Thermodiffusion in Heterogeneous Elastic Solids and Homogenization

摘要

Overall behavior of microheterogeneous elastic solids in which thermodiffusionoccurs is studied by using homogenization methods. Heterogeneities are characterized by a small positive parameter epsilon. The material coefficients of the coupled system of linear equations describing thermodiffusion depend on epsilon. In the periodic case, when heterogeneities are distributed periodically, the homogenization is performed by applying the method of two-scale asymptotic expansions. The convergence and corrector theorems are formulated for a nonperiodic microstructure. It is shown that the initial conditions for the temperature and chemical potential of the homogenized system are changed in comparison with the primal one provided that the initial conditions for the latter system are nonhomogenous. For a layered composite with periodically distributed layers analytical formulas are derived for all the effective material coefficients. Particular cases are studied by exploiting some available experimental data. The analysis itself and homogenization problem are preceded by an overview of the results concerning thermal problems in microheterogeneous solids and composites.