将点阵玻尔兹曼方法推广到非线性弹性动力学

IF 6.9 1区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY
Henning Müller , Erik Faust , Alexander Schlüter , Ralf Müller
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引用次数: 0

摘要

本文概述了一种用于几何和本构非线性固体力学的晶格玻尔兹曼方法(LBM),以模拟动态加载条件下的大变形。该方法利用矩链方法,其中非线性本构律通过强迫项被纳入。应力和变形措施在参考构形中表示。梯度和散度计算采用有限差分格式,引入了Neumann型和dirichlet型边界条件。数值研究进行了评估所提出的方法,并说明其能力。弱动态单轴拉伸和简单剪切在泊松比范围内的基准试验证明了该方案的可行性,并作为实施的验证。此外,一个涉及弯曲波在悬臂梁中传播的动态测试案例突出了该方法模拟复杂动态现象的潜力。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Extending the Lattice Boltzmann Method to non-linear elastodynamics
This work outlines a Lattice Boltzmann Method (LBM) for geometrically and constitutively non-linear solid mechanics to simulate large deformations under dynamic loading conditions. The method utilises the moment chain approach, where the non-linear constitutive law is incorporated via a forcing term. Stress and deformation measures are expressed in the reference configuration. Finite difference schemes are employed for gradient and divergence computations, and Neumann- and Dirichlet-type boundary conditions are introduced.
Numerical studies are performed to assess the proposed method and illustrate its capabilities. Benchmark tests for weakly dynamic uniaxial tension and simple shear across a range of Poisson’s ratios demonstrate the feasibility of the scheme and serve as validation of the implementation. Furthermore, a dynamic test case involving the propagation of bending waves in a cantilever beam highlights the potential of the method to model complex dynamic phenomena.
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来源期刊
CiteScore
12.70
自引率
15.30%
发文量
719
审稿时长
44 days
期刊介绍: Computer Methods in Applied Mechanics and Engineering stands as a cornerstone in the realm of computational science and engineering. With a history spanning over five decades, the journal has been a key platform for disseminating papers on advanced mathematical modeling and numerical solutions. Interdisciplinary in nature, these contributions encompass mechanics, mathematics, computer science, and various scientific disciplines. The journal welcomes a broad range of computational methods addressing the simulation, analysis, and design of complex physical problems, making it a vital resource for researchers in the field.
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