On the Mori-Tanaka's method in cracked bodies
On the Mori-Tanaka's method in cracked bodies
复制标题
DOI：
10.1016/0093-6413(86)90018-2
复制
发表时间：
1986-07
影响因子：
2.4
通讯作者：
Y. Benveniste
中科院分区：
文献类型：
--
作者：
Y. Benveniste
本文的目的是将 Mori-Tanaka 方法 [I] 应用于计算裂纹体的有效模量，而不使用等效包含和本征应变概念。这种源自异质介质研究的强大方法修改了Eshelby的等价包含形式主义[2]，从而考虑到非均质性之间的相互作用。它几乎总是应用于涉及椭圆体颗粒或椭圆体孔隙合并成裂缝的问题，它总是与等效包含和本征应变概念联系在一起，例如参见 [3]、[4]、[5]、[6] 和 Mura [7] 的书，以全面介绍这些想法。从本质上讲，该方法的作用是以一种特殊的方式使用全基体介质中单个夹杂物的解，其中考虑了颗粒之间的相互作用。本文提出了森田中方法在直接计算裂纹体有效模量中的应用。为了说明所提出的理论版本并强调其基本假设，我们选择首先在简短的开场部分中将其应用于计算具有球形颗粒的颗粒复合材料的有效体积模量。本文的第二部分也是主要部分涉及具有随机方向裂纹的物体的有效模量。据作者所知，随机裂纹体背景下的现有模型是自洽方案（例如参见[8]、[9]和[10]）和广义自洽方法[11]。本节表明，应用于计算裂纹体有效常数的 Mori-Tanaka 方法的提出版本非常简单。它确实不使用等效包含和本征应变思想，也不使用能量概念，并且很容易从稀浓度分析中发展而来。
The purpose of this paper is to apply the Mori-Tanaka's method [I] to the computation of the effective moduli of cracked bodies without using the equivalent inclusion and eigenstrain concepts. This powerful method which originated in studies of heterogeneous media modifies Eshelby's equivalent inclusion formalism [2], so as to take into account the interaction between the inhomogeneities. Having almost always been applied to problems involving ellipsoidal particles or ellipsoidal pores coalescing into cracks, it has been invariantly linked with the equivalent inclusion and eigenstrain concepts, see for example [3],[4],[5],[6] and the book by Mura [7] for a comprehensive presentation of these ideas. In essence, what the method does, is to use the solution of a single inclusion in the all-matrix medium in a special way which incorporates the interaction between the particles.The present paper presents the application of the Mori-Tanaka's method to the computation of the effective moduli of cracked bodies in a direct manner. In order to illustrate the presented version of the theory and highlight its essential assumptions we chose to apply it first, in the brief opening section, to the computation of the effective bulk modulus of a particulate composite with spherical particles. The second and main section of the paper is concerned with the effective moduli of a body with randomly oriented cracks. To the best knowledge of the author, the existing models in this context of randomly cracked bodies are the self-consistent scheme (see for example [8],[9] and [10]) and the generalized self-conslstent method [11]. It is shown in this section that the presented version of the Mori-Tanaka's method as applied to the computation of the effective constants of cracked bodies is of striking simplicity; it does net use the equivalent inclusion and eigenstrain ideas nor energy concepts, and is readily developed from the dilute concentration anal ysi s.