Computer Methods in Applied Mechanics and Engineering最新文献_第10页

A unified Minkowski sum model for largely deformed granular materials with arbitrary morphologies 具有任意形态的大变形颗粒材料的统一闵科夫斯基和模型

IF 6.9 1区工程技术

Computer Methods in Applied Mechanics and Engineering Pub Date : 2024-09-30 DOI: 10.1016/j.cma.2024.117427

{"title":"A unified Minkowski sum model for largely deformed granular materials with arbitrary morphologies","authors":"","doi":"10.1016/j.cma.2024.117427","DOIUrl":"10.1016/j.cma.2024.117427","url":null,"abstract":"<div><div>Since deformable granular materials with arbitrary morphologies constructed by different dilated non-spherical models in complex structures remain challenging for numerical simulations using the discrete element method (DEM), a unified Minkowski sum model was proposed for calculating collision forces and large deformations of arbitrarily shaped granular materials and structures. In this model, dilated superquadric equations, dilated spherical harmonic functions, and dilated polyhedrons were developed to construct arbitrarily shaped particles, and Fibonacci and automatic mesh simplification algorithms were established to determine the surface meshes of the particles with controlled accuracy. Subsequently, the Minkowski sum model based on chain-linked meshes and granular skeletons was proposed to calculate collision forces and large deformations of rigid and deformable granular materials. To investigate the conservation, accuracy, and robustness of the proposed model, six sets of numerical examples were conducted and compared with the theoretical and finite element results, which included the static analysis of a deformable granular skeleton, the mechanical analysis of a single deformable structure, a single deformable particle impacting a rigid wall, the collision between two rigid and deformable particles, the accumulation of multiple rigid particles on a deformable structure, and compression of multiple deformable particles within a deformable structure. The corresponding numerical results are in good agreement with the theoretical and finite element results, which verifies that the present DEM model can accurately predict the large deformation characteristics of different dilated DEM models and can be extensively applied to the dynamic flows and deformation behaviors of arbitrarily shaped granular materials involving multiple DEM models in deformable structures.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":null,"pages":null},"PeriodicalIF":6.9,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142358155","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

Variationally consistent magnetodynamic computational homogenization of particulate composites using an incremental potential 利用增量势能对颗粒复合材料进行变量一致的磁动力计算均质化

IF 6.9 1区工程技术

Computer Methods in Applied Mechanics and Engineering Pub Date : 2024-09-28 DOI: 10.1016/j.cma.2024.117421

{"title":"Variationally consistent magnetodynamic computational homogenization of particulate composites using an incremental potential","authors":"","doi":"10.1016/j.cma.2024.117421","DOIUrl":"10.1016/j.cma.2024.117421","url":null,"abstract":"<div><div>If composites made of conductive particles embedded in a nonconductive matrix are subject to highly dynamic magnetization processes, then microscopic eddy currents may lead to high magnetodynamic losses and heating of the material. Less obvious, the microscopic eddy currents also induce a dynamic macroscopic magnetization in accordance with Lenz’ law. Conventional homogenization theories based on volume averaging of the magnetic field strength disregard this effect and thus fail to properly predict the dynamic material response. In this work, the variationally consistent homogenization framework by Larsson et al. (2010), originally developed for transient heat conduction, is transferred to the aforementioned particulate composites, in order to properly reproduce this dynamic effect. It turns out that this approach predicts the macroscopic magnetization to be the volume averaged sum of the particles’ (conventional) magnetization and a non-standard dynamic magnetization due to microscopic eddy currents. Some first numerical examples illustrate the improved predictability of the variationally consistent homogenization method with respect to experimental complex permeability data. The resulting theory is shown to exhibit a two-scale incremental potential structure, which is exploited in several ways.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":null,"pages":null},"PeriodicalIF":6.9,"publicationDate":"2024-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142358062","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

A coupled virtual element-interface model for analysis of fracture propagation in polycrystalline composites 用于分析多晶复合材料断裂扩展的虚拟元素-界面耦合模型

IF 6.9 1区工程技术

Computer Methods in Applied Mechanics and Engineering Pub Date : 2024-09-28 DOI: 10.1016/j.cma.2024.117383

引用次数: 0

A multidimensional quasi-bond method for refined modelling of continuous and discontinuous problems in solids 用于对固体中的连续和不连续问题进行精细建模的多维准结合方法

IF 6.9 1区工程技术

Computer Methods in Applied Mechanics and Engineering Pub Date : 2024-09-28 DOI: 10.1016/j.cma.2024.117417

{"title":"A multidimensional quasi-bond method for refined modelling of continuous and discontinuous problems in solids","authors":"","doi":"10.1016/j.cma.2024.117417","DOIUrl":"10.1016/j.cma.2024.117417","url":null,"abstract":"<div><div>This paper presents an extended quasi-bond method in order to provide a robust numerical tool for refined modelling of continuous and discontinuous problems in solids. Firstly, the bond-scale constitutive formulations are enriched by incorporating the effect of shear and lateral deformations. In that process, we tackle successfully the persistent theoretical issue on the limitation of Poisson’s ratio, which appears in the form of negative shear stiffness in most bond/spring-based methods. Secondly, the property of flexible placement of quasi-bonds is found and the binding relationship between bonds and material particles is thus removed. Additionally, a quasi-bond operator is proposed to transform the Laplace operator into an integral form, thereby extending the applicability of the quasi-bond method to various physical problems. These new developments facilitate discretizing an elementary solid region into a limit number of quasi-bonds, and avoiding the use of complex material models such as anisotropic damage ones, which paves a new way to elucidate and simulate complex dissipation problems in solid materials and structures. At this stage, the effectiveness and efficiency of the proposed approach are assessed through typical continuous/discontinuous problems.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":null,"pages":null},"PeriodicalIF":6.9,"publicationDate":"2024-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142358156","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

AsPINN: Adaptive symmetry-recomposition physics-informed neural networks AsPINN：自适应对称重组物理信息神经网络

IF 6.9 1区工程技术

Computer Methods in Applied Mechanics and Engineering Pub Date : 2024-09-27 DOI: 10.1016/j.cma.2024.117405

{"title":"AsPINN: Adaptive symmetry-recomposition physics-informed neural networks","authors":"","doi":"10.1016/j.cma.2024.117405","DOIUrl":"10.1016/j.cma.2024.117405","url":null,"abstract":"<div><div>Physics-informed neural networks (PINNs) have shown promise for solving partial differential equations (PDEs). However, PINNs’ loss, the regularization terms, can only guarantee that the prediction results conform to the physical constraints in the average sense, which results in PINNs’ inability to strictly adhere to implied physical laws such as conservation laws and symmetries. This limits the optimization speed and accuracy of PINNs. Although some feature-enhanced PINNs attempt to address this issue by adding explicit constraints, their generality is limited due to specific question settings. To overcome this limitation, our study proposes the adaptive symmetry-recomposition PINN (AsPINN). By analyzing the parameter-sharing patterns of fully connected PINNs, specific network structures are developed to provide predictions with strict symmetry constraints. These structures are incorporated into diverse subnetworks to provide constrained intermediate outputs, then a specialized multi-head attention mechanism is attached to evaluate and composite them into final predictions adaptively. Thus, AsPINN maintains precise constraints while addressing the inability of individual structural subnetworks’ generality. This method is then applied to address several physically significant PDEs, including both forward and inverse problems. The numerical results demonstrates AsPINN’s mathematical consistency and generality, offering advantages in terms of optimization speed and accuracy with a reduced number of trainable parameters. The results also manifest that AsPINN mitigates the impact of ill-conditioned data.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":null,"pages":null},"PeriodicalIF":6.9,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142326464","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

Adaptive optimization of isogeometric multi-patch discretizations using artificial neural networks 利用人工神经网络自适应优化等距多斑块离散法

IF 6.9 1区工程技术

Computer Methods in Applied Mechanics and Engineering Pub Date : 2024-09-27 DOI: 10.1016/j.cma.2024.117400

{"title":"Adaptive optimization of isogeometric multi-patch discretizations using artificial neural networks","authors":"","doi":"10.1016/j.cma.2024.117400","DOIUrl":"10.1016/j.cma.2024.117400","url":null,"abstract":"<div><div>In isogeometric analysis, isogeometric function spaces are employed for accurately representing the solution to a partial differential equation (PDE) on a parameterized domain. They are generated from a tensor-product spline space by composing the basis functions with the inverse of the parameterization. Depending on the geometry of the domain and on the data of the PDE, the solution might not have maximum Sobolev regularity, leading to a reduced convergence rate. In this case it is necessary to reduce the local mesh size close to the singularities. The classical approach is to perform adaptive <span><math><mi>h</mi></math></span>-refinement, which either leads to an unnecessarily large number of degrees of freedom or to a spline space that does not possess a tensor-product structure. Based on the concept of <span><math><mi>r</mi></math></span>-adaptivity we present a novel approach for finding a suitable isogeometric function space for a given PDE without sacrificing the tensor-product structure of the underlying spline space. In particular, we use the fact that different reparameterizations of the same computational domain lead to different isogeometric function spaces while preserving the geometry. Starting from a multi-patch domain consisting of bilinearly parameterized patches, we aim to find the biquadratic multi-patch parameterization that leads to the isogeometric function space with the smallest best approximation error of the solution. In order to estimate the location of the optimal control points, we employ a trained residual neural network that is applied to the graph surfaces of the approximated solution and its derivatives. In our experimental results, we observe that our new method results in a vast improvement of the approximation error for different PDE problems on multi-patch domains.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":null,"pages":null},"PeriodicalIF":6.9,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142326465","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

A novel semi-explicit numerical algorithm for efficient 3D phase field modelling of quasi-brittle fracture 准脆性断裂高效三维相场建模的新型半显式数值算法

IF 6.9 1区工程技术

Computer Methods in Applied Mechanics and Engineering Pub Date : 2024-09-27 DOI: 10.1016/j.cma.2024.117416

{"title":"A novel semi-explicit numerical algorithm for efficient 3D phase field modelling of quasi-brittle fracture","authors":"","doi":"10.1016/j.cma.2024.117416","DOIUrl":"10.1016/j.cma.2024.117416","url":null,"abstract":"<div><div>Phase field models have become an effective tool for predicting complex crack configurations including initiation, propagation, branching, intersecting and merging. However, several computational issues have hindered their utilisation in engineering practice, such as the convergence challenge in implicit algorithms, numerical stability issues in explicit methods and significant computational costs. Aiming to providing a more efficient numerical algorithm, this work integrates the explicit integral operator with the recently developed neighbored element method, for the first time, to solve the coupled governing equations in phase field models. In addition, the damage irreversibility can be ensured automatically, avoiding the need to introduce extra history variable for the maximum driving force in traditional algorithms. Six representative fracture benchmarks with different failure modes are simulated to verify the effectiveness of the proposed method, including the multiple cracks in heterogeneous concrete at mesoscale. It is found that this semi-explicit numerical algorithm yields consistent crack profiles and load capacities for all examples to the available experimental data and literature. In particular, the computational cost is significantly reduced when compared to the traditional explicit modelling. Therefore, the presented numerical algorithm is highly attractive and promising for phase-field simulations of complicated 3D solid fractures in structural-level engineering practices.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":null,"pages":null},"PeriodicalIF":6.9,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142326463","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

Physics-Informed Holomorphic Neural Networks (PIHNNs): Solving 2D linear elasticity problems 物理信息全形态神经网络（PIHNNs）：解决二维线性弹性问题

IF 6.9 1区工程技术

Computer Methods in Applied Mechanics and Engineering Pub Date : 2024-09-27 DOI: 10.1016/j.cma.2024.117406

{"title":"Physics-Informed Holomorphic Neural Networks (PIHNNs): Solving 2D linear elasticity problems","authors":"","doi":"10.1016/j.cma.2024.117406","DOIUrl":"10.1016/j.cma.2024.117406","url":null,"abstract":"<div><div>We propose physics-informed holomorphic neural networks (PIHNNs) as a method to solve boundary value problems where the solution can be represented via holomorphic functions. Specifically, we consider the case of plane linear elasticity and, by leveraging the Kolosov–Muskhelishvili representation of the solution in terms of holomorphic potentials, we train a complex-valued neural network to fulfill stress and displacement boundary conditions while automatically satisfying the governing equations. This is achieved by designing the network to return only approximations that inherently satisfy the Cauchy-Riemann conditions through specific choices of layers and activation functions. To ensure generality, we provide a universal approximation theorem guaranteeing that, under basic assumptions, the proposed holomorphic neural networks can approximate any holomorphic function. Furthermore, we suggest a new tailored weight initialization technique to mitigate the issue of vanishing/exploding gradients. Compared to the standard PINN approach, noteworthy benefits of the proposed method for the linear elasticity problem include a more efficient training, as evaluations are needed solely on the boundary of the domain, lower memory requirements, due to the reduced number of training points, and <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>∞</mi></mrow></msup></math></span> regularity of the learned solution. Several benchmark examples are used to verify the correctness of the obtained PIHNN approximations, the substantial benefits over traditional PINNs, and the possibility to deal with non-trivial, multiply-connected geometries via a domain-decomposition strategy.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":null,"pages":null},"PeriodicalIF":6.9,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142322445","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

Cross interpolation for solving high-dimensional dynamical systems on low-rank Tucker and tensor train manifolds 求解低阶塔克流形和张量列车流形上的高维动力系统的交叉插值法

IF 6.9 1区工程技术

Computer Methods in Applied Mechanics and Engineering Pub Date : 2024-09-26 DOI: 10.1016/j.cma.2024.117385

{"title":"Cross interpolation for solving high-dimensional dynamical systems on low-rank Tucker and tensor train manifolds","authors":"","doi":"10.1016/j.cma.2024.117385","DOIUrl":"10.1016/j.cma.2024.117385","url":null,"abstract":"<div><div>We present a novel tensor interpolation algorithm for the time integration of nonlinear tensor differential equations (TDEs) on the tensor train and Tucker tensor low-rank manifolds, which are the building blocks of many tensor network decompositions. This paper builds upon our previous work (Donello et al., 2023) on solving nonlinear matrix differential equations on low-rank matrix manifolds using CUR decompositions. The methodology we present offers multiple advantages: (i) It delivers near-optimal computational savings both in terms of memory and floating-point operations by leveraging cross algorithms based on the discrete empirical interpolation method to strategically sample sparse entries of the time-discrete TDEs to advance the solution in low-rank form. (ii) Numerical demonstrations show that the time integration is robust in the presence of small singular values. (iii) High-order explicit Runge–Kutta time integration schemes are developed. (iv) The algorithm is easy to implement, as it requires the evaluation of the full-order model at strategically selected entries and does not use tangent space projections, whose efficient implementation is intrusive. We demonstrate the efficiency of the presented algorithm for several test cases, including a nonlinear 100-dimensional TDE for the evolution of a tensor of size <span><math><mrow><mn>7</mn><msup><mrow><mn>0</mn></mrow><mrow><mn>100</mn></mrow></msup><mo>≈</mo><mn>3</mn><mo>.</mo><mn>2</mn><mo>×</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mn>184</mn></mrow></msup></mrow></math></span> and a stochastic advection–diffusion–reaction equation with a tensor of size <span><math><mrow><mn>4</mn><mo>.</mo><mn>7</mn><mo>×</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mn>9</mn></mrow></msup></mrow></math></span>.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":null,"pages":null},"PeriodicalIF":6.9,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142322748","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

A symmetric interior-penalty discontinuous Galerkin isogeometric analysis spatial discretization of the self-adjoint angular flux form of the neutron transport equation 中子输运方程的自联合角通量形式的对称内部惩罚性非连续 Galerkin 等几何分析空间离散化

IF 6.9 1区工程技术

Computer Methods in Applied Mechanics and Engineering Pub Date : 2024-09-26 DOI: 10.1016/j.cma.2024.117414

{"title":"A symmetric interior-penalty discontinuous Galerkin isogeometric analysis spatial discretization of the self-adjoint angular flux form of the neutron transport equation","authors":"","doi":"10.1016/j.cma.2024.117414","DOIUrl":"10.1016/j.cma.2024.117414","url":null,"abstract":"<div><div>This paper presents the first application of a symmetric interior-penalty discontinuous Galerkin isogeometric analysis (SIP-DG-IGA) spatial discretization to the self-adjoint angular flux (SAAF) form of the multi-group neutron transport equation. The penalty parameters are determined, for general element types, from a mathematically rigorous coercivity analysis of the bilinear form. The proposed scheme produces a compact spatial discretization stencil. It also yields symmetric positive-definite (SPD) matrices, which can be efficiently solved using pre-conditioned conjugate gradient (PCG) solution algorithms. The proposed discretization scheme is verified using the method of manufactured solutions (MMS) and several nuclear reactor physics benchmark verification test cases. For sufficiently smooth elliptic problems, the proposed spatial discretization can exploit higher-order continuity, or <span><math><mi>k</mi></math></span>-refinement, of the NURBS basis to consistently yield greater numerical accuracy per degree of freedom (DoF) than standard <span><math><mi>h</mi></math></span>-refinement. Since this is a discontinuous scheme, it can also accurately model significant changes in the neutron scalar flux that may occur near the material interfaces of heterogeneous problems.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":null,"pages":null},"PeriodicalIF":6.9,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142322442","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