Computer Methods in Applied Mechanics and Engineering最新文献

英文中文

Adaptive finite element interpolated neural networks

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-02-08 DOI: 10.1016/j.cma.2025.117806

Santiago Badia , Wei Li , Alberto F. Martín

The use of neural networks to approximate partial differential equations (PDEs) has gained significant attention in recent years. However, the approximation of PDEs with localised phenomena, e.g., sharp gradients and singularities, remains a challenge, due to ill-defined cost functions in terms of pointwise residual sampling or poor numerical integration. In this work, we introduce

h

-adaptive finite element interpolated neural networks. The method relies on the interpolation of a neural network onto a finite element space that is gradually adapted to the solution during the training process to equidistribute a posteriori error indicator. The use of adaptive interpolation is essential in preserving the non-linear approximation capabilities of the neural networks to effectively tackle problems with localised features. The training relies on a gradient-based optimisation of a loss function based on the (dual) norm of the finite element residual of the interpolated neural network. Automatic mesh adaptation (i.e., refinement and coarsening) is performed based on a posteriori error indicators till a certain level of accuracy is reached. The proposed methodology can be applied to indefinite and nonsymmetric problems. We carry out a detailed numerical analysis of the scheme and prove several a priori error estimates, depending on the expressiveness of the neural network compared to the interpolation mesh. Our numerical experiments confirm the effectiveness of the method in capturing sharp gradients and singularities for forward and inverse PDE problems, both in 2D and 3D scenarios. We also show that the proposed preconditioning strategy (i.e., using a dual residual norm of the residual as a cost function) enhances training robustness and accelerates convergence.

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引用次数: 0

Efficient global adaptive Kriging approximation method in terms of moment for reliability-based design optimization

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-02-08 DOI: 10.1016/j.cma.2025.117813

Meide Yang, Hongfei Zhang, Dequan Zhang, Fang Wang, Xu Han

Reliability-based design optimization (RBDO) methods based on the most probable point (MPP) have been extensively studied and applied to practical engineering problems. Nevertheless, these methods are not viable when MPP is not straightforward to be searched or multiple MPPs may exhibit. Fortunately, moment method can circumvent the computation of partial derivatives for performance function and iteration to search for MPPs, which is considered as an effective way to solve such problem. However, direct application of moment method to RBDO often incurs high computational cost, which greatly hinders its practicability. To enhance the computational efficiency of the moment-based RBDO methods, an efficient global adaptive Kriging approximation method for RBDO is proposed in this study. The strategy is that a new initial design of experiment scheme according to Gaussian-Hermite integration nodes is innovatively proposed. On this basis, a feasibility check criterion for probabilistic constraints and a selection strategy for candidate samples are respectively proposed to efficiently establish Kriging models of performance functions in the probabilistic constraints. In addition, an enhanced univariate dimension-reduction method with high robustness is presented to calculate the first four-order statistical moments of the above constructed Kriging models. Consequently, the failure probability of each probabilistic constraint can be calculated by Edgeworth series. Finally, a deterministic optimization algorithm is executed to derive the optimal solution. Three numerical examples and two structural examples are exemplified to demonstrate the effectiveness of the proposed moment-based method compared to prevailing MPP-based and Kriging-based RBDO methods.

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引用次数: 0

A multiscale Pseudo-DNS approach for solving turbulent boundary-layer problems

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-02-08 DOI: 10.1016/j.cma.2025.117804

Juan M. Gimenez , Francisco M. Sívori , Axel E. Larreteguy , Sabrina I. Montaño , Horacio J. Aguerre , Norberto M. Nigro , Sergio R. Idelsohn

Efficiently simulating turbulent fluid flow within a boundary layer is one of the major challenges in fluid mechanics. While skin friction may have a limited impact on drag at high Reynolds numbers, it plays a crucial role in determining the location of fluid separation points. Shifts in these separation points can dramatically alter drag and lift, underscoring the importance of accurately accounting for viscous effects. It is generally accepted that the Navier–Stokes equations contain all the necessary physical ingredients to accurately simulate fluid flows, even in complex scenarios. With a sufficiently fine mesh, we could simulate all fluid flows without relying on additional empirical approximations. However, this Direct Numerical Simulation (DNS) strategy is computationally impractical with current technology. The Pseudo-DNS (P-DNS) method offers a novel approach to solve the governing equations with the mesh refinement needed to achieve DNS-level accuracy. The solution is divided into fine and coarse scales, and through an iterative process, both scales are solved until convergence. Computational cost is affordable due to parametrize and solving the fine scale under different boundary conditions in simple domains, which allows performing these calculations offline – prior to and independent of the global solution – only once. The key novelty introduced in this work is the wall representative volume element (RVE), which models the time developing of turbulent boundary layers and its outputs can be adapted for adverse and favorable pressure gradient scenarios. The multiscale method enables accurate prediction of aerodynamic forces using relatively coarse meshes for boundary layers, without the need for empirical parameters or case-specific models. Several case studies involving 2D and 3D flows over both streamlined and bluff bodies validate the ability of P-DNS to deliver reliable results while maintaining modest computational requirements.

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引用次数: 0

Accelerating the data-driven multiscale finite element analysis for elastoplastic materials by using proper orthogonal decomposition and transformer architecture

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-02-08 DOI: 10.1016/j.cma.2025.117827

Suhan Kim, Hyunseong Shin

Nonlinear history-dependent behaviors and heterogeneity render multiscale finite element (FE²) simulation of elastoplastic materials challenging. Concurrently addressing micro- and macroscales involves discretizing the macro structure into representative volume elements (RVEs) and iteratively solving microscale problems under complex loading paths. Therefore, we proposed a novel integrated surrogate model that combines proper orthogonal decomposition (POD) with a transformer (TF) to capture the evolution of physical state variables in the local microstructure. This framework accelerates FE² simulations at the micro level for history-dependent materials. In the microscopic offline computing stage, sequential data were obtained from FE simulations conducted on an elasto–plastic composite RVE subjected to random and cyclic loading paths. Prior to use for training, the high-dimensional micro–stress field data were reduced to low-dimensional POD coefficient data, extracting information by using a small number of modes. This reduction in data dimensions renders operation easy and maintains essential features. The encoder-based TF model effectively captured global dependencies by using a self-attention mechanism. The proposed POD-TF surrogate model constructed in this manner plays a crucial role in accelerating FE². In the online computing stage, a nonlinear FE² combined with the proposed POD-TF surrogate model was conducted in a single simulation on a commercial FE. Therefore, the proposed approach allows simultaneous observation of physical states distributions at both micro-and macro scales, providing a comprehensive representation of the underlying multiscale phenomena. Additionally, fine-tuning enables the pre-trained POD-TF surrogate model to efficiently adapt to small variations in microstructure and material properties, enhancing flexibility and computational efficiency.

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引用次数: 0

On the numerical approximation of hyperbolic mean curvature flows for surfaces

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-02-08 DOI: 10.1016/j.cma.2025.117800

Klaus Deckelnick , Robert Nürnberg

The paper addresses the numerical approximation of two variants of hyperbolic mean curvature flow of surfaces in

R^{3}

. For each evolution law we propose both a finite element method, as well as a finite difference scheme in the case of axially symmetric surfaces. We present a number of numerical simulations, including convergence tests as well as simulations suggesting the onset of singularities.

引用次数: 0

HYDRA: Symbolic feature engineering of overparameterized Eulerian hyperelasticity models for fast inference time

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-02-07 DOI: 10.1016/j.cma.2025.117792

Nhon N. Phan , WaiChing Sun , John D. Clayton

We introduce HYDRA, a learning algorithm that generates symbolic hyperelasticity models designed for running in 3D Eulerian hydrocodes that require fast and robust inference time. Classical deep learning methods require a large number of neurons to express a learned hyperelasticity model adequately. Large neural network models may lead to slower inference time when compared to handcrafted models expressed in symbolic forms. This expressivity-speed trade-off is not desirable for high-fidelity hydrocodes that require one inference per material point per time step. Pruning techniques may speed up inference by removing/deactivating less important neurons, but often at a non-negligible expense of expressivity and accuracy. In this work, we introduce a post-hoc procedure to convert a neural network model into a symbolic one to reduce inference time. Rather than directly confronting NP-hard symbolic regression in the ambient strain space, HYDRA leverages a data-driven projection to map strain onto a hyperplane and a neural additive model to parameterize the hyperplane via univariate bases. This setting enables us to convert the univariate bases into symbolic forms via genetic programming with explicit control of the expressivity-speed trade-off. Additionally, the availability of analytical models provides the benefits of ensuring the enforcement of physical constraints (e.g., material frame indifference, material symmetry, growth condition) and enabling symbolic differentiation that may further reduce the memory requirement of high-performance solvers. Benchmark numerical examples of material point simulations for shock loading in

β

-octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (

β

-HMX) are performed to assess the practicality of using the discovered machine learning models for high-fidelity simulations.

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引用次数: 0

Coupled semi-Lagrangian and poroelastic peridynamics for modeling hydraulic fracturing in porous media

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-02-07 DOI: 10.1016/j.cma.2025.117794

Zirui Lu , Fan Zhu , Yosuke Higo , Jidong Zhao

A novel peridynamics-based computational approach is proposed for modeling hydraulic fracturing in porous media with consideration of leak-off effect. The approach features the use of the semi-Lagrangian peridynamics (PD) formulation which simulates fluid, and the poroelastic PD formulation which simulates deformation and fracture of porous solid with seepage flow. A new porous flow equation, which suits in the state-based PD, is derived using Non-local Differential Operators (NDOs) and based on Darcy’s law. A novel fluid-solid interface (FSI) model is proposed by coupling the two PD formulations. The FSI considers both the hydraulic forces applied on the fracture surfaces and the leak-off of fluid into poroelastic media. The proposed model is verified by benchmark cases including one-dimensional consolidation, 2-D Mandel’s problem, and constant head permeability test, for which analytical solutions are available. It is then applied to simulate hydraulic fracturing in porous media with consideration of the fluid leak-off and benchmarked with the analytical solutions from the Kristianovich-Geertsma-de Klerk (KGD) model and Carter’s equation. Simulation results demonstrate that the proposed model can reasonably capture the porous flow and pore pressure variation with solid deformation, the mass exchange between the fluid in the fracture and porous flow, and the fracture propagation in the porous media with concurrent leak-off.

{"title":"Coupled semi-Lagrangian and poroelastic peridynamics for modeling hydraulic fracturing in porous media","authors":"Zirui Lu , Fan Zhu , Yosuke Higo , Jidong Zhao","doi":"10.1016/j.cma.2025.117794","DOIUrl":"10.1016/j.cma.2025.117794","url":null,"abstract":"<div><div>A novel peridynamics-based computational approach is proposed for modeling hydraulic fracturing in porous media with consideration of leak-off effect. The approach features the use of the semi-Lagrangian peridynamics (PD) formulation which simulates fluid, and the poroelastic PD formulation which simulates deformation and fracture of porous solid with seepage flow. A new porous flow equation, which suits in the state-based PD, is derived using Non-local Differential Operators (NDOs) and based on Darcy’s law. A novel fluid-solid interface (FSI) model is proposed by coupling the two PD formulations. The FSI considers both the hydraulic forces applied on the fracture surfaces and the leak-off of fluid into poroelastic media. The proposed model is verified by benchmark cases including one-dimensional consolidation, 2-D Mandel’s problem, and constant head permeability test, for which analytical solutions are available. It is then applied to simulate hydraulic fracturing in porous media with consideration of the fluid leak-off and benchmarked with the analytical solutions from the Kristianovich-Geertsma-de Klerk (KGD) model and Carter’s equation. Simulation results demonstrate that the proposed model can reasonably capture the porous flow and pore pressure variation with solid deformation, the mass exchange between the fluid in the fracture and porous flow, and the fracture propagation in the porous media with concurrent leak-off.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"437 ","pages":"Article 117794"},"PeriodicalIF":6.9,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143275943","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Topology optimization considering shielding and penetrating features based on fictitious physical model

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-02-06 DOI: 10.1016/j.cma.2025.117805

Daiki Soma , Kota Sakai , Takayuki Yamada

This paper proposes topology optimization for considering shielding and penetrating features. Based on the fictitious physical model, which is a useful approach to control geometric features, the proposed method analyzes fictitious steady-state temperature fields and interprets target geometric features by examining the temperature change. First, the concept of topology optimization based on the level set method is introduced. Next, the basic idea of the fictitious physical model for considering geometric features is explained. Then, the differences between the shielding and penetrating features are clarified, and the fictitious physical model for evaluating these features is proposed. Furthermore, topology optimization for the minimum mean compliance problem with geometric conditions is formulated. Finally, 2D and 3D numerical examples are presented to validate the proposed method.

引用次数: 0

An extensible set of parent elements to facilitate the isoparametric concept for polygons at finite strains: A scaled boundary finite element approach

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-02-06 DOI: 10.1016/j.cma.2025.117803

E.T. Ooi , B. Sauren , S. Natarajan , C. Song

We present a generalisation of the isoparametric concept to construct finite element interpolation functions on any star-convex polygonal parametric space. The approach is based on the solution to Laplace’s equation by employing the scaled boundary finite element method (SBFEM). We construct these interpolation functions for generic shapes of polygons, leading to a family of parent elements. By employing the flexibility of the SBFEM to model star-convex polygons of arbitrary number of sides, the family of parent elements can be extended straightforwardly. Similar to the standard isoparametric concept for triangles and quadrilaterals, polygonal elements in physical space are mapped to their corresponding parent element. In the preprocessing stage, each element is assigned its most affine parent element to ensure an optimal mapping. An integration scheme is developed to effectively integrate each triangular sector forming a polygon element. The novel isoparametric concept retains the use of standard procedures of the finite element method, including its ability to incorporate geometric and material nonlinearities. We demonstrate the application of the developed formulation to finite strain elasticity problems. Several numerical benchmark problems considering these aspects are used to validate the feasibility and demonstrate the advantages of the proposed method.

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引用次数: 0

Continuum-kinematics-inspired peridynamics for transverse isotropy

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-02-05 DOI: 10.1016/j.cma.2025.117780

A.M. de Villiers , J. Stadler , G. Limbert , A.T. McBride , A. Javili , P. Steinmann

Accounting for the combined effects of mechanical anisotropy and nonlocality is critical for capturing a wide range of material behaviour. Continuum-kinematics-inspired peridynamics (CPD) provides the essential underpinning theoretical and numerical framework to realise this objective. The formalism of rational mechanics is employed here to rigorously extend CPD to the important case of transverse isotropy at finite deformations while retaining the fundamental deformation measures of length, area and volume intrinsic to classical continuum mechanics. Details of the anisotropic contribution to the potential energy density due to length, area and volume elements are given. A series of numerical examples serve to elucidate the theory presented.

引用次数: 0

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全部 ACS Publications Elsevier ieeexplore Springer The Royal Society of Chemistry Wiley

期刊

Computer Methods in Applied Mechanics and Engineering

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