Homogenization of a thermoelasticity model for a composite with imperfect interface

The goal of this paper is to obtain a macroscopic model for an ε-periodic thermoelastic composite material formed by two components with imperfect contact at the interface. We consider that on the interface between the two materials the tractions and the temperature fluxes are continuous, but both the temperature and the displacement fields have a jump, proportional to the temperature flux and, respectively, to the normal component of the stress tensor. Under suitable hypotheses on the order of magnitude with respect to ε of the elasticity tensors and of the temperature-displacement tensors in the two components of the medium, we derive, via the periodic unfolding method, the homogenized problem, which contains new coupling terms between the limits of the displacements and, respectively, the temperatures from the two components of the composite material.