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

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.