Sensitivity Analysis of a Scalar Mechanical Contact Problem with Perturbation of the Tresca’s Friction Law

This paper investigates the sensitivity analysis of a scalar mechanical contact problem described by boundary value involving Tresca’s friction law. The is performed with respect to right-hand source and terms perturbations. In particular, threshold involved in law perturbed, which constitutes main novelty present work existing literature. Hence, we introduce parameterized Tresca its solution characterized using proximal operator associated corresponding perturbed nonsmooth convex functional. Then, invoking extended notion twice epi-differentiability depending on parameter, prove differentiability problem, characterizing derivative as Signorini unilateral conditions. Finally, numerical simulations are provided order illustrate our result.