  We study a mathematical model for deformation of glued elastic bodies in 2D
or 3D, which is a linear elasticity system with adhesive force on the glued
surface. We reveal a variational structure of the model and prove the unique
existence of a weak solution based on it. Furthermore, we also consider an
alternating iteration method and show that it is nothing but an alternating
minimizing method of the total energy. The convergence of a monolithic
formulation and the alternating iteration method are numerically studied with
the finite element method.
