UNILATERAL CONTACT OF 2 SOLIDS SUBJECT TO LARGE DEFORMATIONS - FORMULATION AND EXISTENCE RESULTS

The approach that is currently the most widely used for formulating th e unilateral frictionless contact between two deformable solids involv es two key elements: the orthogonal projection of one potential contac t material surface on another and the action-reaction principle of con tact 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 c onditions 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 conta ct surfaces. Assuming the solids under consideration can be described by polyconvex hyperelastic laws, we formulate the associated unilatera l frictionless boundary value problem as a minimum principle and show the existence of a solution to it.