确定均质化法中精确周期性边界条件的新解法及其在复合材料刚度预测中的应用

NEW METHOD TO DETERMINE THE EXACT PERIODIC BOUNDARY CONDITIONS FOR MACRO-MICROSCOPIC HOMOGENIZATION ANALYSIS AND ITS APPLICATION ON THE PREDICTION OF EFFECTIVE ELASTIC CONSTANTS OF PERIODIC MATERIALS

通过引进新的特征函数,提出一种新的求解方法,将均质化法中计算特征函数的非奇次积分方程转化为奇次积分方程,得到具有精确的周期性边界条件的均质化方法。利用该方法预测孔洞材料、短纤维增强复合材料刚度的变化,所得结果与用经典方法得到的结果进行比较,验证该方法的可靠性。对于短纤维增强复合材料,分析纤维排列方式对刚度的影响,这是经典的Halpin-Tsai法和Mori-Tanaka法无法预测的,因而文中的方法具有更高的精确度和更广的适应性。

A new method is proposed to determine the exact periodic boundary conditions for the macro-microscopic homogenization analysis of materials with periodic micro-structures. A homogeneous integral equation is derived to replace the conventional inhomogeneous integral equation related to the microscopic mechanical behavior in the basic unit cell by introducing a new characteristic function. Based on the new solution method, the computational problem of the characteristic function subject to initial strains and periodic boundary conditions is reduced to a simple displacement boundary value problem without initial strains, which simplifies the computational process. Applications to the predication of effective elastic constants of materials with various two-dimensional and three-dimensional periodic microstructures are presented. The numerical results are compared with empirical results obtained from the Halpin-Tsai equations, Mori- Tanaka method and conventional homogenization calculations, which proves that the present method is valid and efficient for prediction of the effective elastic constants of materials with various periodic microstructures.