Corner contact problem for an elastic body with a wedge shaped rigid inclusion

This paper presents a new class of contact problems between solids having wedge shaped edges, focusing on the analysis of contact problems in three dimensions defined over a non-convex admissible set. Specifically, contact between a composite body and a rigid obstacle is studied, where the composite consists of an elastic matrix and an incorporated rigid inclusion interacting with an obstacle. A system of inequality type conditions for displacements ensuring non-penetration of solid points is derived. According to the system of restrictions, the set of admissible displacements is provided. The existence of a solution to an energy minimization problem over the admissible set is established. For particular cases of considered contact problems corresponding differential formulations are derived. The main result of this study lays the foundation for a new type of mathematical model for contact problems involving three-dimensional composite materials.