Problem of the equilibrium of a two-dimensional elastic body with two contacting thin rigid inclusions

A new nonlinear mathematical model is proposed that describes the equilibrium of a two-dimensional elastic body with two thin rigid inclusions. The problem is formulated as a minimizing problem for the energy functional over a nonconvex set of possible displacements defined in a suitable Sobolev space. The existence of a variational solution to the problem is proved. Optimality conditions and differential relations are obtained that characterize the properties of the solution in the domain and on the inclusion; these conditions are satisfied for sufficiently smooth solutions.