Thermodynamic analysis of multiphase periodic structures based on a spatial and temporal multiple scale method
周期性结构热动力时间-空间多尺度分析

A spatial and temporal multiscale asymptotic homogenization method simulating the wave propagation problem in periodic multiphase materials is systematically studied. Generalized function field governing equations of wave propagation are expressed in a unified form with both inertia and velocity items. Amplified spatial and reduced temporal scales are, respectively, introduced to account for spatial and temporal fluctuations and nonlocal effect of the homogenized solution due to material heterogeneity on different time scales, The model is derived from the higher-order homogenization theory with multiple spatial and temporal scales. By combining various orders of homogenized function field equations, the reduced time dependence is eliminated and then the fourth-order differential equations are derived. To avoid the necessity of C^1-continuity in finite element implementation, the C^0-continuous mixed finite element approximation of the resulting nonlocal equations of function field is put forward. Non-FoUrier heat conduction and thermal dynamic problem are computed to demonstrate the efficiency and validity of the theories and models developed and indicate the disadvantages of the classical spatial homogenization.