Computer Methods in Applied Mechanics and Engineering最新文献

{"title":"A dual-energy physics-informed multi-material topology optimization method within the phase-field framework","authors":"Sijing Lai ,&nbsp;Jiachen Feng ,&nbsp;Zhixian Lv ,&nbsp;Junseok Kim ,&nbsp;Yibao Li","doi":"10.1016/j.cma.2025.118338","DOIUrl":"10.1016/j.cma.2025.118338","url":null,"abstract":"<div><div>In this paper, we propose a dual-energy physics-informed multi-material topology optimization method within the phase-field framework. The method employs a dual-network collaborative architecture, utilizing two fully connected networks incorporating Fourier transformations to approximate the displacement field and the multiphase field, respectively. This approach enables a fully physics-driven optimization process throughout the entire workflow. The displacement field is approximated via the deep energy method, using the principle of minimum potential energy as the driving mechanism. Within the phase-field framework, an energy functional is constructed that incorporates the classical Ginzburg-Landau free energy, elastic strain energy and volume fraction constraints. This functional serves as the loss function that couples the displacement and phase fields, promoting the balancing of mechanical performance, interface thickness, material volume fractions, and phase repulsion during network training. Thus it achieves a deep integration of multi-material physical information. The pretraining strategy effectively reduces convergence time and enhances optimization performance. Automatic differentiation replaces traditional sensitivity analysis, enhancing computational efficiency, while appropriate control of sampling points balances training cost and accuracy. Several numerical experiments validate the effectiveness of the proposed method.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"447 ","pages":"Article 118338"},"PeriodicalIF":7.3,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144922361","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 low-level teamwork hybrid model based swarm intelligent algorithm for engineering design optimization","authors":"Amanjot Kaur Lamba ,&nbsp;Rohit Salgotra ,&nbsp;Nitin Mittal","doi":"10.1016/j.cma.2025.118317","DOIUrl":"10.1016/j.cma.2025.118317","url":null,"abstract":"<div><div>We introduce a multi-algorithm hybrid strategy, named WIFN, to mitigate the poor performance of the naked mole-rat algorithm (NMRA). The proposed WIFN algorithm employs the best exploration and exploitation properties of existing algorithms, viz. weighted mean of vectors (INFO), whale optimization algorithm (WOA) and fission fusion optimization (FuFiO). These algorithms are integrated into the worker phase of the NMRA. A new stagnation phase is introduced in WIFN to minimize the effect of local optima stagnation. To add self-adaptivity, five new mutation/inertia weight strategies are added to the parameters of WIFN. To assess its performance, four data sets are used: classical benchmarks, CEC 2014, CEC 2017 and CEC 2019. An experimental study is carried out using i) five constrained engineering design problems and ii) 15 real-world constrained problems from the CEC 2020 benchmark dataset to analyze the applicability of WIFN for computationally expensive problems. In addition, WIFN is applied to multilevel image thresholding with type-II fuzzy sets. It is tested using a real image set that features different histogram distributions for three different threshold numbers. Experimental results suggest that WIFN perform significantly better than the existing state-of-the-art algorithms in terms of quality metrics, viz. mean squared error (MSE), peak signal-to-noise ratio (PSNR), and structural similarity index (SSIM). Wilcoxon’s ranksum and the Friedman test establish the superiority of WIFN statistically.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"447 ","pages":"Article 118317"},"PeriodicalIF":7.3,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144922358","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":"Adaptive physics-informed system modeling with control for nonlinear structural system estimation","authors":"Biqi Chen ,&nbsp;Chenyu Zhang ,&nbsp;Jun Zhang ,&nbsp;Ying Wang","doi":"10.1016/j.cma.2025.118330","DOIUrl":"10.1016/j.cma.2025.118330","url":null,"abstract":"<div><div>Accurately capturing the nonlinear dynamic behavior of structures remains a significant challenge in mechanics and engineering. Traditional physics-based models and data-driven approaches often struggle to simultaneously ensure model interpretability, noise robustness, and estimation optimality. To address this issue, this paper proposes an Adaptive Physics-Informed System Modeling with Control (APSMC) framework. By integrating Kalman filter-based state estimation with physics-constrained proximal gradient optimization, the framework adaptively updates time-varying state-space model parameters while processing real-time input–output data under white noise disturbances. Theoretically, this process is equivalent to real-time tracking of the Jacobian matrix of a nonlinear dynamical system. Within this framework, we leverage the theoretical foundation of stochastic subspace identification to demonstrate that, as observational data accumulates, the APSMC algorithm yields state-space model estimates that converge to the theoretically optimal solution. The effectiveness of the proposed framework is validated through numerical simulations of a Duffing oscillator and the seismic response of a frame structure, as well as experimental tests on a scaled bridge model and real wind turbine health monitoring data. Experimental results show that, under noisy conditions, APSMC successfully predicts 19 consecutive 10-second time series using only a single initial 10-second segment for model updating, achieving a minimum normalized mean square error (NMSE) of 0.398 %. Furthermore, APSMC achieves the best performance among classical time-domain algorithms on measured wind turbine acceleration data. These findings demonstrate that the APSMC framework not only offers superior online identification and denoising performance but also provides a reliable foundation for downstream applications such as structural health monitoring, real-time control, adaptive filtering, and system identification. An open-source Python implementation is available on <span><span>GitHub</span><svg><path></path></svg></span>.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"447 ","pages":"Article 118330"},"PeriodicalIF":7.3,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144922359","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":"Improving long-term autoregressive spatiotemporal predictions: A proof of concept with fluid dynamics","authors":"Hao Zhou ,&nbsp;Sibo Cheng","doi":"10.1016/j.cma.2025.118332","DOIUrl":"10.1016/j.cma.2025.118332","url":null,"abstract":"<div><div>Data-driven approaches have emerged as a powerful alternative to traditional numerical methods for forecasting physical systems, offering fast inference and reduced computational costs. However, for complex systems and those without prior knowledge, the accuracy of long-term predictions frequently deteriorates due to error accumulation. Existing solutions often adopt an autoregressive approach that unrolls multiple time steps during each training iteration; although effective for long-term forecasting, this method requires storing entire unrolling sequences in GPU memory, leading to high resource demands. Moreover, optimizing for long-term accuracy in autoregressive frameworks can compromise short-term performance. To address these challenges, we introduce the Stochastic PushForward (SPF) training framework in this paper. SPF preserves the one-step-ahead training paradigm while still enabling multi-step-ahead learning. It dynamically constructs a supplementary dataset from the model’s predictions and uses this dataset in combination with the original training data. By drawing inputs from both the ground truth and model-generated predictions through a stochastic acquisition strategy, SPF naturally balances short- and long-term predictive performance and further reduces overfitting and improves generalization. Furthermore, the training process is executed in a one-step-ahead manner, with multi-step-ahead predictions precomputed between epochs-thus eliminating the need to retain entire unrolling sequences in memory, thus keeping memory usage stable. We demonstrate the effectiveness of SPF on the Burgers’ equation and the Shallow Water benchmark. Experimental results demonstrated that SPF delivers superior long-term accuracy compared to autoregressive approaches while reducing memory consumption. This positions SPF as a promising solution for resource-constrained environments and complex physical simulations.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"447 ","pages":"Article 118332"},"PeriodicalIF":7.3,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144922360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Green’s function-based method for wave attenuation on random matrix-inclusion microstructures with local isotropy","authors":"Feihong Liu ,&nbsp;Andrea P. Argüelles ,&nbsp;Christian Peco","doi":"10.1016/j.cma.2025.118334","DOIUrl":"10.1016/j.cma.2025.118334","url":null,"abstract":"<div><div>A numerical Green’s function-based approach is developed for attenuation characterization in two-phase matrix-inclusion microstructures. This approach avoids the critical boundary enforcement in plane wave modeling and is extensively tested and compared to current analytical methodologies based on the First-Order Smoothing Approximation (FOSA). Assuming each phase is isotropic with constant density, we examine the effects of varying density and elasticity. When only elasticity differences are present, the numerical and analytical predictions show good agreement. However, the results demonstrate that the FOSA overestimates attenuation when both density and elasticity differences are introduced, leading to a divergence in high wavenumbers. The discrepancies observed in density-related terms under the FOSA underscore its limitations and point to the need for more refined analytical models in multiphase wave propagation.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"446 ","pages":"Article 118334"},"PeriodicalIF":7.3,"publicationDate":"2025-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144912281","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":"Nucleation and propagation of fracture in viscoelastic elastomers: A complete phase-field theory","authors":"Farhad Kamarei ,&nbsp;Evan Breedlove ,&nbsp;Oscar Lopez-Pamies","doi":"10.1016/j.cma.2025.118337","DOIUrl":"10.1016/j.cma.2025.118337","url":null,"abstract":"<div><div>This paper presents a macroscopic theory, alongside its numerical implementation, aimed at describing, explaining, and predicting the nucleation and propagation of fracture in viscoelastic materials subjected to quasistatic loading conditions. The focus is on polymers, in particular, on elastomers. To this end, the starting point of this work is devoted to summarizing the large body of experimental results on how elastomers deform, nucleate cracks, and propagate cracks when subjected to mechanical loads. When viewed collectively, the experiments make it plain that there are three basic ingredients that any attempt at a complete macroscopic theory of fracture in elastomers ought to account for: <em>i</em>) the viscoelasticity of the elastomer; <em>ii</em>) its strength; and <em>iii</em>) its fracture energy. A theory is then introduced that accounts for all these three basic ingredients by extending the phase-field theory initiated by Kumar, Francfort, and Lopez-Pamies (<em>J. Mech. Phys. Solids</em> 112 (2018), 523–551) for elastic brittle materials to seamlessly incorporate viscous energy dissipation by deformation, a generalized strength surface that is a hypersurface in stress-deformation space (and not just in stress space as for elastic brittle materials), and the pertinent Griffith criticality condition for materials that dissipate energy not just by the creation of surface but also by deformation, in this case, by viscous deformation (Shrimali and Lopez-Pamies (2023) <em>Extreme Mech. Lett.</em> 58, 101944). From an applications point of view, the proposed theory amounts to solving an initial-boundary-value problem comprised of two nonlinear PDEs coupled with a nonlinear ODE for the deformation field <span><math><mrow><mi>y</mi><mo>(</mo><mi>X</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow></math></span>, a tensorial internal variable <span><math><mrow><msup><mrow><mi>C</mi></mrow><mi>v</mi></msup><mrow><mo>(</mo><mi>X</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span>, and the phase field <span><math><mrow><mi>z</mi><mo>(</mo><mi>X</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow></math></span>. A robust scheme is presented to generate solutions for these equations that makes use of a non-conforming Crouzeix-Raviart finite-element discretization of space and a high-order accurate explicit Runge-Kutta finite-difference discretization of time. To illustrate the descriptive and predictive capabilities of the theory, the last part of this paper presents simulations of prototypical experiments dealing with nucleation of fracture in the bulk, nucleation of fracture from a pre-existing crack, and propagation of fracture in different types of elastomers under various types of loading conditions.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"446 ","pages":"Article 118337"},"PeriodicalIF":7.3,"publicationDate":"2025-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144912326","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-field proper orthogonal decomposition for nonlinear model reduction via a Hellinger-Reissner variational formulation","authors":"Wenxiang Zhou ,&nbsp;Kai Luo ,&nbsp;Qiang Tian ,&nbsp;Haiyan Hu","doi":"10.1016/j.cma.2025.118325","DOIUrl":"10.1016/j.cma.2025.118325","url":null,"abstract":"<div><div>The proper orthogonal decomposition (POD) enables effective reduced-order modeling of geometrically nonlinear structures through low-dimensional subspace projection. The conventional POD-based methods construct the reduced-order model solely from the reduced-order bases of global displacement field, leading to the high-order internal force vector and stiffness tensor of reduced coordinates. In this study, the method of a two-field POD is proposed with the introduction of both displacement and stress bases. First, the previous POD-based model reduction of nonlinear structures is reviewed, including the Galerkin projection-based reduction and the stiffness invariants-based reduction. Then, the two-field POD-based reduction is constructed via the Hellinger-Reissner variational formulation so that the reduced-order dynamics equations with stiffness invariants are deduced from the displacement and stress bases. The trade-off of computational cost between the reduced inertial forces and the reduced internal forces is balanced and the computational complexity of stiffness invariants is reduced from a quartic order to a cubic order. Three numerical examples are presented to verify the model reduction for geometrically nonlinear dynamics, including the free swing of a flexible pendulum, the large deformation of a continuum arm and the vibration of an aircraft wing skeleton. The proposed reduced-order model exhibits both high efficiency and high accuracy, outperforming typical reduction approaches.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"446 ","pages":"Article 118325"},"PeriodicalIF":7.3,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144908976","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":"Nitsche’s serendipity virtual element method for the eigenvalue problem","authors":"Jian Meng ,&nbsp;Xu Qian ,&nbsp;Fang Su ,&nbsp;Bing-Bing Xu","doi":"10.1016/j.cma.2025.118336","DOIUrl":"10.1016/j.cma.2025.118336","url":null,"abstract":"<div><div>In this paper, we study the Nitsche’s extended serendipity virtual element method for the eigenvalue problem in two and three dimensions. We start from the introduction of two- and three-dimensional serendipity virtual element spaces, in which the serendipity technique helps us drop all internal-to-face and internal-to-element degrees of freedom with the suitable projection operators fitting into virtual element spaces. Meanwhile, we give the Nitsche’s extended serendipity virtual element scheme of the eigenvalue problem. At the next stage, we prove the spectral approximation and the optimal error estimates of the proposed numerical method. By using the standard interpolation and polynomial approximation properties, we prove the <span><math><msup><mi>H</mi><mn>1</mn></msup></math></span>-norm error bound of the associated source problem. To consider the <span><math><msup><mi>L</mi><mn>2</mn></msup></math></span>-norm error bound, the Ritz-Volterra projection based on the formulation of Nitsche’s virtual element bilinear form is defined. Then we rigorously analyze its approximation properties. After that, we build the <span><math><msup><mi>L</mi><mn>2</mn></msup></math></span> error estimate of the associated source problem. In the main theorems, we prove the error estimates of eigenfunctions and eigenvalues obtained by the Nitsche’s extended serendipity virtual element method. At the final stage, we extend the Nitsche’s idea to arbitrary curved domains by modifying the virtual element scheme with Taylor expansion terms. Numerical experiments confirm the theoretical results, using the Nitsche’s serendipity virtual element method to solve the Laplacian and Shrödinger eigenvalue problems on plane and curved domains.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"446 ","pages":"Article 118336"},"PeriodicalIF":7.3,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144908719","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 robust and efficient adaptive NURBS contact enrichment technique","authors":"Sumit Kumar Das,&nbsp;Sachin Singh Gautam","doi":"10.1016/j.cma.2025.118313","DOIUrl":"10.1016/j.cma.2025.118313","url":null,"abstract":"<div><div>A new contact enrichment technique is proposed to improve accuracy and efficiency in contact simulations. While traditional finite element analysis (FEA) is commonly used, it can lead to geometric approximation errors and become computationally expensive when high accuracy is required, especially in contact problems. Isogeometric analysis (IGA) addresses these issues by providing exact geometric representation and smoother solution fields using spline-based basis functions, such as non-uniform rational B-splines (NURBS). Most existing NURBS-based contact enrichment techniques apply uniform refinement across the entire contact surface, regardless of the evolving nature of the actual contact zone under external loading. The proposed <em>adaptive NURBS contact enrichment</em> technique addresses this limitation by adaptively refining only the actual contact zone, based on real-time contact surface detection. This targeted refinement significantly improves the accuracy of the contact results while reducing unnecessary computations. Numerical experiments demonstrate that the proposed technique achieves higher accuracy and efficiency than standard uniform contact enrichment techniques. Even lower-order adaptively enriched contact elements outperform higher-order uniformly enriched contact elements, with further improvements observed when using higher-order adaptively enriched contact elements.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"446 ","pages":"Article 118313"},"PeriodicalIF":7.3,"publicationDate":"2025-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144908763","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":"Full-scale isogeometric topology optimization of freeform fiber-reinforced composite shells","authors":"Mingzhe Huang ,&nbsp;Mi Xiao ,&nbsp;Yingjun Wang ,&nbsp;Xiaowei Deng ,&nbsp;Liang Gao","doi":"10.1016/j.cma.2025.118320","DOIUrl":"10.1016/j.cma.2025.118320","url":null,"abstract":"<div><div>This paper proposes a full-scale isogeometric topology optimization (ITO) method based on Bézier extraction for design of freeform fiber-reinforced composite (FRC) shells. In this method, freeform shells are modeling by multiple NURBS patches, where a penalty method is introduced to enhance displacement and rotation continuity at the coupling interfaces between multiple NURBS patches. A multi-patch isogeometric Kirchhoff–Love shell model based on Bézier extraction is established for modeling and analysis of freeform FRC shell structures with high efficiency and precision. A multi-material topology optimization framework is adopted to simultaneously optimize the topology of the matrix material, the morphology and path of the fiber, where two sets of design variables are set at control points to describe the topology of composite and fiber materials, respectively. In full-scale ITO, a multi-material constraint strategy with a global volume constraint of the composite material and a local volume constraint of the fiber material is developed to promote the generation of slender, continuous and uniformly distributed fiber structure in the matrix material. Several numerical examples of compliance minimization are provided to validate the effectiveness of the proposed method. The optimized results indicate that the proposed method has a great design freedom and can obtain FRC shells with continuous fiber path on freeform surfaces.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"446 ","pages":"Article 118320"},"PeriodicalIF":7.3,"publicationDate":"2025-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144903872","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}