Computer Methods in Applied Mechanics and Engineering最新文献_第8页

S-PINN: Stabilized physics-informed neural networks for alleviating barriers between multi-level co-optimization S-PINN：稳定的物理信息神经网络，用于减轻多层次协同优化之间的障碍

IF 7.3 1区工程技术

Computer Methods in Applied Mechanics and Engineering Pub Date : 2025-09-11 DOI: 10.1016/j.cma.2025.118348

Tengmao Yang , Zhihao Qian , Nianzhi Hang , Moubin Liu

{"title":"S-PINN: Stabilized physics-informed neural networks for alleviating barriers between multi-level co-optimization","authors":"Tengmao Yang , Zhihao Qian , Nianzhi Hang , Moubin Liu","doi":"10.1016/j.cma.2025.118348","DOIUrl":"10.1016/j.cma.2025.118348","url":null,"abstract":"<div><div>Physics-informed neural networks (PINNs) have rapidly evolved since their robust capabilities of integrating physical laws into data-driven models. However, the multi-level co-optimization mechanism hidden in the collocation-type loss function in PINNs leads to conflicts between data and physical equations, as well as conflicts among pointwise residuals, which results in poor stability and conservation. In this paper, a stabilized physics-informed neural network (S-PINN) framework is proposed to alleviate these limitations. First, S-PINN incorporates local domains around collocation points for evaluating residuals of conserved quantities. These domains can be flexibly established by creating a square centered on the collocation point of the original PINN, without constructing any mesh with topological relations. During online training, S-PINN mitigates conflicts in the multi-level co-optimization by minimizing a novel loss function based on the cumulative residuals of conserved quantities in all subdomains, significantly enhancing conservation. Finally, the novel approach is applied to predict the dynamic characteristics of incompressible fluid problems, with benchmarks including the pressure Poisson equation of fluid, Burgers' equation, heat diffusion equation, and the Navier-Stokes equations. Results demonstrate notable advancements in both the conservation and accuracy of the S-PINN. While traditional PINN lays a solid foundation for model interpretability and integration of physical laws, the newly proposed S-PINN exhibits improved performances in multiples aspects compared to PINN. These improvements promote extensive applicability in solving partial differential equations integrated with observational data, which is crucial for the application of complex dynamic systems.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"447 ","pages":"Article 118348"},"PeriodicalIF":7.3,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145050056","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}

引用次数: 0

Consistent pressure formulation of the Stokes problem and approximation thereof 斯托克斯问题的一致压力公式及其近似

IF 7.3 1区工程技术

Computer Methods in Applied Mechanics and Engineering Pub Date : 2025-09-10 DOI: 10.1016/j.cma.2025.118333

Melvin Creff, Jean-Luc Guermond

引用次数: 0

Provably third-order energy stable adaptive algorithm for modeling square pattern in phase field crystal 可证明的三阶能量稳定自适应相场晶体方图建模算法

IF 7.3 1区工程技术

Computer Methods in Applied Mechanics and Engineering Pub Date : 2025-09-10 DOI: 10.1016/j.cma.2025.118361

Ren-jun Qi, Xuan Zhao

{"title":"Provably third-order energy stable adaptive algorithm for modeling square pattern in phase field crystal","authors":"Ren-jun Qi, Xuan Zhao","doi":"10.1016/j.cma.2025.118361","DOIUrl":"10.1016/j.cma.2025.118361","url":null,"abstract":"<div><div>Square pattern emerges widely in crystallography, ranging from soft matters to thermal convection in fluid dynamics. The square phase field crystal equation models such pattern formation on atomic length and diffusive time scales. The governing equation, derived from a conserved gradient flow of a free energy, involves sixth-order spatial derivatives and Laplacian-gradient type nonlinear term, which result in severe stability restriction on the time stepsizes and difficulty in theoretical analysis. In this paper, we propose a novel unconditionally energy stable, third-order adaptive BDF scheme. The convex-splitting and a multistep stabilization are leveraged to maintain energy stable with arbitrary time stepsizes, and the adaptive time-stepping control based on evolution rate is applied to efficiently obtain high-resolution results. We strictly prove optimal error estimate in the variable-step setting under a mild step ratio constraint by enhancing the discrete kernel framework proposed recently. Numerical tests in 2D/3D demonstrate the square pattern evolution in crystallization process from random or supercooled liquid initial states over a long time. The adaptive algorithm reduces computation time by 95 % while capturing details of phases, confirming the effectiveness of our method. This is the first systematic work on adaptive high-order structure-preserving method for square phase field crystal.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"447 ","pages":"Article 118361"},"PeriodicalIF":7.3,"publicationDate":"2025-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145050055","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}

引用次数: 0

Model order reduction of hæmodynamics by space–time reduced basis and reduced fluid–structure interaction h - æ动力学的时空约简基和流固耦合的模型降阶

IF 7.3 1区工程技术

Computer Methods in Applied Mechanics and Engineering Pub Date : 2025-09-09 DOI: 10.1016/j.cma.2025.118347

Riccardo Tenderini, Simone Deparis

{"title":"Model order reduction of hæmodynamics by space–time reduced basis and reduced fluid–structure interaction","authors":"Riccardo Tenderini, Simone Deparis","doi":"10.1016/j.cma.2025.118347","DOIUrl":"10.1016/j.cma.2025.118347","url":null,"abstract":"<div><div>In this work, we apply the space–time Galerkin reduced basis (ST–GRB) method to a reduced fluid–structure interaction model, for the numerical simulation of hæmodynamics in arteries. In essence, ST–GRB extends the classical reduced basis (RB) method, exploiting a data–driven low–dimensional linear encoding of the temporal dynamics to further cut the computational costs. The current investigation brings forth two key enhancements, compared to previous works on the topic. On the one side, we model blood flow through the Navier–Stokes equations, hence accounting for convection. In this regard, we implement a hyper–reduction scheme, based on approximate space–time reduced affine decompositions, to deal with nonlinearities effectively. On the other side, we move beyond the constraint of modelling blood vessels as rigid structures, acknowledging the importance of elasticity for the accurate simulation of complex blood flow patterns. To limit computational complexity, we adopt the Coupled Momentum model, incorporating the effect of wall compliance in the fluid’s equations through a generalized Robin boundary condition. In particular, we propose an efficient strategy for handling the spatio–temporal projection of the structural displacement, which ultimately configures as a by–product. The performances of ST–GRB are assessed in three different numerical experiments. The results confirm that the proposed approach can outperform the classical RB method, yielding precise approximations of high–fidelity solutions at more convenient costs. However, the computational gains of ST–GRB vanish if the number of retained temporal modes is too large, which occurs either when complex dynamics arise or if very precise solutions are sought.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"447 ","pages":"Article 118347"},"PeriodicalIF":7.3,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145020410","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}

引用次数: 0

Sharp-PINNs: Staggered hard-constrained physics-informed neural networks for phase field modelling of corrosion Sharp-PINNs：用于腐蚀相场建模的交错硬约束物理信息神经网络

IF 7.3 1区工程技术

Computer Methods in Applied Mechanics and Engineering Pub Date : 2025-09-08 DOI: 10.1016/j.cma.2025.118346

Nanxi Chen , Chuanjie Cui , Rujin Ma , Airong Chen , Sifan Wang

{"title":"Sharp-PINNs: Staggered hard-constrained physics-informed neural networks for phase field modelling of corrosion","authors":"Nanxi Chen , Chuanjie Cui , Rujin Ma , Airong Chen , Sifan Wang","doi":"10.1016/j.cma.2025.118346","DOIUrl":"10.1016/j.cma.2025.118346","url":null,"abstract":"<div><div>Physics-informed neural networks have shown significant potential in solving partial differential equations (PDEs) across diverse scientific fields. However, their performance often deteriorates when addressing PDEs with intricate and strongly coupled solutions. In this work, we present a novel Sharp-PINN framework to tackle complex phase field corrosion problems. Instead of minimizing all governing PDE residuals simultaneously, the Sharp-PINNs introduce a staggered training scheme that alternately minimizes the residuals of Allen-Cahn and Cahn-Hilliard equations, which govern the corrosion system. To further enhance its efficiency and accuracy, we design an advanced neural network architecture that integrates random Fourier features as coordinate embeddings, employs a modified multi-layer perceptron as the primary backbone, and enforces hard constraints in the output layer. This framework is benchmarked through simulations of corrosion problems with multiple pits, where the staggered training scheme and network architecture significantly improve both the efficiency and accuracy of PINNs. Moreover, in three-dimensional cases, our approach is 5–10 times faster than traditional finite element methods while maintaining competitive accuracy, demonstrating its potential for real-world engineering applications in corrosion prediction.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"447 ","pages":"Article 118346"},"PeriodicalIF":7.3,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145020409","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}

引用次数: 0

A curvilinear surface ALE formulation for self-evolving Navier-Stokes manifolds – stabilized finite element formulation 自演化Navier-Stokes流形的曲线曲面ALE公式-稳定有限元公式

IF 7.3 1区工程技术

Computer Methods in Applied Mechanics and Engineering Pub Date : 2025-09-08 DOI: 10.1016/j.cma.2025.118331

Roger A. Sauer

{"title":"A curvilinear surface ALE formulation for self-evolving Navier-Stokes manifolds – stabilized finite element formulation","authors":"Roger A. Sauer","doi":"10.1016/j.cma.2025.118331","DOIUrl":"10.1016/j.cma.2025.118331","url":null,"abstract":"<div><div>This work presents a stabilized finite element formulation of the arbitrary Lagrangian-Eulerian (ALE) surface theory for Navier-Stokes flow on self-evolving manifolds developed in Sauer [1]. The formulation is physically frame-invariant, applicable to large deformations, and relevant to fluidic surfaces such as soap films, capillary menisci and lipid membranes, which are complex and inherently unstable physical systems. It is applied here to area-incompressible surface flows using a stabilized pressure-velocity (or surface tension-velocity) formulation based on quadratic finite elements and implicit time integration. The unknown ALE mesh motion is determined by membrane elasticity such that the in-plane mesh motion is stabilized without affecting the physical behavior of the system. The resulting three-field system is monolithically coupled, and fully linearized within the Newton-Rhapson solution method. The new formulation is demonstrated on several challenging examples including shear flow on self-evolving surfaces and inflating soap bubbles with partial inflow on evolving boundaries. Optimal convergence rates are obtained in all cases. Particularly advantageous are <span><math><msup><mi>C</mi><mn>1</mn></msup></math></span>-continuous surface discretizations, for example based on NURBS.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"447 ","pages":"Article 118331"},"PeriodicalIF":7.3,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145020408","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}

引用次数: 0

System reliability-based design optimization of structures using non-probabilistic ellipsoidal convex model 基于非概率椭球体凸模型的结构系统可靠性优化设计

IF 7.2 1区工程技术

Computer Methods in Applied Mechanics and Engineering Pub Date : 2025-09-07 DOI: 10.1016/j.cma.2025.118354

Zirui Liu, Jinglei Gong, Yongxiang Mu, Xiaojun Wang

{"title":"System reliability-based design optimization of structures using non-probabilistic ellipsoidal convex model","authors":"Zirui Liu, Jinglei Gong, Yongxiang Mu, Xiaojun Wang","doi":"10.1016/j.cma.2025.118354","DOIUrl":"https://doi.org/10.1016/j.cma.2025.118354","url":null,"abstract":"This paper proposes a system non-probabilistic reliability-based design optimization (SNRBDO) framework for engineering structural systems. In view of the limitations of traditional probabilistic methods due to insufficient uncertainty information, the ellipsoidal convex model is used to quantify the uncertainty while considering the parameter correlation. The non-probabilistic credible set uncertainty method is employed to quantify the ellipsoidal uncertainty domain of uncertain parameters. A system non-probabilistic reliability index, defined as the volume ratio of safe regions to uncertainty domains, is introduced to evaluate structural safety under multiple failure modes. To enhance computational efficiency, Kriging surrogate model is utilized to replace the finite element analysis during optimization, and a localized sampling strategy is developed to refine accuracy near critical design points. The method is validated through a mathematical example and two engineering applications. The results demonstrate significant improvements in computational efficiency and design precision compared to conventional methods.","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"86 1","pages":""},"PeriodicalIF":7.2,"publicationDate":"2025-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145059446","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}

引用次数: 0

A locking free multiscale method for linear elasticity in stress-displacement formulation with high contrast coefficients 高对比系数应力-位移方程线性弹性的无锁多尺度方法

IF 7.3 1区工程技术

Computer Methods in Applied Mechanics and Engineering Pub Date : 2025-09-07 DOI: 10.1016/j.cma.2025.118342

Eric T. Chung, Changqing Ye, Xiang Zhong

{"title":"A locking free multiscale method for linear elasticity in stress-displacement formulation with high contrast coefficients","authors":"Eric T. Chung, Changqing Ye, Xiang Zhong","doi":"10.1016/j.cma.2025.118342","DOIUrl":"10.1016/j.cma.2025.118342","url":null,"abstract":"<div><div>Achieving strongly symmetric stress approximations for linear elasticity problems in high-contrast media poses a significant computational challenge. Conventional methods often struggle with prohibitively high computational costs due to excessive degrees of freedom, limiting their practical applicability. To overcome this challenge, we introduce an efficient multiscale model reduction method and a computationally inexpensive coarse-grid simulation technique for linear elasticity equations in highly heterogeneous, high-contrast media. We first utilize a stable stress-displacement mixed finite element method to discretize the linear elasticity problem and then present the construction of multiscale basis functions for the displacement and the stress. The mixed formulation offers several advantages such as direct stress computation without post-processing, local momentum conservation (ensuring physical consistency), and robustness against locking effects, even for nearly incompressible materials. Theoretical analysis confirms that our method is inf-sup stable and locking-free, with first-order convergence relative to the coarse mesh size. Notably, the convergence remains independent of contrast ratios as enlarging oversampling regions. Numerical experiments validate the method’s effectiveness, demonstrating its superior performance even under extreme contrast conditions.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"447 ","pages":"Article 118342"},"PeriodicalIF":7.3,"publicationDate":"2025-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145011156","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}

引用次数: 0

Peridynamic correspondence model for nearly-incompressible finite elasticity 近不可压缩有限弹性的周动力对应模型

IF 7.3 1区工程技术

Computer Methods in Applied Mechanics and Engineering Pub Date : 2025-09-06 DOI: 10.1016/j.cma.2025.118350

Francesco Scabbia , Vito Diana , Francesca Fantoni , Mirco Zaccariotto , Ugo Galvanetto

{"title":"Peridynamic correspondence model for nearly-incompressible finite elasticity","authors":"Francesco Scabbia , Vito Diana , Francesca Fantoni , Mirco Zaccariotto , Ugo Galvanetto","doi":"10.1016/j.cma.2025.118350","DOIUrl":"10.1016/j.cma.2025.118350","url":null,"abstract":"<div><div>This paper presents a correspondence model for use with peridynamic states in the context of nearly incompressible finite elasticity. An isochoric/volumetric decomposition is adopted, enabling the derivation of the peridynamic force state from a purely spherical, pointwise non-local deformation gradient and a deviatoric, bond-level non-local deformation gradient. This approach leads to a stable one-field, state-based peridynamic formulation that is free from zero-energy modes and capable of accurately capturing the mechanical behavior of elastic materials under large deformations, including those with low or negligible compressibility, typical of unfilled elastomers and isotropic soft biological tissues. Notably, the proposed correspondence model, based on a selective bond-associated deformation gradient, avoids the artificial stiffening commonly observed in standard displacement-based formulations near the incompressible limit. Moreover, its performance is shown to be independent of the specific compressibility ratio assumed in the hyperelastic constitutive law. The model has been successfully validated using classical polynomial strain energy functions through a series of illustrative examples involving both homogeneous and inhomogeneous finite deformations in isotropic hyperelastic solids.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"447 ","pages":"Article 118350"},"PeriodicalIF":7.3,"publicationDate":"2025-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145003618","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}

引用次数: 0

A robust-weighted hybrid nonlinear regression for reliability based topology optimization with multi-source uncertainties 基于可靠性的多源不确定性拓扑优化鲁棒加权混合非线性回归

IF 7.3 1区工程技术

Computer Methods in Applied Mechanics and Engineering Pub Date : 2025-09-05 DOI: 10.1016/j.cma.2025.118360

Shiyuan Yang , Debiao Meng , Mahmoud Alfouneh , Behrooz Keshtegar , Shun-Peng Zhu

{"title":"A robust-weighted hybrid nonlinear regression for reliability based topology optimization with multi-source uncertainties","authors":"Shiyuan Yang , Debiao Meng , Mahmoud Alfouneh , Behrooz Keshtegar , Shun-Peng Zhu","doi":"10.1016/j.cma.2025.118360","DOIUrl":"10.1016/j.cma.2025.118360","url":null,"abstract":"<div><div>The computational burden in topology optimization (TO) under probabilistic constraints is a major challenge for both topology optimization and reliability analysis methods. The machine learning method can be applied for controlling the computational burden of inverse TO method for approximating the optimal volume fraction (Vf) which is related to max/min a probabilistic constraint. In this current work a hybrid nonlinear modelling training method is proposed by using the exponential nonlinear function and improved harmony search optimization for approximating the optimal Vf applied in reliability-based TO (RBTO) problems. For improving the accuracy predictions of nonlinear model a weighted training scheme is proposed given based on absolute bi-linear loss function applied as robust learning format. The applied weights given from near optimal constraints computed by Vf and loss function is determined based on two absolute function with different slop as 1 and 0.1. The proposed learning approach for nonlinear function is compared with the results of TO-based bisection under multi-source uncertainties for both accuracy and computational burden through four engineering problems. Results indicated that the proposed robust-weighted hybrid learning method computed by hybrid nonlinear regression and harmony search optimization is strongly improved the computational burden for evaluating the optimal Vf in TO and RBTO problems compared to TO and RBTO using bisection while it is more accurate as the nonlinear regression.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"447 ","pages":"Article 118360"},"PeriodicalIF":7.3,"publicationDate":"2025-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144997035","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}

引用次数: 0