Simple Implementation of Asymptotic Homogenization Method for Periodic Composite Materials

Abstract

In this paper, a simple implementation method of Asymptotic homogenization (AH) method is developed with the aid of commercial FEM software as a tool box. Then, abundant structural elements (like beam, shell and solid elements) in commercial software can be used to model unit cell with various complex substructures of periodic materials, while simultaneously reducing the model to a small scale with less amount of calculation. During the implementation, a set of simple displacement boundary conditions are assumed for unit cell, and final effective elastic constant can be directly calculated after several static analysis. Two representative examples of applications are chosen and discussed to verify the validity and applicability of the new implementation method by comparing with other methods. The proposed method is expected to become an effective benchmark for assessing other homogenization theories and extended to other homogenization problems (such as thermal expansion coefficient) in the future.