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. Copyright © 2006 John Wiley & Sons, Ltd.