单向复合材料损伤刚度的双重均匀化方法

研究了单向复合材料的细观损伤刚度问题。假设单向复合材料具有周期性的细观结构，通过渐近展开方法建立与两尺度坐标主量相关的控制方程。细观损伤用两个损伤变量来描述：裂纹线密度和面密度。通过所提出的双重均匀化方法来探讨它们对复合材料刚度的影响，上述问题结合数值分析，得到复合材料损伤刚度随损伤变量的变化关系。

Double Homogenization Method for Analyzing the Damaged Stiffnesses of Unidirectional Composites

The stiffness reduction induced by micro-damage of unidirectionalcomposites is studied in this paper. The unidirectional composites are supposed tobe composed of periodic microstructures. Through the use of asymptotic expansionmethod, control equations are established which are concerned with two-scalelevel coordinate variables. The damage state is described by two damagevariables: crack density D1 and D2. The influence of the damage variables isconsidered by the double homogenization method. Combined with numericalanalysis, the relations between damaged stiffnesses and damage variables areobtained.