工程材料或多或少地含有某些缺陷,如位错,夹杂物,裂纹等等。这些缺陷的存存,往往严重地影响材料的物理性质。关于缺陷对材料机械性质的影响的专门研究可以追溯到1934年Taylor关于位错的工作,1961年Eshelby处理非均匀夹质物的巧妙方法,1960年Bristow关于含有微观裂纹的弹性体的研究以及1962年Hashin和Shtrikman处理非均匀弹性材料的变分原理。 我们知道这些非统计的方法确实能对某些含有缺陷的材料的有效机械性质给出合理的估计,但是在另外一些情形它们却不适用。这是由于在这些方法中所使用的缺陷的周期分布或均匀随机分布的假定并不真实地反映了材料的微观结构。因此有必要研究某种能考虑到材料微观结构的模型。此外,在实际材料中,不同类型的缺陷往往同时存在。可是以往处理不同的缺陷却要使用不同的方法。因此寻找出一种统一处理的方法可以使问题得以简化。 本文的目的就是要试图解决这两个问题。使用由Siems,Kovacs以及Zhou和Hsieh等发展起来的模拟缺陷的弹性多极子方法,对应地我们发展一个基于微观力学分析的统计理论。这个理论使我们有可能在缺陷的离散微观结构与宏观的连续近似之间建立起一座桥梁,并且可以使我们从一个共同的基础上导出各种类型的缺陷体的宏观性质。 作为这个理论的具体应用,文中 Engineering materials contain more or less certain defects, such as dislocations, inclusions, cracks and so on. The storage of these defects often severely affects the physical properties of the material. Specific studies on the effects of defects on the mechanical properties of materials can be traced back to Taylor’s work on dislocation in 1934, Eshelby’s clever method of handling heterogeneous material in 1961, Bristow’s 1960 study of microcracks containing elastomers, and 1962 Hashin and Shtrikman treat variational principles of inhomogeneous elastic materials. We know that these non-statistical methods do give a reasonable estimate of the effective mechanical properties of some materials that contain defects, but they do not apply in others. This is because the assumption of the periodic or even random distribution of the defects used in these methods does not truly reflect the microstructure of the material. It is therefore necessary to study a model that takes into account the microstructure of the material. In addition, different types of defects tend to coexist in the actual material. But in the past to deal with different shortcomings but to use a different approach. So looking for a unified approach to handling issues can be simplified. The purpose of this article is to try to solve both of these problems. Using the elastic multipole method of simulated defects developed by Siems, Kovacs, and Zhou and Hsieh et al., We develop a statistical theory based on micromechanics analysis. This theory allows us to establish a bridge between the discrete microstructures and macroscopic continuums of defects and allows us to derive the macroscopic properties of various types of defects from a common basis. As a concrete application of this theory, the article