The meso-scale behavior of anisotropic particle-reinforced thermo-elastic composites

Linear thermo-elasticity equations are derived in this paper for anisotropic, particle-reinforced composite structures at mesoscale. The full set of equations is first derived at microscale where the structure is represented as a three-dimensional body with spherical inclusions of known spatial distribution. Limiting the consideration by infinitesimal strains and assuming that the inclusions are embedded into the body firmly and that there are no any defects at the interface of inclusions, the mesoscale limit of the set of equations is derived as the scale parameter decreases to 0. Convergence of the corresponding solutions is established. Material characteristics at mesoscale are expressed in terms of Dirac distribution corresponding to a structure with point inhomogeneities. It is shown that the effective or macroscale material characteristics evaluated in terms of the mesoscale ones, match the well-known rule of mixtures. A particular case of Ambarcumyan plate with random distribution of spherical inclusions is studied numerically.