Computer Methods in Applied Mechanics and Engineering最新文献_第7页

Consistent Eulerian and Lagrangian variational formulations of non-linear kinematic hardening for solid media undergoing large strains and shocks 经历大应变和冲击的固体介质的非线性运动硬化的欧拉和拉格朗日一致变分公式

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-10-28 DOI: 10.1016/j.cma.2024.117480

Thomas Heuzé , Nicolas Favrie

In this paper, two Eulerian and Lagrangian variational formulations of non-linear kinematic hardening are derived in the context of finite thermoplasticity. These are based on the thermo-mechanical variational framework introduced by Heuzé and Stainier (2022), and follow the concept of pseudo-stresses introduced by Mosler and Bruhns (2009). These formulations are derived from a thermodynamical framework and are based on the multiplicative split of the deformation gradient in the context of hyperelasticity. Both Lagrangian and Eulerian formulations are derived in a consistent manner via some transport associated with the mapping, and use quantities consistent with those updated by the set of conservation or balance laws written in these two cases. These Eulerian and Lagrangian formulations aims at investigating the importance of non-linear kinematic hardening for bodies submitted to cyclic impacts in dynamics, where Bauschinger and/or ratchetting effects are expected to occur. Continuous variational formulations of the local constitutive problems as well as discrete variational constitutive updates are derived in the Eulerian and Lagrangian settings. The discrete updates are coupled with the second order accurate flux difference splitting finite volume method, which permits to solve the sets of conservation laws. A set of test cases allow to show on the one hand the good behavior of variational constitutive updates, and on the other hand the good consistency of Lagrangian and Eulerian numerical simulations.

本文以有限热塑性为背景，推导了非线性运动硬化的两种欧拉和拉格朗日变分公式。这些公式基于 Heuzé 和 Stainier（2022 年）提出的热力学变分框架，并遵循 Mosler 和 Bruhns（2009 年）提出的伪应力概念。这些公式源于热力学框架，并基于超弹性背景下变形梯度的乘法分割。拉格朗日公式和欧拉公式都是通过与映射相关的一些传输以一致的方式推导出来的，并且使用的量与这两种情况下编写的一组守恒或平衡定律所更新的量一致。这些欧拉和拉格朗日公式旨在研究非线性运动硬化对于在动力学中受到周期性冲击的物体的重要性，在这种情况下，预计会出现鲍辛格和/或棘轮效应。在欧拉和拉格朗日背景下，推导出了局部构造问题的连续变量公式以及离散变量构造更新。离散更新与二阶精确通量差分有限体积法相结合，可以求解守恒定律集。通过一组测试案例，一方面展示了变构更新的良好行为，另一方面展示了拉格朗日和欧拉数值模拟的良好一致性。

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引用次数: 0

Exploring the roles of numerical simulations and machine learning in multiscale paving materials analysis: Applications, challenges, best practices 探索数值模拟和机器学习在多尺度铺路材料分析中的作用：应用、挑战和最佳实践

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-10-28 DOI: 10.1016/j.cma.2024.117462

Mahmoud Khadijeh, Cor Kasbergen, Sandra Erkens, Aikaterini Varveri

The complex structure of bituminous mixtures ranging from nanoscale binder components to macroscale pavement performance requires a comprehensive approach to material characterization and performance prediction. This paper provides a critical analysis of advanced techniques in paving materials modeling. It focuses on four main approaches: finite element method (FEM), discrete element method (DEM), phase field method (PFM), and artificial neural networks (ANNs). The review highlights how these computational methods enable more accurate predictions of material behavior, from asphalt binder rheology to mixture performance, while reducing reliance on extensive empirical testing. Key advances, such as the smooth integration of information across multiple scales and the emergence of physics-informed neural networks (PINNs), are discussed as promising avenues for enhancing model accuracy and computational efficiency. This review not only provides a comprehensive overview of current methodologies but also outlines future research directions aimed at developing more sustainable, cost-effective, and durable paving solutions through advanced multiscale modeling techniques.

从纳米级粘结剂成分到宏观路面性能，沥青混合物的结构十分复杂，因此需要一种全面的材料表征和性能预测方法。本文对铺路材料建模的先进技术进行了批判性分析。本文重点介绍了四种主要方法：有限元法 (FEM)、离散元法 (DEM)、相场法 (PFM) 和人工神经网络 (ANN)。综述重点介绍了这些计算方法如何能够更准确地预测材料行为，从沥青粘结剂流变到混合料性能，同时减少对大量经验测试的依赖。文中讨论了一些重要进展，如跨尺度信息的平滑集成以及物理信息神经网络（PINNs）的出现，这些都是提高模型准确性和计算效率的可行途径。本综述不仅全面概述了当前的方法，还概述了未来的研究方向，旨在通过先进的多尺度建模技术，开发更具可持续性、成本效益和耐久性的铺路解决方案。

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引用次数: 0

Quo vadis, wave? Dispersive-SUPG for direct van der Waals simulation (DVS) 何去何从，波浪？用于直接范德华模拟（DVS）的 Dispersive-SUPG

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-10-28 DOI: 10.1016/j.cma.2024.117471

Tianyi Hu, Hector Gomez

Partial differential equations whose solution is dominated by a combination of hyperbolic and dispersive waves are common in multiphase flows. We show that for these problems, the application of classical stabilized finite elements based on Streamline-Upwind/Petrov–Galerkin (SUPG) without accounting for the dispersive features of the solution leads to a downwind discretization and an unstable numerical solution. To address this challenge, we propose the Dispersive-SUPG (D-SUPG) formulation. We apply the Dispersive-SUPG formulation to the Korteweg–de Vries equation and Direct van der Waals Simulations. Numerical results show that Dispersive-SUPG is a high-order accurate and efficient stabilized method, capable of producing stable results when the solution is dominated by either hyperbolic or dispersive waves. We finally applied the proposed algorithm to study cavitating flow over a 2D wedge and a 3D hemisphere and obtained good agreement with theory and experiments.

在多相流中，解由双曲波和色散波组合主导的偏微分方程很常见。我们的研究表明，对于这些问题，应用基于流线-上风/Petrov-Galerkin（SUPG）的经典稳定有限元而不考虑解的色散特征会导致顺风离散化和不稳定的数值解。为了应对这一挑战，我们提出了分散-SUPG（D-SUPG）公式。我们将 Dispersive-SUPG 公式应用于 Korteweg-de Vries 方程和直接范德华模拟。数值结果表明，Dispersive-SUPG 是一种高阶精确、高效的稳定方法，能够在双曲波或色散波主导解的情况下产生稳定的结果。最后，我们应用所提出的算法研究了二维楔形和三维半球上的空化流，结果与理论和实验吻合。

引用次数: 0

Sampling-based adaptive Bayesian quadrature for probabilistic model updating 基于采样的自适应贝叶斯正交法用于概率模型更新

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-10-25 DOI: 10.1016/j.cma.2024.117467

Jingwen Song , Zhanhua Liang , Pengfei Wei , Michael Beer

Bayesian (probabilistic) model updating is a fundamental concept in computational science, allowing for the incorporation of prior beliefs with observed data to reduce prediction uncertainty of a computer simulator. However, the efficient evaluation of posterior probability density functions (PDFs) of model parameters poses challenges, particularly for computationally expansive simulators. This work presents a sampling-based adaptive Bayesian quadrature method to fill this gap. The method is based on approximating the simulator under investigation with a Gaussian process (GP) model, and then a conditional sampling procedure is introduced for generating sample paths, this way to infer a probability distribution for the evidence term. This inferred probability distribution indeed measures the prediction uncertainty of the evidence term, and thus based on which, an acquisition function is proposed to identify the site at which the prediction uncertainty of the GP model contributes the most to that of the evidence term. All the above ingredients finally form an adaptive algorithm for updating the posterior PDFs of model parameters with pre-specified accuracy tolerance. Case studies across numerical examples and engineering applications validate the ability of the proposed method to deal with multi-modal problems, and demonstrate its superiority in terms of computational efficiency and precision for estimating model evidence and posterior PDFs.

贝叶斯（概率）模型更新是计算科学中的一个基本概念，它允许将先验信念与观测数据相结合，以减少计算机模拟器预测的不确定性。然而，对模型参数的后验概率密度函数（PDF）进行有效评估是一项挑战，尤其是对计算量巨大的模拟器而言。本研究提出了一种基于采样的自适应贝叶斯正交方法来填补这一空白。该方法基于用高斯过程（GP）模型逼近所研究的模拟器，然后引入条件采样程序生成样本路径，从而推断出证据项的概率分布。这种推断出的概率分布确实衡量了证据项的预测不确定性，因此在此基础上提出了一种获取函数，以确定 GP 模型的预测不确定性对证据项的预测不确定性影响最大的位置。所有上述要素最终形成了一种自适应算法，用于更新模型参数的后验 PDF，并预先指定精度容限。通过对数值实例和工程应用的案例研究，验证了所提方法处理多模式问题的能力，并证明了其在估计模型证据和后验 PDF 的计算效率和精度方面的优越性。

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引用次数: 0

Neural differentiable modeling with diffusion-based super-resolution for two-dimensional spatiotemporal turbulence 针对二维时空湍流的基于扩散的超分辨率神经可微分建模

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-10-25 DOI: 10.1016/j.cma.2024.117478

Xiantao Fan , Deepak Akhare , Jian-Xun Wang

Simulating spatiotemporal turbulence with high fidelity remains a cornerstone challenge in computational fluid dynamics (CFD) due to its intricate multiscale nature and prohibitive computational demands. Traditional approaches typically employ closure models, which attempt to represent small-scale features in an unresolved manner. However, these methods often sacrifice accuracy and lose high-frequency/wavenumber information, especially in scenarios involving complex flow physics. In this paper, we introduce an innovative neural differentiable modeling framework designed to enhance the predictability and efficiency of spatiotemporal turbulence simulations. Our approach features differentiable hybrid modeling techniques that seamlessly integrate deep neural networks with numerical PDE solvers within a differentiable programming framework, synergizing deep learning with physics-based CFD modeling. Specifically, a hybrid differentiable neural solver is constructed on a coarser grid to capture large-scale turbulent phenomena, followed by the application of a Bayesian conditional diffusion model that generates small-scale turbulence conditioned on large-scale flow predictions. Two innovative hybrid architecture designs are studied, and their performance is evaluated through comparative analysis against conventional large eddy simulation techniques with physics-based subgrid-scale closures and purely data-driven neural solvers. The findings underscore the potential of the neural differentiable modeling framework to significantly enhance the accuracy and computational efficiency of turbulence simulations. This study not only demonstrates the efficacy of merging deep learning with physics-based numerical solvers but also sets a new precedent for advanced CFD modeling techniques, highlighting the transformative impact of differentiable programming in scientific computing.

由于复杂的多尺度性质和过高的计算要求，高保真地模拟时空湍流仍然是计算流体动力学（CFD）的一项基本挑战。传统方法通常采用闭合模型，试图以未解决的方式表示小尺度特征。然而，这些方法往往会牺牲精度并丢失高频/波数信息，尤其是在涉及复杂流动物理的情况下。在本文中，我们介绍了一种创新的神经可微分建模框架，旨在提高时空湍流模拟的可预测性和效率。我们的方法以可微分混合建模技术为特色，在可微分编程框架内将深度神经网络与数值 PDE 求解器无缝集成，使深度学习与基于物理的 CFD 建模协同增效。具体来说，在较粗的网格上构建混合可微分神经求解器，捕捉大尺度湍流现象，然后应用贝叶斯条件扩散模型，以大尺度流动预测为条件生成小尺度湍流。研究了两种创新的混合架构设计，并通过与传统的大涡度模拟技术（基于物理的子网格尺度闭合）和纯数据驱动的神经求解器进行比较分析，评估了它们的性能。研究结果强调了神经可微分建模框架在显著提高湍流模拟的精度和计算效率方面的潜力。这项研究不仅证明了将深度学习与基于物理的数值求解器相结合的功效，还为先进的 CFD 建模技术开创了新的先例，凸显了可微分编程在科学计算中的变革性影响。

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引用次数: 0

Peridynamic topology optimization to improve fracture resistance of structures 优化围动力拓扑结构，提高结构的抗断裂能力

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-10-24 DOI: 10.1016/j.cma.2024.117455

Francisco S. Vieira, Aurélio L. Araújo

In this work we propose a novel peridynamic topology optimization formulation to improve fracture resistance. The main strength of peridynamics is based on the straightforwardness in which crack propagation can be predicted, as a natural part of a peridynamic numerical simulation. This property can be leveraged in a topology optimization framework, in order to obtain fracture resistance designs. Hence, we formulate a meshfree density-based nonlocal topology optimization framework using a bond-based peridynamic formulation. As it is demonstrated in this paper, the classical compliance based solutions are far from optimal in terms of fracture resistance and the designs obtained with the proposed formulation can provide fracture resistant solutions while only reducing slightly the structural stiffness. The proposed formulation is presented along with all the details of the sensitivity analysis and additional numerical aspects of the implementation. Moreover, the peridynamic material model used is presented along with its numerical implementation. Numerical examples demonstrate the accuracy of the computed sensitivities and illustrate the impact and effectiveness of the presented formulation. A thorough study of the optimization parameters is presented and various optimization convergence studies are taken in order to obtain a stable optimization process. All the results are compared to classical compliance minimization designs to illustrate the advantages and capabilities of the proposed framework.

在这项工作中，我们提出了一种新颖的周动态拓扑优化方案，以提高抗断裂性。周向动力学的主要优势在于可以直接预测裂纹扩展，这是周向动力学数值模拟的自然组成部分。这一特性可以在拓扑优化框架中加以利用，以获得抗断裂设计。因此，我们利用基于粘结的周动态计算方法，制定了一个基于无网格密度的非局部拓扑优化框架。正如本文所展示的那样，基于顺应性的经典解决方案在抗断裂性方面远未达到最佳效果，而使用所提出的方案进行设计，可以提供抗断裂解决方案，同时仅略微降低结构刚度。本文介绍了所提出的方案，以及敏感性分析的所有细节和实施过程中的其他数值方面。此外，还介绍了所使用的围动力材料模型及其数值实现。数值示例证明了计算敏感性的准确性，并说明了所提出公式的影响和有效性。对优化参数进行了深入研究，并进行了各种优化收敛研究，以获得稳定的优化过程。所有结果都与经典的顺应性最小化设计进行了比较，以说明拟议框架的优势和能力。

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引用次数: 0

An elasto-visco-plastic constitutive model for snow: Theory and finite element implementation 雪的弹性-粘弹性构成模型：理论与有限元实施

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-10-24 DOI: 10.1016/j.cma.2024.117465

Gianmarco Vallero, Monica Barbero, Fabrizio Barpi, Mauro Borri-Brunetto, Valerio De Biagi

Snow exhibits unique mechanical behaviour due to its evolving properties influenced by temperature, stress conditions, and viscous effects. This paper introduces a nonlinear constitutive model for snow, featuring new formulations for the yield function and strain rate potential, and incorporating viscosity, sintering, and degradation effects. The model is numerically integrated into the Abaqus/Standard FEM software using a fully implicit backward Euler method for time integration and Powell’s hybrid method for linearizing the nonlinear system of equations. The robustness and stability of the numerical scheme ensure accurate simulation of snow behaviour under various loading conditions. The model is finally validated against experimental data available in the literature, demonstrating its effectiveness and reliability in capturing the complex mechanical response of snow.

雪因其受温度、应力条件和粘性效应影响而不断变化的特性，表现出独特的力学行为。本文介绍了雪的非线性结构模型，包括屈服函数和应变率势的新公式，并纳入了粘度、烧结和降解效应。该模型采用全隐式后向欧拉法进行时间积分，并采用鲍威尔混合法对非线性方程组进行线性化，从而在 Abaqus/Standard FEM 软件中实现了数值积分。数值方案的鲁棒性和稳定性确保了在各种加载条件下对雪地行为的精确模拟。该模型最后根据文献中的实验数据进行了验证，证明了其在捕捉雪的复杂机械响应方面的有效性和可靠性。

引用次数: 0

Conditional score-based diffusion models for solving inverse elasticity problems 用于解决反弹性问题的基于条件分值的扩散模型

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-10-24 DOI: 10.1016/j.cma.2024.117425

Agnimitra Dasgupta , Harisankar Ramaswamy , Javier Murgoitio-Esandi , Ken Y. Foo , Runze Li , Qifa Zhou , Brendan F. Kennedy , Assad A. Oberai

We propose a framework to perform Bayesian inference using conditional score-based diffusion models to solve a class of inverse problems in mechanics involving the inference of a specimen’s spatially varying material properties from noisy measurements of its mechanical response to loading. Conditional score-based diffusion models are generative models that learn to approximate the score function of a conditional distribution using samples from the joint distribution. More specifically, the score functions corresponding to multiple realizations of the measurement are approximated using a single neural network, the so-called score network, which is subsequently used to sample the posterior distribution using an appropriate Markov chain Monte Carlo scheme based on Langevin dynamics. Training the score network only requires simulating the forward model. Hence, the proposed approach can accommodate black-box forward models and complex measurement noise. Moreover, once the score network has been trained, it can be re-used to solve the inverse problem for different realizations of the measurements. We demonstrate the efficacy of the proposed approach on a suite of high-dimensional inverse problems in mechanics that involve inferring heterogeneous material properties from noisy measurements. Some examples we consider involve synthetic data, while others include data collected from actual elastography experiments. Further, our applications demonstrate that the proposed approach can handle different measurement modalities, complex patterns in the inferred quantities, non-Gaussian and non-additive noise models, and nonlinear black-box forward models. The results show that the proposed framework can solve large-scale physics-based inverse problems efficiently.

我们提出了一种利用基于条件分值的扩散模型进行贝叶斯推断的框架，以解决力学中的一类逆问题，这些问题涉及根据对试样加载机械响应的噪声测量结果推断试样的空间变化材料特性。基于条件分值的扩散模型是一种生成模型，它利用联合分布的样本来学习近似条件分布的分值函数。更具体地说，使用一个神经网络（即所谓的分数网络）来逼近与测量的多个实现相对应的分数函数，然后使用基于朗文动力学的适当马尔可夫链蒙特卡洛方案对后验分布进行采样。训练得分网络只需要模拟前向模型。因此，所提出的方法可以适应黑箱前向模型和复杂的测量噪声。此外，一旦得分网络训练完成，就可以重新使用它来解决不同测量现实的逆问题。我们在力学领域的一系列高维逆问题上演示了所提方法的功效，这些问题涉及从噪声测量中推断异质材料属性。我们考虑的一些例子涉及合成数据，而其他例子则包括从实际弹性成像实验中收集的数据。此外，我们的应用表明，所提出的方法可以处理不同的测量模式、推断量的复杂模式、非高斯和非加性噪声模型以及非线性黑箱前向模型。结果表明，所提出的框架可以高效地解决基于物理学的大规模逆问题。

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引用次数: 0

Variational Bayesian optimal experimental design with normalizing flows 带有归一化流量的变异贝叶斯优化实验设计

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-10-24 DOI: 10.1016/j.cma.2024.117457

Jiayuan Dong , Christian Jacobsen , Mehdi Khalloufi , Maryam Akram , Wanjiao Liu , Karthik Duraisamy , Xun Huan

Bayesian optimal experimental design (OED) seeks experiments that maximize the expected information gain (EIG) in model parameters. Directly estimating the EIG using nested Monte Carlo is computationally expensive and requires an explicit likelihood. Variational OED (vOED), in contrast, estimates a lower bound of the EIG without likelihood evaluations by approximating the posterior distributions with variational forms, and then tightens the bound by optimizing its variational parameters. We introduce the use of normalizing flows (NFs) for representing variational distributions in vOED; we call this approach vOED-NFs. Specifically, we adopt NFs with a conditional invertible neural network architecture built from compositions of coupling layers, and enhanced with a summary network for data dimension reduction. We present Monte Carlo estimators to the lower bound along with gradient expressions to enable a gradient-based simultaneous optimization of the variational parameters and the design variables. The vOED-NFs algorithm is then validated in two benchmark problems, and demonstrated on a partial differential equation-governed application of cathodic electrophoretic deposition and an implicit likelihood case with stochastic modeling of aphid population. The findings suggest that a composition of 4–5 coupling layers is able to achieve lower EIG estimation bias, under a fixed budget of forward model runs, compared to previous approaches. The resulting NFs produce approximate posteriors that agree well with the true posteriors, able to capture non-Gaussian and multi-modal features effectively.

贝叶斯最优实验设计（OED）寻求模型参数预期信息增益（EIG）最大化的实验。使用嵌套蒙特卡罗直接估计 EIG 的计算成本很高，而且需要明确的似然。与此相反，变异 OED（vOED）通过用变异形式逼近后验分布来估计 EIG 的下限，而无需进行似然法评估，然后通过优化其变异参数来收紧下限。我们引入了归一化流（NFs）来表示 vOED 中的变分分布；我们称这种方法为 vOED-NFs。具体来说，我们采用了由耦合层组成的条件可逆神经网络架构的 NFs，并通过一个用于降低数据维度的汇总网络进行了增强。我们提出了蒙特卡洛下界估计值和梯度表达式，以便对变分参数和设计变量进行基于梯度的同步优化。然后在两个基准问题中验证了 vOED-NFs 算法，并在阴极电泳沉积的偏微分方程控制应用和蚜虫种群随机建模的隐含似然案例中进行了演示。研究结果表明，与以前的方法相比，在前向模型运行的固定预算下，4-5 个耦合层的组合能够实现较低的 EIG 估计偏差。由此产生的 NF 产生的近似后验与真实后验非常吻合，能够有效捕捉非高斯和多模式特征。

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引用次数: 0

Particle Virtual Element Method (PVEM): an agglomeration technique for mesh optimization in explicit Lagrangian free-surface fluid modelling 粒子虚拟元素法（PVEM）：用于显式拉格朗日自由表面流体建模中网格优化的集聚技术

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-10-24 DOI: 10.1016/j.cma.2024.117461

Cheng Fu , Massimiliano Cremonesi , Umberto Perego , Blaž Hudobivnik , Peter Wriggers

Explicit solvers are commonly used for simulating fast dynamic and highly nonlinear engineering problems. However, these solvers are only conditionally stable, requiring very small time-step increments determined by the characteristic length of the smallest, and often most distorted, element in the mesh. In the Lagrangian description of fluid motion, the computational mesh quickly deteriorates. To circumvent this problem, the Particle Finite Element Method (PFEM) creates a new mesh (e.g., through a Delaunay tessellation, based on node positions) when the current one becomes overly distorted. A fast and efficient remeshing technique is therefore of pivotal importance for an effective PFEM implementation in explicit dynamics. Unfortunately, the 3D Delaunay tessellation does not guarantee well-shaped elements, often generating zero- or near-zero-volume elements (slivers), which drastically reduce the stable time-step size. Available mesh optimization techniques have limited applicability due to their high computational cost when runtime remeshing is required. An innovative possibility to overcome this problem is the use of the Virtual Element Method (VEM), a variant of the finite element method that can make use of polyhedral elements of arbitrary shapes and number of nodes. This paper presents the formulation of a 3D first-order Particle Virtual Element Method (PVEM) for weakly compressible flows. Starting from a tetrahedral mesh, poorly shaped elements, such as slivers, are agglomerated to form polyhedral Virtual Elements (VEs) with a controlled characteristic length. This approach ensures full control over the minimum time-step size in explicit dynamics simulations, maintaining stability throughout the entire analysis.

显式求解器通常用于模拟快速动态和高度非线性工程问题。然而，这些求解器仅具有条件稳定性，需要非常小的时间步长增量，该增量由网格中最小元素（通常是扭曲最严重的元素）的特征长度决定。在流体运动的拉格朗日描述中，计算网格会迅速恶化。为了避免这一问题，粒子有限元法（PFEM）会在当前网格过度扭曲时创建一个新网格（例如，通过基于节点位置的 Delaunay 细分）。因此，快速高效的重网格技术对于在显式动力学中有效实施 PFEM 至关重要。遗憾的是，三维 Delaunay 细分并不能保证元素形状良好，经常会产生零或接近零体积元素（切片），从而大大减少了稳定的时间步长。由于需要在运行时重新网格化，现有网格优化技术的计算成本较高，因此适用性有限。克服这一问题的一种创新方法是使用虚拟元素法（VEM），它是有限元法的一种变体，可以使用任意形状和节点数的多面体元素。本文介绍了针对弱可压缩流的三维一阶粒子虚拟元素法（PVEM）。从四面体网格开始，将形状不佳的元素（如切片）聚集在一起，形成具有受控特征长度的多面体虚拟元素（VE）。这种方法可确保在显式动力学模拟中完全控制最小时间步长，并在整个分析过程中保持稳定。

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引用次数: 0