Computer Methods in Applied Mechanics and Engineering最新文献

{"title":"Real-time inference and extrapolation with Time-Conditioned UNet: Applications in hypersonic flows, incompressible flows, and global temperature forecasting","authors":"Oded Ovadia ,&nbsp;Vivek Oommen ,&nbsp;Adar Kahana ,&nbsp;Ahmad Peyvan ,&nbsp;Eli Turkel ,&nbsp;George Em Karniadakis","doi":"10.1016/j.cma.2025.117982","DOIUrl":"10.1016/j.cma.2025.117982","url":null,"abstract":"<div><div>Neural Operators are fast and accurate surrogates for nonlinear mappings between functional spaces within training domains. Extrapolation beyond the training domain remains a grand challenge across all application areas. We present Time-Conditioned UNet (TC-UNet) as an operator learning method to solve time-dependent PDEs continuously in time without any temporal discretization, including in extrapolation scenarios. TC-UNet incorporates the temporal evolution of the PDE into its architecture by combining a parameter conditioning approach with the attention mechanism from the Transformer architecture. After training, TC-UNet makes real-time inferences on an arbitrary temporal grid. We demonstrate its extrapolation capability on a climate problem by estimating the global temperature for several years and also for inviscid hypersonic flow around a double cone. We propose different training strategies involving temporal bundling and sub-sampling. We demonstrate performance improvements for several benchmarks, performing extrapolation for long time intervals and zero-shot super-resolution time.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"441 ","pages":"Article 117982"},"PeriodicalIF":6.9,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143834453","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-Informed Extreme Learning Machine (PIELM) for Stefan problems","authors":"Fei Ren ,&nbsp;Pei-Zhi Zhuang ,&nbsp;Xiaohui Chen ,&nbsp;Hai-Sui Yu ,&nbsp;He Yang","doi":"10.1016/j.cma.2025.118015","DOIUrl":"10.1016/j.cma.2025.118015","url":null,"abstract":"<div><div>Stefan problems describe heat transfer through a material undergoing phase change, and solving these problems poses a real challenge due to the existence of a time-dependent moving boundary at the phase change interface. We propose an efficient and reliable physics-informed extreme learning machine (PIELM) framework for solving Stefan problems, which is achieved by replacing deep neural networks in the widely used physics-informed neural network (PINN) with extreme learning machines (ELM). We use a dual-network structure to approximate the latent solution and the moving boundary by two separate ELM networks, and in each ELM we incorporate physical laws of governing equations as well as initial and boundary conditions. Then, determining ELM layer weights is transformed from minimising loss into solving a system of equations. These equations are nonlinear because of the moving boundary, and we tackle them using an iterative least-squares procedure. The feasibility and validity of the proposed PIELM framework are demonstrated by carrying out six numerical case studies. Compared to conventional PINN frameworks, it shows that our PIELM framework can significantly improve the accuracy and efficiency for solving Stefan problems, reducing relative <em>L</em>₂ errors from the orders of 10^–3∼10^–5 to 10^–6∼ 10^–8.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"441 ","pages":"Article 118015"},"PeriodicalIF":6.9,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143829214","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 wrinkling model for general hyperelastic materials based on tension field theory","authors":"H.M. Verhelst ,&nbsp;M. Möller ,&nbsp;J.H. Den Besten","doi":"10.1016/j.cma.2025.117955","DOIUrl":"10.1016/j.cma.2025.117955","url":null,"abstract":"<div><div>Wrinkling is the phenomenon of out-of-plane deformation patterns in thin walled structures, as a result of a local compressive (internal) loads in combination with a large membrane stiffness and a small but non-zero bending stiffness. Numerical modelling typically involves thin shell formulations. As the mesh resolution depends on the wrinkle wave lengths, the analysis can become computationally expensive for shorter ones. Implicitly modelling the wrinkles using a modified kinematic or constitutive relationship based on a taut, slack or wrinkled state derived from a so-called tension field, a simplification is introduced in order to reduce computational efforts. However, this model was restricted to linear elastic material models in previous works. Aiming to develop an implicit isogeometric wrinkling model for large strain and hyperelastic material applications, a modified deformation gradient has been assumed, which can be used for any strain energy density formulation. The model is an extension of a previously published model for linear elastic material behaviour and is generalised to other types of discretisation as well. The extension for hyperelastic materials requires the derivative of the material tensor, which can be computed numerically or derived analytically. The presented model relies on a combination of dynamic relaxation and a Newton–Raphson solver, because of divergence in early Newton–Raphson iterations as a result of a changing tension field, which is not included in the stress tensor variation. Using four benchmarks, the model performance is evaluated. Convergence with the expected order for Newton–Raphson iterations has been observed, provided a fixed tension field. The model accurately approximates the mean surface of a wrinkled membrane with a reduced number of degrees of freedom in comparison to a shell solution.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"441 ","pages":"Article 117955"},"PeriodicalIF":6.9,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143829215","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":"Mesh free Hamiltonian method for solid dynamics simulation","authors":"Jie Zhang ,&nbsp;Eric P. Fahrenthold","doi":"10.1016/j.cma.2025.117991","DOIUrl":"10.1016/j.cma.2025.117991","url":null,"abstract":"<div><div>A wide range of solid dynamics problems include a central focus on fracture, fragmentation, and thermomechanical failure processes difficult to accommodate in current continuum, particle, or mixed particle-continuum formulations. In recent research the authors have developed a new mesh-free method for solid dynamics simulation which addresses this class of problems. The method uses a nonholonomic Hamiltonian modeling technique to combine a continuum level description of large strain elastic–plastic deformation with a system level model incorporating discontinuous fracture and fragmentation processes. No partial differential equations are used. The method avoids the mesh distortion problems of Lagrangian finite element methods, the mass diffusion problems of Eulerian finite volume methods, and a range of complications associated with various particle based simulation algorithms. Application of the method shows good agreement with exact solutions in one dimensional test problems and good agreement with experimental results in three dimensional shock physics simulations incorporating fracture, fragmentation, and large strain elastic–plastic deformation.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"441 ","pages":"Article 117991"},"PeriodicalIF":6.9,"publicationDate":"2025-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143824125","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":"Computational multi-physics modeling of membranes in proton exchange membrane water electrolyzers","authors":"Alberto Antonini ,&nbsp;Yousef Heider ,&nbsp;Giovanna Xotta ,&nbsp;Valentina Salomoni ,&nbsp;Fadi Aldakheel","doi":"10.1016/j.cma.2025.117974","DOIUrl":"10.1016/j.cma.2025.117974","url":null,"abstract":"<div><div>The present work provides a modeling framework to capture the complex multi-physics <em>electro-chemical-hydro-mechanical</em> processes in membranes of multilayer Proton Exchange Membrane Water Electrolysis (PEMWE) cells. It relies on the Theory of Porous Media (TPM) to establish a continuum-based framework suitable for efficient simulation of the coupled interactions of porous multiphase materials. This macroscopic framework is capable of accurately representing the local interactions among the immiscible phases, including membrane deformation, water transport, nanopore pressure dynamics, and proton diffusion, all of which are essential for PEMWE functionality. Numerical simulations in two- and three-dimensional space are presented to verify the capabilities of the model and to address key numerical stability challenges of the strongly coupled problem. The numerical implementations are carried out using the open-access finite element package FEniCSx. The corresponding source codes are openly available at [ <span><span>https://doi.org/10.25835/5s3p3a8s</span><svg><path></path></svg></span>], allowing reproducibility by interested researchers.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"441 ","pages":"Article 117974"},"PeriodicalIF":6.9,"publicationDate":"2025-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143824124","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":"Patch based unbiased 3D frictional contact formulation for finite element algorithms","authors":"Indrajeet Sahu,&nbsp;Nik Petrinic","doi":"10.1016/j.cma.2025.117958","DOIUrl":"10.1016/j.cma.2025.117958","url":null,"abstract":"<div><div>A new truly unbiased frictional contact formulation exclusively leveraging the midplane-based segment-to-segment (STS) interaction with a predictor–corrector approach is presented. Unlike the traditional master–slave based dual pass approaches, this formulation only requires a single pass providing a computational advantage in comparison. This work details the development of a penalty-regularised frictional contact between discretised surfaces following an equivalent description in the continuum space. The relative motion between the contacting segments is studied through changes in the interacting convective coordinates in overlapping regions, thus ensuring an unbiased formulation without labelling surfaces as master and slave. Here, the stick–slip frictional states are enforced over interacting regions (patches) of all STS pairs instead of the node on segment pairs by utilising the return mapping algorithm. The formulation inherently maintains the traction equality on opposite surfaces of all contact pairs. The robustness of the formulation is demonstrated through several examples with varying contact conditions of stick–slip states and transition in static and dynamic problems including flat and curved surfaces, rolling effect, self-contact and impact.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"441 ","pages":"Article 117958"},"PeriodicalIF":6.9,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143814874","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":"Integral parameterization of volumetric domains via deep neural networks","authors":"Zheng Zhan ,&nbsp;Wenping Wang ,&nbsp;Falai Chen","doi":"10.1016/j.cma.2025.117988","DOIUrl":"10.1016/j.cma.2025.117988","url":null,"abstract":"<div><div>Isogeometric Analysis (IGA) is a promising technique that integrates geometric modeling with numerical analysis. An essential step in IGA is domain parameterization, which aims to establish a parametric representation for a given computational domain. Specifically, it involves defining a spline-based mapping from the standard parametric domain to the computational domain. Typically, domain parameterization is performed in two stages: identifying an appropriate boundary correspondence and then parameterizing the interior region. However, this separation of the parameterization process often leads to a degradation in the quality of the parameterization. To attain high-quality parameterization, it is essential to optimize both the boundary correspondence and the interior mapping simultaneously. This approach is referred to as integral parameterization. Previous research has introduced integral parameterization methods for planar domains using neural networks. The goal of the current paper is to extend the method to handle integral parameterization of volumetric domains. We utilize Multi-Layer Perceptrons (MLPs) to represent the inverse parameterization mappings, incorporating efficient distortion measures into the loss function. To ensure stable training and achieve accurate results, we employ several techniques, including a four-stage training procedure and the smooth cuboid approach. The performance of our method is evaluated on multiple volumetric domains, and experimental results demonstrate its superiority over existing state-of-the-art techniques.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"441 ","pages":"Article 117988"},"PeriodicalIF":6.9,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143814875","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":"Orientation-aware interaction-based deep material network in polycrystalline materials modeling","authors":"Ting-Ju Wei ,&nbsp;Tung-Huan Su ,&nbsp;Chuin-Shan Chen","doi":"10.1016/j.cma.2025.117977","DOIUrl":"10.1016/j.cma.2025.117977","url":null,"abstract":"<div><div>Multiscale simulations are indispensable for connecting microstructural features to the macroscopic behavior of polycrystalline materials, but their high computational demands limit their practicality. Deep material networks (DMNs) have been proposed as efficient surrogate models, yet they fall short of capturing texture evolution. To address this limitation, we propose the orientation-aware interaction-based deep material network (ODMN), which incorporates an orientation-aware mechanism and an interaction mechanism grounded in the Hill–Mandel principle. The orientation-aware mechanism learns the crystallographic textures, while the interaction mechanism captures stress-equilibrium directions among representative volume element (RVE) subregions, offering insight into internal microstructural mechanics. Notably, ODMN requires only linear elastic data for training yet generalizes effectively to complex nonlinear and anisotropic responses. Our results show that ODMN accurately predicts both mechanical responses and texture evolution under complex plastic deformation, thus expanding the applicability of DMNs to polycrystalline materials. By balancing computational efficiency with predictive fidelity, ODMN provides a robust framework for multiscale simulations of polycrystalline materials.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"441 ","pages":"Article 117977"},"PeriodicalIF":6.9,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143814873","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 hybrid discrete and continuum framework for multiscale modeling of granular media","authors":"Maytee Chantharayukhonthorn ,&nbsp;Peter Yichen Chen ,&nbsp;Yonghao Yue ,&nbsp;Eitan Grinspun ,&nbsp;Ken Kamrin","doi":"10.1016/j.cma.2025.117936","DOIUrl":"10.1016/j.cma.2025.117936","url":null,"abstract":"<div><div>This work provides key advancements to a nascent simulation approach (Yue et al., 2018; Chen et al., 2021), which hybridizes two common simulation methodologies: discrete element methods and continuum methods. Discrete element methods (DEM), commonly used in granular media simulation, model every single micro-constituent and are thus accurate; however, in light of the enormous number of particles frequently required, they scale poorly. By contrast, continuum methods can be faster by greatly reducing the degrees of freedom represented. However, they can lose accuracy due to constitutive modeling assumptions of system behavior. The hybrid method is a multiscale approach utilizing a discrete representation in regions where flow behavior is complex and a continuum representation in larger-scale regions where behavior is simpler. The method adaptively determines these subregions, and can homogenize discrete grains into continuum material points, enrich continuum regions into discrete grains, and then couple these systems in a thin hybrid zone. This study presents work on all components of the hybrid method to expand its accuracy and robustness, resolving several known problems that occur in the existing hybrid method. We first introduce new granular packing methods capable of generating ad hoc granular assemblies that can meet user-defined criteria, so as to better match the underlying continuum representation during enrichment. Second, we discuss new enrichment and homogenization operators that conserve mass and momentum while also preserving higher-order packing properties such as fabric. Finally, we discuss a higher-order hybrid zone coupling, which better represents the two disparate simulation methods at the grid level. With these updates to the hybrid method, we subsequently demonstrate the ability to accurately simulate large length- and time-scale granular systems in geometries of geomechanical and industrial relevance. The results of the hybrid method compare favorably to purely discrete simulations albeit with much faster computation times.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"441 ","pages":"Article 117936"},"PeriodicalIF":6.9,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143814877","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":"Efficient Bayesian inversion for simultaneous estimation of geometry and spatial field using the Karhunen-Loève expansion","authors":"Tatsuya Shibata ,&nbsp;Michael C. Koch ,&nbsp;Iason Papaioannou ,&nbsp;Kazunori Fujisawa","doi":"10.1016/j.cma.2025.117960","DOIUrl":"10.1016/j.cma.2025.117960","url":null,"abstract":"<div><div>Detection of abrupt spatial changes in physical properties representing unique geometric features such as buried objects, cavities, and fractures is an important problem in geophysics and many engineering disciplines. In this context, simultaneous spatial field and geometry estimation methods that explicitly parameterize the background spatial field and the geometry of the embedded anomalies are of great interest. This paper introduces an advanced inversion procedure for simultaneous estimation using the domain independence property of the Karhunen-Loève (K-L) expansion. Previous methods pursuing this strategy face significant computational challenges. The associated integral eigenvalue problem (IEVP) needs to be solved repeatedly on evolving domains, and the shape derivatives in gradient-based algorithms require costly computations of the Moore–Penrose inverse. Leveraging the domain independence property of the K-L expansion, the proposed method avoids both of these bottlenecks, and the IEVP is solved only once on a fixed bounding domain. Comparative studies demonstrate that our approach yields two orders of magnitude improvement in K-L expansion gradient computation time. Inversion studies on one-dimensional and two-dimensional seepage flow problems highlight the benefits of incorporating geometry parameters along with spatial field parameters. The proposed method captures abrupt changes in hydraulic conductivity with a lower number of parameters and provides accurate estimates of boundary and spatial-field uncertainties, outperforming spatial-field-only estimation methods.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"441 ","pages":"Article 117960"},"PeriodicalIF":6.9,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143814876","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}