Comparison and Validation of Numerical Homogenization Based on Asymptotic Method and Representative Volume Element Method in Thermal Composites

Abstract

This work aims to investigate numerical homogenization methods for thermal composites. Specifically, the accuracy of asymptotic homogenization and representative volume element methods is compared and validated by performing the multiscale and direct analyses of thermal composites. The mathematical formulation of asymptotic homogenization is derived in a heat conduction problem, and the procedure for representative volume method is summarized. To validate the effective thermal conductivity calculated using the homogenization methods, temperature distribution of a homogeneous model is quantitatively compared with the distribution of a heterogeneous model. In a homogeneous model, multiscale analysis is performed by replacing heterogeneous composite microstructure with the homogeneous media whose effective property is calculated from the homogenization methods. On the contrary, a heterogeneous model performs the direct analysis of actual periodic heterogeneous microstructures. In three numerical examples, the accuracy of the homogenization methods is investigated by comparing the maximum and average temperatures of homogeneous and heterogeneous models.