New solution method for homogenization analysis and its application to the prediction of macroscopic elastic constants of materials with periodic microstructures

摘要

A new solution method is proposed for the homogenization analysis of materials with periodic microstructures. 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 macroscopic elastic constants of materials with various two-dimensional and three-dimensional periodic microstructures are presented. The numerical results are compared with previous results obtained from the Hapin-Tsai equations, Mori-Tanaka method and conventional homogenization calculations, which proves that the present method is valid and efficient for prediction of the macroscopic elastic constants of materials with various periodic microstructures.