Computational Mechanics最新文献_第4页

Physics-informed data-driven discovery of constitutive models with application to strain-rate-sensitive soft materials 应用于应变速率敏感软材料的物理信息数据驱动的构成模型发现

IF 4.1 2区工程技术

Computational Mechanics Pub Date : 2024-06-17 DOI: 10.1007/s00466-024-02497-x

Kshitiz Upadhyay, Jan N. Fuhg, Nikolaos Bouklas, K. T. Ramesh

{"title":"Physics-informed data-driven discovery of constitutive models with application to strain-rate-sensitive soft materials","authors":"Kshitiz Upadhyay, Jan N. Fuhg, Nikolaos Bouklas, K. T. Ramesh","doi":"10.1007/s00466-024-02497-x","DOIUrl":"https://doi.org/10.1007/s00466-024-02497-x","url":null,"abstract":"A novel data-driven constitutive modeling approach is proposed, which combines the physics-informed nature of modeling based on continuum thermodynamics with the benefits of machine learning. This approach is demonstrated on strain-rate-sensitive soft materials. This model is based on the viscous dissipation-based visco-hyperelasticity framework where the total stress is decomposed into volumetric, isochoric hyperelastic, and isochoric viscous overstress contributions. It is shown that each of these stress components can be written as linear combinations of the components of an irreducible integrity basis. Three Gaussian process regression-based surrogate models are trained (one per stress component) between principal invariants of strain and strain rate tensors and the corresponding coefficients of the integrity basis components. It is demonstrated that this type of model construction enforces key physics-based constraints on the predicted responses: the second law of thermodynamics, the principles of local action and determinism, objectivity, the balance of angular momentum, an assumed reference state, isotropy, and limited memory. The three surrogate models that constitute our constitutive model are evaluated by training them on small-size numerically generated data sets corresponding to a single deformation mode and then analyzing their predictions over a much wider testing regime comprising multiple deformation modes. Our physics-informed data-driven constitutive model predictions are compared with the corresponding predictions of classical continuum thermodynamics-based and purely data-driven models. It is shown that our surrogate models can reasonably capture the stress–strain-strain rate responses in both training and testing regimes and improve prediction accuracy, generalizability to multiple deformation modes, and compatibility with limited data.","PeriodicalId":55248,"journal":{"name":"Computational Mechanics","volume":"45 1","pages":""},"PeriodicalIF":4.1,"publicationDate":"2024-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141547674","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Interpolation-based immersogeometric analysis methods for multi-material and multi-physics problems 基于插值的多材料和多物理场分析方法

IF 4.1 2区工程技术

Computational Mechanics Pub Date : 2024-06-17 DOI: 10.1007/s00466-024-02506-z

Jennifer E. Fromm, Nils Wunsch, Kurt Maute, John A. Evans, Jiun-Shyan Chen

{"title":"Interpolation-based immersogeometric analysis methods for multi-material and multi-physics problems","authors":"Jennifer E. Fromm, Nils Wunsch, Kurt Maute, John A. Evans, Jiun-Shyan Chen","doi":"10.1007/s00466-024-02506-z","DOIUrl":"https://doi.org/10.1007/s00466-024-02506-z","url":null,"abstract":"Immersed boundary methods are high-order accurate computational tools used to model geometrically complex problems in computational mechanics. While traditional finite element methods require the construction of high-quality boundary-fitted meshes, immersed boundary methods instead embed the computational domain in a structured background grid. Interpolation-based immersed boundary methods augment existing finite element software to non-invasively implement immersed boundary capabilities through extraction. Extraction interpolates the structured background basis as a linear combination of Lagrange polynomials defined on a foreground mesh, creating an interpolated basis that can be easily integrated by existing methods. This work extends the interpolation-based immersed isogeometric method to multi-material and multi-physics problems. Beginning from level-set descriptions of domain geometries, Heaviside enrichment is implemented to accommodate discontinuities in state variable fields across material interfaces. Adaptive refinement with truncated hierarchically refined B-splines (THB-splines) is used to both improve interface geometry representations and to resolve large solution gradients near interfaces. Multi-physics problems typically involve coupled fields where each field has unique discretization requirements. This work presents a novel discretization method for coupled problems through the application of extraction, using a single foreground mesh for all fields. Numerical examples illustrate optimal convergence rates for this method in both 2D and 3D, for partial differential equations representing heat conduction, linear elasticity, and a coupled thermo-mechanical problem. The utility of this method is demonstrated through image-based analysis of a composite sample, where in addition to circumventing typical meshing difficulties, this method reduces the required degrees of freedom when compared to classical boundary-fitted finite element methods.","PeriodicalId":55248,"journal":{"name":"Computational Mechanics","volume":"17 1","pages":""},"PeriodicalIF":4.1,"publicationDate":"2024-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141522312","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

An improved polygon mesh generation and its application in SBFEM using NURBS boundary 改进的多边形网格生成及其在使用 NURBS 边界的 SBFEM 中的应用

IF 4.1 2区工程技术

Computational Mechanics Pub Date : 2024-06-17 DOI: 10.1007/s00466-024-02504-1

Xinqing Li, Hailiang Su, Yingjun Wang

{"title":"An improved polygon mesh generation and its application in SBFEM using NURBS boundary","authors":"Xinqing Li, Hailiang Su, Yingjun Wang","doi":"10.1007/s00466-024-02504-1","DOIUrl":"https://doi.org/10.1007/s00466-024-02504-1","url":null,"abstract":"Aiming to address the challenge of inaccurately describing the curve boundary of the complex design domain in traditional finite element mesh, this paper proposes an improved polygon mesh generation and polygon scaled boundary finite element method (PSBFEM) using non-uniform rational B-spline (NURBS) boundary. In the improved mesh generation scheme, the domain boundary will be accurately described using NURBS curves. Within this framework, a NURBS updating strategy is proposed, allowing the NURBS curve information on the boundary to be updated as the mesh changes. By employing point inversion and knot insertion, additional control points are introduced to ensure that some coincide with the nodes of the elements, thereby guaranteeing the accuracy of subsequent analyses. The boundary elements can be discretized into NURBS elements and conventional elements using SBFEM, whose physical fields are respectively constructed using NURBS basis functions and Lagrange shape functions in the circumferential direction. In the radial direction, by transforming a system of partial differential equations into a system of ordinary differential equations, which can be analytically solved without fundamental solutions. Furthermore, the internal elements can be solved directly with the traditional polygon SBFEM. The numerical examples demonstrate that the proposed method can achieve a high-quality polygon mesh with NURBS updating. Moreover, it effectively solves the corresponding polygon elements and significantly improves the accuracy of the displacement and stress solutions compared to the traditional polygon SBFEM.","PeriodicalId":55248,"journal":{"name":"Computational Mechanics","volume":"25 1","pages":""},"PeriodicalIF":4.1,"publicationDate":"2024-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141547673","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Correction to: Time domain coupling of the boundary and discrete element methods for 3D problems 更正：三维问题中边界法和离散元法的时域耦合

IF 4.1 2区工程技术

Computational Mechanics Pub Date : 2024-06-11 DOI: 10.1007/s00466-024-02483-3

Guilherme Barros, Andre Pereira, Jerzy Rojek, John Carter, Klaus Thoeni

引用次数: 0

Machine learning assisted discovery of effective viscous material laws for shear-thinning fiber suspensions 机器学习辅助发现剪切稀化纤维悬浮液的有效粘性材料定律

IF 4.1 2区工程技术

Computational Mechanics Pub Date : 2024-06-04 DOI: 10.1007/s00466-024-02490-4

Benedikt Sterr, Andrew Hrymak, Matti Schneider, Thomas Böhlke

{"title":"Machine learning assisted discovery of effective viscous material laws for shear-thinning fiber suspensions","authors":"Benedikt Sterr, Andrew Hrymak, Matti Schneider, Thomas Böhlke","doi":"10.1007/s00466-024-02490-4","DOIUrl":"https://doi.org/10.1007/s00466-024-02490-4","url":null,"abstract":"In this article, we combine a Fast Fourier Transform based computational approach and a supervised machine learning strategy to discover models for the anisotropic effective viscosity of shear-thinning fiber suspensions. Using the Fast Fourier Transform based computational approach, we study the effects of the fiber orientation state and the imposed macroscopic shear rate tensor on the effective viscosity for a broad range of shear rates of engineering process interest. We visualize the effective viscosity in three dimensions and find that the anisotropy of the effective viscosity and its shear rate dependence vary strongly with the fiber orientation state. Combining the results of this work with insights from literature, we formulate four requirements a model of the effective viscosity should satisfy for shear-thinning fiber suspensions with a Cross-type matrix fluid. Furthermore, we introduce four model candidates with differing numbers of parameters and different theoretical motivations, and use supervised machine learning techniques for non-convex optimization to identify parameter sets for the model candidates. By doing so, we leverage the flexibility of automatic differentiation and the robustness of gradient based, supervised machine learning. Finally, we identify the most suitable model by comparing the prediction accuracy of the model candidates on the fiber orientation triangle, and find that multiple models predict the anisotropic shear-thinning behavior to engineering accuracy over a broad range of shear rates.","PeriodicalId":55248,"journal":{"name":"Computational Mechanics","volume":"89 1","pages":""},"PeriodicalIF":4.1,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141259090","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 general-purpose IGA mesh generation method: NURBS Surface-to-Volume Guided Mesh Generation 通用的 IGA 网格生成方法NURBS 面-体引导网格生成法

IF 4.1 2区工程技术

Computational Mechanics Pub Date : 2024-06-04 DOI: 10.1007/s00466-024-02496-y

Takashi Kuraishi, Kenji Takizawa, Tayfun E. Tezduyar

引用次数: 0

Combining the micromechanical approach and boundary element method for estimating the effective permeability of 2D porous materials with arbitrarily shaped pores 结合微机械方法和边界元方法估算具有任意形状孔隙的二维多孔材料的有效渗透率

IF 4.1 2区工程技术

Computational Mechanics Pub Date : 2024-06-04 DOI: 10.1007/s00466-024-02498-w

A.-T. Tran, H. Le Quang, D.-H. Nguyen, V. H. Hoang, T. A. Do, Q.-C. He

{"title":"Combining the micromechanical approach and boundary element method for estimating the effective permeability of 2D porous materials with arbitrarily shaped pores","authors":"A.-T. Tran, H. Le Quang, D.-H. Nguyen, V. H. Hoang, T. A. Do, Q.-C. He","doi":"10.1007/s00466-024-02498-w","DOIUrl":"https://doi.org/10.1007/s00466-024-02498-w","url":null,"abstract":"The primary objective of this work is to determine the effective permeability of porous media consisting of an isotropic permeable solid matrix containing pores of arbitrary shapes. Fluid flow through the matrix phase is modeled by Darcy’s law, while the flow inside the pores follows the Stokes equations. The interfaces between the matrix phase and inclusions are defined by the general form of the Beavers-Joseph-Saffman conditions. To achieve this objective, the Boundary Element Method (BEM) is first developed to solve the coupled Darcy and Stokes problem related to fluid flow through an infinite solid phase containing an arbitrarily shaped pore under a uniform prescribed pressure gradient at infinity. In contrast to the classical BEM where integration equations are often singular, our method, incorporating both finite difference and analytical integration schemes, overcomes this inconvenience. Additionally, compared to the commonly used numerical method based on the finite element method, our approach, which only requires discretization of the solid/fluid interface, significantly enhances computational speed and efficiency. Subsequently, each pore is substituted with an equivalent permeable inclusion, and its permeability is determined. Finally, employing classical micromechanical schemes, the macroscopic permeabilities of the porous material under consideration are estimated. These macroscopic permeability estimates are then compared with the relevant data available in the literature, as well as several numerical results provided by the finite element method.","PeriodicalId":55248,"journal":{"name":"Computational Mechanics","volume":"30 1","pages":""},"PeriodicalIF":4.1,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141259243","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Numerical study on guided-wave reflection and transmission at water pipe joint using hybrid finite element method 利用混合有限元法对导波在水管连接处的反射和传输进行数值研究

IF 4.1 2区工程技术

Computational Mechanics Pub Date : 2024-06-04 DOI: 10.1007/s00466-024-02505-0

Taizo Maruyama, Taisei Matsuo, Kazuyuki Nakahata

{"title":"Numerical study on guided-wave reflection and transmission at water pipe joint using hybrid finite element method","authors":"Taizo Maruyama, Taisei Matsuo, Kazuyuki Nakahata","doi":"10.1007/s00466-024-02505-0","DOIUrl":"https://doi.org/10.1007/s00466-024-02505-0","url":null,"abstract":"This study investigates guided-wave reflection and transmission at a water pipe joint. The system comprises a linearly elastic pipe filled with water with a joint that is modeled as a discontinuity of the solid region. Wave reflection and transmission are solved using the finite element method (FEM) with radiation conditions for reflected and transmitted guided waves into infinite waveguides. For the radiation conditions, the reflected and transmitted waves are expressed by modal expansion using the semi-analytical finite-element (SAFE) dispersion analysis method. This study extends the hybrid SAFE-FEM to the coupled fluid–solid axisymmetric problem. Numerical results demonstrate that the hybrid SAFE-FEM provides sufficiently accurate solutions. The propagation modes, similar to the modes in a solid pipe, are strongly or perfectly reflected by the joint. However, the modes are transmitted through the joint with little scattering after they converge to the modes in a water bar. The crossing of dispersion curves with those for modes in a solid pipe causes mode conversion and induces scattering attenuation.","PeriodicalId":55248,"journal":{"name":"Computational Mechanics","volume":"26 1","pages":""},"PeriodicalIF":4.1,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141259454","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Stabilization-free virtual element method for 3D hyperelastic problems 三维超弹性问题的无稳定虚拟元素法

IF 4.1 2区工程技术

Computational Mechanics Pub Date : 2024-05-27 DOI: 10.1007/s00466-024-02501-4

Bing-Bing Xu, Fan Peng, Peter Wriggers

{"title":"Stabilization-free virtual element method for 3D hyperelastic problems","authors":"Bing-Bing Xu, Fan Peng, Peter Wriggers","doi":"10.1007/s00466-024-02501-4","DOIUrl":"https://doi.org/10.1007/s00466-024-02501-4","url":null,"abstract":"In this work, we present a first-order stabilization-free virtual element method (SFVEM) for three-dimensional hyperelastic problems. Different from the conventional virtual element method, which necessitates additional stabilization terms in the bilinear formulation, the method developed in this work operates without the need for any stabilization. Consequently, it proves highly suitable for the computation of nonlinear problems. The stabilization-free virtual element method has been applied in two-dimensional hyperelasticity and three-dimensional elasticity problems. In this work, the format will be applied to three-dimensional hyperelasticity problems for the first time. Similar to the techniques used in the two-dimensional stabilization-free virtual element method, the new virtual element space is modified to allow the computation of the higher-order (L_2) projection of the gradient. This paper reviews the calculation process of the traditional (mathcal {H}_1) projection operator; and describes in detail how to calculate the high-order (L_2) projection operator for three-dimensional problems. Based on this high-order (L_2) projection operator, this paper extends the method to more complex three-dimensional nonlinear problems. Some benchmark problems illustrate the capability of the stabilization-free VEM for three-dimensional hyperelastic problems.","PeriodicalId":55248,"journal":{"name":"Computational Mechanics","volume":"13 1","pages":""},"PeriodicalIF":4.1,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141166705","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Master–slave elimination scheme for arbitrary smooth nonlinear multi-point constraints 任意平滑非线性多点约束的主从消除方案

IF 4.1 2区工程技术

Computational Mechanics Pub Date : 2024-05-25 DOI: 10.1007/s00466-024-02463-7

Jonas Boungard, Jens Wackerfuß

{"title":"Master–slave elimination scheme for arbitrary smooth nonlinear multi-point constraints","authors":"Jonas Boungard, Jens Wackerfuß","doi":"10.1007/s00466-024-02463-7","DOIUrl":"https://doi.org/10.1007/s00466-024-02463-7","url":null,"abstract":"Nonlinear multi-point constraints are essential in modeling various engineering problems, for example in the context of (a) linking individual degrees of freedom of multiple nodes to model nonlinear joints, (b) coupling different element types in finite element analysis, (c) enforcing various types of rigidity in parts of the mesh and (d) considering deformation-dependent Dirichlet boundary conditions. One method for addressing constraints is the master–slave elimination, which offers the benefit of reducing the problem dimension as opposed to Lagrange multipliers and the penalty method. However, the existing master–slave elimination method is limited to linear constraints. In this paper, we introduce a new master–slave elimination method for handling arbitrary smooth nonlinear multi-point constraints in the system of equations of the discretized system. We present a rigorous mathematical derivation of the method. Within this method, new constraints can be easily considered as an item of a “constraint library”; i.e. no case-by-case-programming is required. In addition to the theoretical aspects, we also provide helpful remarks on the efficient implementation. Among others, we show that the new method results in a reduced computational complexity compared to the existing methods. The study also places emphasis on comparing the new approach with existing methods via numerical examples. We have developed innovative benchmarks which encompass all relevant computational properties, and provide analytical and reference solutions. Our findings demonstrate that our new method is as accurate, robust and flexible as the Lagrange multipliers, and more efficient due to the reduction of the total number of degrees of freedom, which is particularly advantageous when a large number of constraints have to be considered.","PeriodicalId":55248,"journal":{"name":"Computational Mechanics","volume":"34 1","pages":""},"PeriodicalIF":4.1,"publicationDate":"2024-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141149276","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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