基于图分析的复合材料有效电导率计算新方法
Computation of effective electrical conductivity of composite materials: a novel approach based on analysis of graphs
摘要：
在这项工作中，我们继续调查的不同方法的概念和复合材料的建模。我们关注的全局方法被称为“随机均匀化”。在这种方法中，经典的确定性均匀化技术和程序被用来计算复合材料的宏观参数从它的微观性质。随机部分是由于对一些样本系列进行平均，并且这些样本符合RVE（代表性体积元素）的概念，以减少方差效应。在这篇文章中，我们提出了一种新的方法来计算复合材料的有效电性能-它是基于分析的连接图（和相应的邻接矩阵）为每个样品的复合材料。我们描述如何构建这个矩阵，以考虑到复杂的微观几何形状。我们还解释了什么是电导率的均匀化过程，以及所构造的矩阵与问题的关系。所开发的方法被应用到测试研究的复合材料的微观形态对其导电性的影响。
英文摘要：
In this work we continue the investigation of different approaches to conception and modeling of composite materials. The global method we focus on, is called 'stochastic homogenization'. In this approach, the classical deterministic homogenization techniques and procedures are used to compute the macroscopic parameters of a composite starting from its microscopic properties. The stochastic part is due to averaging over some series of samples, and the fact that these samples fit into the concept of RVE (Representative Volume Element) in order to reduce the variance effect. In this article, we present a novel method for computation of effective electric properties of composites -- it is based on the analysis of the connectivity graph (and the respective adjacency matrix) for each sample of a composite material. We describe how this matrix is constructed in order to take into account complex microscopic geometry. We also explain what we mean by homogenization procedure for electrical conductivity, and how the constructed matrix is related to the problem. The developed method is applied to a test study of the influence of micromorphology of composites materials on their conductivity.
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