Quantification of stochastically stable representative volumes for random heterogeneous materials
Quantification of stochastically stable representative volumes for random heterogeneous materials
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DOI：
10.1007/s00419-005-0411-8
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发表时间：
2006-01-01
影响因子：
2.8
通讯作者：
Askes, H
中科院分区：
文献类型：
--
作者：
Gitman, IM;Gitman, MB;Askes, H
本文详细介绍了一个程序，以确定下限的代表性体积元素（RVE）的大小，RVE的大小可以客观地量化为随机非均质材料。在这里，注意力集中在颗粒状材料与各种分布的夹杂物的大小和体积分数的夹杂物。的RVE大小依赖于各种参数进行了广泛的分析。确定性和随机参数进行了分析。此外，加载模式和感兴趣的参数的影响进行了研究。由于RVE尺寸是材料的函数，因此分析了一些材料性质如杨氏模量和泊松比作为影响RVE尺寸的因素。RVE大小的下限被发现作为随机分布的夹杂物的体积分数的函数，从而评估所获得的结果的随机稳定性。为此，一个新定义的随机稳定性（DH稳定性）的概念引入随机效应可以包括在稳定性的考虑。DH稳定性可以看作是经典李雅普诺夫稳定性的推广。如图所示，DH-稳定性提供了一个客观的工具，以建立随机参数波动的RVE的下界性质。
This paper details a procedure to determine lower bounds on the size of representative volume elements (RVEs) by which the size of the RVE can be quantified objectively for random heterogeneous materials. Here, attention is focused on granular materials with various distributions of inclusion size and volume fraction of inclusions. An extensive analysis of the RVE size dependence on the various parameters is performed. Both deterministic and stochastic parameters are analysed. Also, the effects of loading mode and the parameter of interest are studied. As the RVE size is a function of the material, some material properties such as Young's modulus and Poisson's ratio are analysed as factors that influence the RVE size. The lower bound of RVE size is found as a function of the stochastically distributed volume fraction of inclusions; thus the stochastic stability of the obtained results is assessed. To this end a newly defined concept of stochastic stability (DH-stability) is introduced by which stochastic effects can be included in the stability considerations. DH-stability can be seen as an extension of classical Lyapunov stability. As is shown, DH-stability provides an objective tool to establish the lower bound nature of RVEs for fluctuations in stochastic parameters.