含正交排列夹杂和缺陷材料的等效弹性模量和损伤

研究含正交排列夹杂和缺陷材料的等效弹性模量和损伤，推导了以Eshelby－Mori－Tanaka方法求解多相各向异性复合材料等效弹性模量的简便计算公式，针对含三相正交椭球状夹杂的正交各向异性材料，得到了由细观参量（夹杂的形状、方位和体积分数）表示的等效弹性模量的解析表达式．在此基础上，提出了一个宏细观结合的正交各向异性损伤模型，从而建立了以细观量为参量的含损伤材料的应力应变关系．最后，对影响材料损伤的细观结构参数进行了分析．

THE OVERALL ELASTIC MODULI AND DAMAGE OF THE MATERALS CONTAINING ORTHOGONAL INCLUSIONS AND DEFECTS

The effective elastic moduli and damage of materials containing orthogonal inclusions or defects are investigated in this paper. Based on Eshelby-Mori-Tanaka's theory, a simplified formula of the effective moduli for a multiphase, anisotropic composite is developed. The explicit expressions of the effective elastic compliance tensor of an orthotropic composite reinforced by three mutually perpendicular families of ellipsoidal inclusions are then derived. These expressions contain the micro-structural parameters (shape, orientation and volume fraction of the inclusions) of the composite. A model of orthotropic damage of materials that combines macroscopic mechanical properties with micro-structural parameters of the material is proposed. The stress and strain relation with micro-structural parameters is presented. Furthermore, the effects of the microstructural parameters on the damage of material are analyzed.