreement with the reference, with low median and average absolute errors.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"440 ","pages":"Article 117935"},"PeriodicalIF":6.9,"publicationDate":"2025-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143705335","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":"RoePINNs: An integration of advanced CFD solvers with Physics-Informed Neural Networks and application in arterial flow modeling","authors":"J. Orera ,&nbsp;J. Ramírez ,&nbsp;P. García-Navarro ,&nbsp;J. Murillo","doi":"10.1016/j.cma.2025.117933","DOIUrl":"10.1016/j.cma.2025.117933","url":null,"abstract":"<div><div>The characterization of forward and inverse problems describing blood flow dynamics plays a decisive role in numerous biomedical applications. These systems can be modeled using one-dimensional (1D) approaches leading to a hyperbolic system of equations with source terms. Their numerical discretization, associated to the spatial variation of mechanical and geometrical properties, requires advanced numerical solvers that ensure both stability and an accurate description of the dynamics of the system. In this work, we present RoePINNs, a hybrid framework for the embedding of advanced Computational Fluid Dynamics (CFD) solvers into Physics-Informed Neural Networks (PINNs), and give examples of application to Burgers’ equation as well as the propagation of nonlinear waves in elastic arteries, both under the presence of geometric-type source terms, for forward and inverse problems. We demonstrate that Augmented Riemann solvers can be incorporated into the PINN framework with straightforward adjustments to the hyperparameters, providing a promising alternative to automatic differentiation (AD), especially in cases where the solution exhibits strong nonlinearities and physical constraints are required. Benefits of the proposed RoePINN compared with the <em>vanilla</em> PINN based in AD are twofold: on the one hand, this hybrid approach employs numerical differentiation by means of support points in the surroundings of the collocation points, hence the robustness, generalization capacity and tunability of the PINNs are, in most cases, largely enhanced. On the other hand, the RoePINN incorporates the numerical solver, hence it is also capable of capturing sharp discontinuities with an order-of-magnitude improvement in accuracy compared with the vanilla version.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"440 ","pages":"Article 117933"},"PeriodicalIF":6.9,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143688033","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":"Customized Gaussian process for representing polycrystalline texture","authors":"Bingqian Li,&nbsp;Piotr Breitkopf,&nbsp;Ludovic Cauvin","doi":"10.1016/j.cma.2025.117934","DOIUrl":"10.1016/j.cma.2025.117934","url":null,"abstract":"<div><div>A customized Gaussian Process Regression (GPR) model is developed to reconstruct Pole Density Functions in texture analysis. The model integrates spherical-periodic distance measures with conventional stationary kernels, adapting the GPR framework to capture localized texture features. A key contribution is the introduction of a log-linear data transformation, which enforces the non-negativity of both interpolated function values and stochastic intervals, ensuring physically meaningful reconstructions. To assess the model’s effectiveness, a systematic investigation examines the impact of distance measures, kernel selection, and hyperparameter optimization using synthetic texture datasets, provided as part of this work, with evaluations focusing on reconstruction accuracy, feature preservation, and uncertainty quantification in comparison to the conventional spherical harmonics approach. GPR with a log-linear transformation, geodesic distance, and a Matérn <span><math><mi>ν</mi></math></span>=5/2 kernel, shows promise in achieving higher accuracy than traditional spherical harmonics for reconstructing non-negative pole density functions, while additionally providing confidence intervals for uncertainty quantification.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"440 ","pages":"Article 117934"},"PeriodicalIF":6.9,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143688032","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":"Multi-objective Bayesian optimisation of spinodoid cellular structures for crush energy absorption","authors":"Hirak Kansara ,&nbsp;Siamak F. Khosroshahi ,&nbsp;Leo Guo ,&nbsp;Miguel A. Bessa ,&nbsp;Wei Tan","doi":"10.1016/j.cma.2025.117890","DOIUrl":"10.1016/j.cma.2025.117890","url":null,"abstract":"<div><div>In the pursuit of designing safer and more efficient energy-absorbing structures, engineers must tackle the challenge of improving crush performance while balancing multiple conflicting objectives, such as maximising energy absorption and minimising peak impact forces. Accurately simulating real-world conditions necessitates the use of complex material models to replicate the non-linear behaviour of materials under impact, which comes at a significant computational cost. This study addresses these challenges by introducing a multi-objective Bayesian optimisation framework specifically developed to optimise spinodoid structures for crush energy absorption. Spinodoid structures, characterised by their scalable, non-periodic topologies and efficient stress distribution, offer a promising direction for advanced structural design. However, optimising design parameters to enhance crush performance is far from straightforward, particularly under realistic conditions. Conventional optimisation methods, although effective, often require a large number of costly simulations to identify suitable solutions, making the process both time-consuming and resource intensive. In this context, multi-objective Bayesian optimisation provides a clear advantage by intelligently navigating the design space, learning from each evaluation to reduce the number of simulations required, and efficiently addressing the complexities of non-linear material behaviour. By integrating finite element analysis with Bayesian optimisation, the framework developed in this study tackles the dual challenge of improving energy absorption and reducing peak force, particularly in scenarios where plastic deformation plays a critical role. Leveraging scalarisation and hypervolume-based techniques, the framework effectively identifies Pareto-optimal solutions that balance these conflicting objectives while accounting for the complexities of plastic material behaviour. Importantly, the approach also prevents problematic densification, ensuring structural integrity during impact. The results not only demonstrate the framework’s ability to outperform the NSGA-II algorithm but also highlight its potential for wider applications in structural and material optimisation. The framework’s adaptability to various design requirements underscores its capability to address complex, multi-objective optimisation challenges associated with real-world conditions.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"440 ","pages":"Article 117890"},"PeriodicalIF":6.9,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143686905","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 stable and structure-preserving algorithms for the stochastic Galerkin system of 2D shallow water equations","authors":"Yekaterina Epshteyn ,&nbsp;Akil Narayan ,&nbsp;Yinqian Yu","doi":"10.1016/j.cma.2025.117932","DOIUrl":"10.1016/j.cma.2025.117932","url":null,"abstract":"<div><div>Shallow water equations (SWE) are fundamental nonlinear hyperbolic PDE-based models in fluid dynamics that are essential for studying a wide range of geophysical and engineering phenomena. Therefore, stable and accurate numerical methods for SWE are needed. Although some algorithms are well studied for deterministic SWE, more effort should be devoted to handling the SWE with uncertainty. In this paper, we incorporate uncertainty through a stochastic Galerkin (SG) framework, and building on an existing hyperbolicity-preserving SG formulation for 2D SWE, we construct the corresponding entropy flux pair, and develop structure-preserving, well-balanced, second-order energy conservative and energy stable finite volume schemes for the SG formulation of the two-dimensional shallow water system. We demonstrate the efficacy, applicability, and robustness of these structure-preserving algorithms through several challenging numerical experiments.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"440 ","pages":"Article 117932"},"PeriodicalIF":6.9,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143687272","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}