Method of Fundamental Solution in Thermoelasticity of Random Structure Matrix Composites

V. Buryachenko
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Abstract

One considers linear thermoelastic composite media, which consist of a homogeneous matrix containing a statistically homogeneous random set of aligned homogeneous heterogeneities of non-canonical (i.e. non-ellipsoidal) shape. The representations of the effective properties (effective moduli, thermal expansion, and stored energy) are expressed through the statistical averages of the interface polarization tensors (generalizing the initial concepts, see e.g. [1] and [2]) introduced apparently for the first time. The new general integral equations connecting the stress and strain fields in the point being considered with the stress and strain fields in the surrounding points are obtained for the random fields of heterogeneities. The method is based on a recently developed centering procedure where the notion of a perturbator is introduced in terms of boundary interface integrals estimated by the method of fundamental solution for a single inclusion inside the infinite matrix. This enables one to reconsider basic concepts of micromechanics such as effective field hypothesis, quasi-crystalline approximation, and the hypothesis of ellipsoidal symmetry. The results of this reconsideration are quantitatively estimated for some modeled composite reinforced by aligned homogeneous heterogeneities of non canonical shape. Some new effects are detected that are impossible in the framework of a classical background of micromechanics.
随机结构基复合材料热弹性的基本解方法
一种考虑线性热弹性复合介质,它由一个均匀矩阵组成,其中包含一组统计上均匀的非规范(即非椭球形)形状的排列均匀异质性随机集合。有效性质(有效模量、热膨胀和储存能量)的表示是通过首次明显引入的界面极化张量(推广初始概念,参见例[1]和[2])的统计平均来表示的。对于非均质随机场,得到了连接所考虑点的应力场和周围点的应力场和应变场的新的通用积分方程。该方法基于最近发展的定心过程,其中引入了微扰的概念,以边界界面积分的形式由无限矩阵内单个包含的基本解方法估计。这使人们能够重新考虑微观力学的基本概念,如有效场假设、准晶体近似和椭球对称假设。这种重新考虑的结果是定量估计了一些模拟复合材料的非规范形状的排列均匀异质增强。在经典的微观力学背景框架中不可能发现一些新的效应。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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