In this lecture, we present some mathematical contributions in elasticity , with a focus on the energy approach, and numerical results in this field. In particular, it will be shown that the energy approach is very efficient to compute the singularities on the edge of the glue. Plane and curved interfaces will be analyzed, and it will be demonstrated the necessity of a "at least first order asymptotic theory" in the case of similar rigidity between the adherents and the glue.