论非均匀材料的热弹性静力学。II。几个基本假设的分析与概括
On the thermo-elastostatics of heterogeneous materials. II. Analyze and generalization of some basic hypotheses
摘要：
一个考虑线性热弹性复合介质，其中包括一个均匀的矩阵包含一个统计均匀的随机集合的椭球形的未涂覆或涂覆的夹杂物。有效属性（如顺应性和热膨胀），以及在相位的应力的第一统计矩估计的一般情况下的非均匀性的热弹性夹杂物的属性。首先，一个简短地再现了最流行的方法中使用的微观力学的基本假设和命题，即：有效场假设，准微晶近似，和假设的“椭球对称”。通过数值解描述的无限大介质中的一个和两个夹杂物的数值解的一些积木表示的有效热弹性性质和应力集中因子的显式的新的表示受到均匀和非均匀远程加载。该方法以本文中提出的新的广义积分方程为背景，可以抛弃上述细观力学的基本概念。这种放弃的结果进行了定量估计的一些建模复合材料增强对齐连续不均匀的纤维。一些新的影响是不可能的，在一个经典的背景下的微观力学的框架检测。
英文摘要：
One considers linearly thermoelastic composite media, which consist of a homogeneous matrix containing a statistically homogeneous random set of ellipsoidal uncoated or coated inclusions. Effective properties (such as compliance and thermal expansion) as well as the first statistical moments of stresses in the phases are estimated for the general case of nonhomogeneity of the thermoelastic inclusion properties. At first, one shortly reproduces both the basic assumptions and propositions of micromechanics used in most popular methods, namely: effective field hypothesis, quasi-crystallite approximation, and the hypothesis of "ellipsoidal symmetry". The explicit new representations of the effective thermoelastic properties and stress concentration factor are expressed through some building blocks described by numerical solutions for both the one and two inclusions inside the infinite medium subjected to both the homogeneous and inhomogeneous remote loading. The method uses as a background the new general integral equation proposed in the accompanied paper and makes it possible to abandon the basic concepts of micromechanics mentioned above. The results of this abandonment are quantitatively estimated for some modeled composite reinforced by aligned continously inhomogeneous fibers. Some new effects are detected that are impossible in the framework of a classical background of micromechanics.
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