Asymptotic behavior of a thin inclusion in an elastic body: the case of comparable rigidity

We consider two linear elastic solids joined through a thin linear elastic interphase. We study the equilibrium problem and the contact law as the thickness of the interphase goes to zero. In [Abdelmoula et al., 1998], using matched asymptotic expansions, it is shown that at order zero the interphase reduces to a perfect interface while at order one the interphase behaves as an imperfect interface, with a transmission condition involving the displacement and the traction vectors at order zero. Here, we report on a study, still in progress, in which we recover the model of perfect interface using a Γ−convergence argument. The model of imperfect interface is obtained by studying the properties of a suitable (weakly converging) sequence of equilibrium solutions.