On the Analysis and Solution Structure of Generalized Hemivariational Inclusion Problems

This paper introduces and analyzes a new class of generalized hemivariational inclusion problems. We establish the existence and uniqueness of solutions under mild assumptions and develop an efficient iterative algorithm for their numerical approximation. To demonstrate the practical utility of our theoretical framework, we apply it to a frictional contact problem in elasticity. The model involves an elastic body in contact with a rigid foundation, governed by a nonmonotone friction law that depends on both normal and tangential displacements. Our results provide a comprehensive solution, from theory to computation, for this challenging class of nonsmooth systems.