Computer Methods in Applied Mechanics and Engineering最新文献

{"title":"Two-phase fluid deformable surfaces with constant enclosed volume and phase-dependent bending and Gaussian rigidity","authors":"Jan Magnus Sischka ,&nbsp;Axel Voigt","doi":"10.1016/j.cma.2025.118166","DOIUrl":"10.1016/j.cma.2025.118166","url":null,"abstract":"<div><div>We consider two-phase fluid deformable surface models with a constant enclosed volume. Such models consist of incompressible surface Navier–Stokes–Cahn–Hilliard-like equations with bending forces and a constraint on the enclosed volume. The highly nonlinear model accounts for the tight interplay between surface evolution, surface phase composition, surface curvature and surface hydrodynamics and allows to model biomembranes, or at least model systems of biomembranes, such as vesicles. We numerically explore the effect of hydrodynamics on bulging and furrow formation and study the effect of a phase-dependent bending and Gaussian bending rigidity on the dynamics and the equilibrium configuration. The numerical approach builds on a Taylor-Hood element for the surface Navier–Stokes part, a semi-implicit approach for the surface Cahn-Hilliard part, higher order surface parametrizations, appropriate approximations of the geometric quantities, mesh redistribution and an iterative approach to deal with the non-local constraint on the enclosed volume. We demonstrate convergence properties.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"445 ","pages":"Article 118166"},"PeriodicalIF":6.9,"publicationDate":"2025-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144634317","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 Two-scale High-order Damaged Elasticity Theory and Solution Procedure for Quasi-brittle Fracture","authors":"Cao Yuheng,&nbsp;Zhang Chunyu","doi":"10.1016/j.cma.2025.118206","DOIUrl":"10.1016/j.cma.2025.118206","url":null,"abstract":"<div><div>To rigorously capture the tight coupling between elastic deformation and damage initiation/propagation in quasi-brittle fracture processes, a two-scale damaged elasticity theory is proposed that accounts for the meso-scale inhomogeneity of both the strain and the damage fields. It formulates a degraded strain energy density to capture size effects and localized damage initiation and propagation through a homogenization operation. This approach takes a simplified and unified physics and offers a consistent treatment of higher-order deformation and damage, enabling natural incorporation of size effects on fracture strength. No additional regularization is needed to maintain damage localization. Structural deformation is solved using the principle of minimum potential energy, where the Augmented Lagrangian Method (ALM) reduces the order of gradient operators. All boundary conditions are free of high-order terms and can be applied in the conventional manner. Numerical investigations demonstrate the theory's capability to predict non-singular deformation at crack tips, accurately model size-dependent fracture in perforated brittle plates, and achieve mesh-independent failure predictions in benchmark problems.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"445 ","pages":"Article 118206"},"PeriodicalIF":6.9,"publicationDate":"2025-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144634315","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":"Simulations of ultrasonic guided wave scattering using the scaled boundary finite element method","authors":"Daniel Lozano ,&nbsp;Hauke Gravenkamp ,&nbsp;Carolin Birk","doi":"10.1016/j.cma.2025.118204","DOIUrl":"10.1016/j.cma.2025.118204","url":null,"abstract":"<div><div>This paper presents a numerical framework employing the Scaled Boundary Finite Element Method (SBFEM) for efficiently solving ultrasonic guided wave modal scattering problems and constructing scattering matrices (S-matrices). The framework integrates hierarchical octree meshing and an enhanced far field formulation. It incorporates boundary integrals, enabling an accurate representation of defect interactions with guided waves. Validation is performed using a benchmark test supported by an error estimation method based on energy balance. Two practical examples are used to showcase the simulation framework, where the scattering of guided waves with surface-breaking and subsurface cracks near rivet holes is studied.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"445 ","pages":"Article 118204"},"PeriodicalIF":6.9,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144632173","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":"Collaborative moving regression-based surrogate modeling framework for structural low cycle fatigue life reliability assessment","authors":"Xiao-Wei Dong ,&nbsp;Zhen-Ao Li ,&nbsp;Jia-Hao Liang ,&nbsp;Qing-Long Li ,&nbsp;Chun-Yan Zhu ,&nbsp;Ming Wang ,&nbsp;Wei-Kai Li","doi":"10.1016/j.cma.2025.118213","DOIUrl":"10.1016/j.cma.2025.118213","url":null,"abstract":"<div><div>To achieve low-cycle fatigue (LCF) life prediction and reliability assessment for mechanical structures, a collaborative moving regression-based surrogate modeling (CMR-SM) framework is proposed by fusing the collaborative moving regression (CMR) strategy, heuristic algorithm, adaptive hybrid surrogate modeling method, and matrix analysis theory. In this framework, the CMR strategy is developed from the decomposition-coordination (DC) method and moving least squares (MLS) technique to reduce model nonlinearity and acquire effective samples; the optimal radius for compact support region is determined through quadratic interpolation optimization (QIO); Matrix analysis theory is applied to construct vectors and cell arrays of unknown parameters, synchronously establishing the mathematical model. Under this concept, the CMR-based response surface method (CMR-RSM), CMR-based Kriging model (CMR-KM), CMR-based support vector machine (CMR-SVM), and CMR-based artificial neural network (CMR-ANN) are further developed. Considering the robustness of model, an adaptive weighting technique is employed to further develop the collaborative moving regression-based adaptive hybrid surrogate modeling (CMR-AHSM) method. The excellent modeling capabilities and simulation performance of the proposed method are validated through a numerical case (i.e., the probability analysis of a nested nonlinear function) and an engineering case (i.e., the LCF life reliability assessment of turbine blisk). The proposed method provides new insights for LCF life reliability assessment in engineering structures.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"445 ","pages":"Article 118213"},"PeriodicalIF":6.9,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144623390","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":"CuPINN: Optimizing PINNs through curvature minimization and residual landscape flattening","authors":"Raoof Zare Moayedi,&nbsp;Mostafa Abbaszadeh,&nbsp;Mehdi Dehghan","doi":"10.1016/j.cma.2025.118180","DOIUrl":"10.1016/j.cma.2025.118180","url":null,"abstract":"<div><div>Physics-Informed Neural Networks (PINNs) have gained recognition as a powerful framework for solving partial differential equations (PDEs) by incorporating the PDE residual directly into the neural network’s loss function. However, while effective in many cases, standard PINNs often struggle with accuracy. <em>Gradient-Enhanced PINNs (GPINNs)</em> were developed to address these issues by enforcing zero residual gradients, but they have not been able to sufficiently guide the learning process in many demanding physical applications. In this work, we introduce two novel method, RCuPINN, and CuPINN, which significantly improves both the accuracy and training efficiency of PINNs. These methods are built on the key observation that the residual over the entire domain can be viewed as a manifold in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msup></math></span>, where <span><math><mi>d</mi></math></span> is the dimensionality of the problem. Ideally, this manifold should exhibit zero value across the domain with minimal curvature in regions where the solution is smooth. By enforcing a smooth and flat residual manifold with zero curvature, we introduce a stronger inductive bias that promotes more accurate residual learning, backed by theoretical analysis. Furthermore, we demonstrate that minimizing the curvature inherently reduces the gradient, which further enhances the solution’s accuracy. To achieve this, we leverage Hutchinson Trace Estimation to compute the eigenvalues of the curvature, allowing us to directly minimize the curvature of the residual surface. This refined loss function leads to more efficient training and improved accuracy. Additionally, we combine our method with GPINNs to create hybrid approaches, RCuGPINN, CuGPINN. Extensive experiments on both linear and nonlinear PDEs demonstrate that our methods achieve residual and approximation errors on the order of <span><math><mrow><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math></span> compared to existing approaches, including GPINNs. This substantial reduction in error illustrates the superior accuracy and effectiveness of our methods.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"445 ","pages":"Article 118180"},"PeriodicalIF":6.9,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144623392","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":"Enhancing high-dimensional probabilistic model updating: A generic generative model-inspired framework with GAN-embedded implementation","authors":"Jiang Mo ,&nbsp;Wang-Ji Yan ,&nbsp;Ka-Veng Yuen ,&nbsp;Michael Beer","doi":"10.1016/j.cma.2025.118190","DOIUrl":"10.1016/j.cma.2025.118190","url":null,"abstract":"<div><div>Probabilistic model updating (PMU), which seeks to identify the probability distributions of model parameters by aligning model predictions with measured responses, is essential for ensuring the credibility of numerical models. However, PMU faces challenges like high computational costs from repeated solver calls and the curse of dimensionality in optimization. Driven by the intrinsic parallels between generative models and PMU, characterized by iterative processes aimed at minimizing disparities between generated and real data distributions, this study presents an innovative and generic PMU framework that emulates the core principles of generative models. Specifically, based on generative adversarial networks (GANs), the PMU-GAN is designed by integrating a probabilistic interpretable network as a generator and a learnable distance metric as a discriminator. By establishing this connection, the innovative approach offers compelling solutions for high-dimensional PMU, harnessing GANs’ strong fitting capacity, optimization prowess, and excellence in high-dimensional realms. The generator utilizes a Gaussian mixture model (GMM) for input distribution approximation and sampling, alongside a differentiable metamodel to expedite output sample generation in lieu of time-consuming solvers. Compared to conventional neural networks, the GMM simplifies and constrains the input distribution forms, facilitating improved convergence. By employing Gumbel-SoftMax and reparameterization tricks, the class probabilities and Gaussian component parameters unique to GMMs are embedded in the generator as trainable parameters, enabling gradient-based optimization and endowing the generator with interpretability. The discriminator, featuring an invertible network and maximum mean discrepancy, refines its ability to gauge distribution disparities through a learning process. Through adversarial training, both the generator’s generative power and the discriminator’s discernment capability are enhanced. The efficacy of the proposed method in high-dimensional PMU is substantiated through numerical and experimental demonstrations, showcasing its potential in advancing the field.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"445 ","pages":"Article 118190"},"PeriodicalIF":6.9,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144623388","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":"Co-design of magnetic soft robots with large deformation and contacts via material point method and topology optimization","authors":"Liwei Wang","doi":"10.1016/j.cma.2025.118205","DOIUrl":"10.1016/j.cma.2025.118205","url":null,"abstract":"<div><div>Magnetic soft robots embedded with hard magnetic particles enable untethered actuation via external magnetic fields, offering remote, rapid, and precise control, which is highly promising for biomedical applications. However, designing such systems is challenging due to the complex interplay of magneto-elastic dynamics, large deformation, solid contacts, time-varying stimuli, and posture-dependent loading. While these challenges are particularly prominent in magnetic soft robots, they are also fundamental and common to responsive materials in general. As a result, most existing research relies on heuristics and trial-and-error methods or focuses on the independent design of stimuli or structures under static conditions. We propose a topology optimization framework for magnetic soft robots that simultaneously designs structures, location-specific material magnetization, and time-varying magnetic stimuli, accounting for large deformations, dynamic motion, and solid contacts. This is achieved by integrating generalized topology optimization with the magneto-elastic material point method, which supports GPU-accelerated parallel simulations and automatic differentiation for sensitivity analysis. We applied this framework to design magnetic robots for various tasks, including multi-task shape morphing and locomotion, in both 2D and 3D. The method autonomously generates optimized robotic systems to achieve target behaviors without requiring human heuristics. Despite the nonlinear physics and large design space, it demonstrates high computational efficiency, completing all cases within minutes. While we focus on magnetic soft robots in this study, the proposed method can be readily extended to other co-design problems involving stimuli-responsive materials with large deformations and complex dynamics. The framework provides a computational foundation for the autonomous co-design of active soft materials in applications such as metasurfaces, drug delivery, and minimally invasive procedures.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"445 ","pages":"Article 118205"},"PeriodicalIF":6.9,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144623387","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":"Editorial: Generative Artificial Intelligence for Predictive Simulations and Decision-Making in Science and Engineering","authors":"Youssef Marzouk, Benjamin Peherstorfer","doi":"10.1016/j.cma.2025.118228","DOIUrl":"https://doi.org/10.1016/j.cma.2025.118228","url":null,"abstract":"","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"26 1","pages":""},"PeriodicalIF":7.2,"publicationDate":"2025-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144621920","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":"Modeling partially observed nonlinear dynamical systems and efficient data assimilation via discrete-time conditional Gaussian Koopman network","authors":"Chuanqi Chen ,&nbsp;Zhongrui Wang ,&nbsp;Nan Chen ,&nbsp;Jin-Long Wu","doi":"10.1016/j.cma.2025.118189","DOIUrl":"10.1016/j.cma.2025.118189","url":null,"abstract":"<div><div>A discrete-time conditional Gaussian Koopman network (CGKN) is developed in this work to learn surrogate models that can perform efficient state forecast and data assimilation (DA) for high-dimensional complex dynamical systems, e.g., systems governed by nonlinear partial differential equations (PDEs). Focusing on nonlinear partially observed systems that are common in many engineering and earth science applications, this work exploits Koopman embedding to discover a proper latent representation of the unobserved system states, such that the dynamics of the latent states are conditional linear, i.e., linear with the given observed system states. The modeled system of the observed and latent states then becomes a conditional Gaussian system, for which the posterior distribution of the latent states is Gaussian and can be efficiently evaluated via analytical formulae. The analytical formulae of DA facilitate the incorporation of DA performance into the learning process of the modeled system, which leads to a framework that unifies scientific machine learning (SciML) and data assimilation. The performance of discrete-time CGKN is demonstrated on several canonical problems governed by nonlinear PDEs with intermittency and turbulent features, including the viscous Burgers’ equation, the Kuramoto–Sivashinsky equation, and the 2-D Navier–Stokes equations, with which we show that the discrete-time CGKN framework achieves comparable performance as the state-of-the-art SciML methods in state forecast and provides efficient and accurate DA results. The discrete-time CGKN framework also serves as an example to illustrate unifying the development of SciML models and their other outer-loop applications such as design optimization, inverse problems, and optimal control.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"445 ","pages":"Article 118189"},"PeriodicalIF":6.9,"publicationDate":"2025-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144604211","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 new approach for topology optimization with design-following Neumann boundary conditions","authors":"Christos Kostopoulos ,&nbsp;Ameer Marzok ,&nbsp;Haim Waisman","doi":"10.1016/j.cma.2025.118122","DOIUrl":"10.1016/j.cma.2025.118122","url":null,"abstract":"<div><div>This work introduces a novel approach to tackle topology optimization problems where both the external load and stiffness matrix are boundary-dependent. The proposed algorithm is based on the concept of density gradient methods, a class of density-based approaches that do not require additional fields or parametric curves for the boundary recognition, unlike other methods in the literature. The core idea behind density gradient methods is that boundaries can be identified as regions in the design domain in which the solution exhibits significant gradients, transitioning from material-filled areas to voids. Building on this concept, the new algorithm offers significant advantages over existing density gradient methods. First, it achieves higher accuracy by solving boundary integrals directly, avoiding the transition to volume integrals commonly employed in other methods. Second, it is substantially more efficient due to two key factors: much of the computation occurs during preprocessing, and it avoids the need for fine meshes or frequent remeshing required for accurate volume integral solutions. These benefits are enabled by the distinct algorithmic approach and design choices of this method. The efficacy of the algorithm is demonstrated through two physical problems. The first involves heat conduction with convective boundary conditions, where both the external load and stiffness matrix are boundary-dependent. The second addresses warping function topology optimization, a challenging problem requiring both boundary detection and definition of the boundary line outwards direction. The proposed algorithm demonstrates excellent accuracy and efficiency in all case studies.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"445 ","pages":"Article 118122"},"PeriodicalIF":6.9,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144596670","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}