Computer Methods in Applied Mechanics and Engineering最新文献

{"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}

{"title":"On a canonical interface model with application to micro-heterogeneous elastic solids","authors":"Ali Javili ,&nbsp;Fredrik Larsson ,&nbsp;Kenneth Runesson ,&nbsp;Paul Steinmann","doi":"10.1016/j.cma.2025.117925","DOIUrl":"10.1016/j.cma.2025.117925","url":null,"abstract":"<div><div>Finite-thickness interphases between different constituents in heterogeneous materials are often replaced by a zero-thickness interface model. Due to increasing area-to-volume ratio with decreasing size of microstructures, interfaces introduce a physical length into the effective response at the macroscale. The most commonly studied interface models are the <em>cohesive interface model</em> and the <em>elastic interface model</em>. The cohesive interface model allows for a displacement jump across the interface, in contrast to the elastic interface model that requires displacement continuity across the interface. The <em>classical general interface model</em> assumes that the interface displacement itself must coincide with the displacement average across the interface. The recently proposed <em>extended general interface model</em> defines the interface displacement <em>kinematically</em> via the weighted average of displacement across the interface. Here, we propose a <em>canonical interface model</em> based on a variationally consistent approach, which encompasses all previous interface models. We implement our model with the finite element method and illustrate its consequences through a series of numerical examples. Moreover, variationally consistent homogenization is employed to upscale an elastic composite with particles surrounded by a canonical interface and embedded in a matrix. The numerical results highlight the significance of the canonical interface model on the overall response of composites, at times leading to counter-intuitive behavior at the macroscale.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"440 ","pages":"Article 117925"},"PeriodicalIF":6.9,"publicationDate":"2025-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143687269","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":"Boundary settings for seismic dynamic analysis of rock masses using the nodal-based continuous-discontinuous deformation analysis method","authors":"Yang Xia ,&nbsp;Yongtao Yang ,&nbsp;Hong Zheng ,&nbsp;He Liu ,&nbsp;Shuilin Wang","doi":"10.1016/j.cma.2025.117941","DOIUrl":"10.1016/j.cma.2025.117941","url":null,"abstract":"<div><div>The nodal-based continuous-discontinuous deformation analysis method (NCDDAM) proposed by the authors has demonstrated its potential for dynamic analysis of rock masses with discontinuities. However, the existing boundary conditions applied in NCDDAM are not suitable for seismic dynamic analysis, as they can cause fictitious reflected waves. To further apply the NCDDAM for seismic dynamic analysis, this paper introduces five boundary conditions: viscous boundary, viscoelasticity boundary, seismic input boundary, free field boundary, and static-dynamic unified boundary. Several numerical examples are conduced to validate the enriched NCDDAM. The numerical results demonstrate the capacity of the enriched NCDDAM for seismic dynamic analysis of rock masses. The nonreflecting boundaries applied in NCDDAM can effectively absorb wave energy and avoid fictitious scattered waves, while the free field boundary applied in NCDDAM effectively simulates wave propagation in a semi-infinite domain. Based on the static-dynamic unified boundary, the seamless transition of boundary condition settings between the quasi-static and dynamic stages can be achieved. The entire evolution process of earthquake-induced disasters, including initiation, movement, run-out, and deposition can be effectively simulated within a unified framework using the enriched NCDDAM.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"440 ","pages":"Article 117941"},"PeriodicalIF":6.9,"publicationDate":"2025-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143686906","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}