复合材料中的渐近均匀化方法

本文将非均质弹性体的渐近均匀化方法应用于复合材料的宏观与细观分析之中。该方法基于平均化的思想，将复合材料视作由周期性的细观结构所构成，其场变量依赖于宏观和细观两个尺度的坐标变量而变化。通过建立位移和应力的渐近表达式，推导出关于周期性基元的细观平衡方程和细观本构关系，并与有限元数值方法相结合，得到材料的宏观等效性能和细观应力分布。对典型算例的分析，反映出该方法的有效性及准确性。

THE METHOD OF ASYMPTOTIC HOMOGENIZATION IN THE RESEARCH OF COMPOSITE MATERIALS

In this paper, the method of asymptotic homogenization for periodic media is employed for predicting macro and microscopic properties of unidirectional composites. Through the use of asymptotic expansions of the displacement and stress fields and appropriate variational principles, the global homogenized equations and local constitutive relations are established and hence FEM numerical procedure is carried out to solve these equations. By this method,the distributions of stresses and strains at the two levels may be obtained. Examples are given to depict the effectiveness and accuracy of this method.