In this paper an asymptotic homogenization method for the analysis of
composite materials with periodic microstructure in presence of thermodiffusion
is described. Appropriate down-scaling relations correlating the microscopic
fields to the macroscopic displacements, temperature and mass concentration are
introduced. The effects of the material inhomogeneities are described by
perturbation functions derived from the solution of recursive cell problems.
Exact expressions for the overall elastic and thermodiffusive constants of the
equivalent first order thermodiffusive continuum are derived. The proposed
approach is applied to the case of a two-dimensional bi-phase orthotropic
layered material, where the effective elastic and thermodiffusive properties
can be determined analytically. Considering this illustrative example and
assuming periodic body forces, heat and mass sources acting on the medium, the
solution performed by the first order homogenization approach is compared with
the numerical results obtained by the heterogeneous model.Comment: 40 pages, 13 figure