中文摘要：

将均匀化方法和渐近分析（Asymptotic Analysis）与参变量变分原理相结合提出了一种模拟复合材料非线性性能的多尺度数值方法．该方法用渐近分析建立宏一细观变量之间的联系，利用参变量变分原理计算非线性响应，求解过程采用迭代算法．为提高计算精度，针对Von—Mises准则和Tsai—Hill准则，提出了一个基于参变量变分原理的改进算法，算例表明该方法可以显著消除传统方法采用线性展开式构造线性互补条件所带来的误差．

英文摘要：

A numerical method is proposed for elasto-plastic analysis of composite material. Homogenization method using asymptotic expansion is employed to establish the relations between Micro-scale and Meso-scale, while the elasto-plastic responses are solved by a proposed method based on Parametric Variational Principles. An implicit algorithm is employed, but the numerical results are not very accurate because the Parametric Variational Principles just include the first-order approximation of yielding functions in solving linear complementary problems with Lemek algorithm. Therefore, modified Parametric Variation Principles are proposed to solve non-linear complementary problems with second-order approximation of yielding functions. The result is euough accurate when both the two constituted materials satisfy the von-Mises criterion.