Thermo-mechanical analysis of periodic multiphase materials by a multiscale asymptotic homogenization approach

A spatial and temporal multiscale asymptotic homogenization method used to simulate thermo-dynamic wave propagation in periodic multiphase materials is systematically studied. A general field governing equation of thermo-dynamic wave propagation is expressed in a unified form with both inertia and velocity terms. Amplified spatial and reduced temporal scales are, respectively, introduced to account for spatial and temporal fluctuations and non-local effects in the homogenized solution due to material heterogeneity and diverse time scales. The model is derived from the higher-order homogenization theory with multiple spatial and temporal scales. It is also shown that the modified higher-order terms bring in a non-local dispersion effect of the microstructure of multiphase materials. One-dimensional non-Fourier heat conduction and dynamic problems under a thermal shock are computed to demonstrate the efficiency and validity of the developed procedure. The results indicate the disadvantages of classical spatial homogenization.