Unilateral contact of two solids subject to large deformations: Formulation and existence results

The approach that is currently the most widely used for formulating the unilateral frictionless contact between two deformable solids involves two key elements: the orthogonal projection of one potential contact material surface on another and the action-reaction principle of contact forces. In the present paper, we investigate this approach in the general case of large deformations and study unilateral frictionless boundary value problems of elasticity formulated by means of it. The conditions for the orthogonal projection to be unique or further a C-1-diffeomorphism are established. An extended action-reaction principle is explicitly given for the forces acting on a pair of potential contact surfaces. Assuming the solids under consideration can be described by polyconvex hyperelastic laws, we formulate the associated unilateral frictionless boundary value problem as a minimum principle and show the existence of a solution to it.