On asymptotic properties for some parameter-dependent variational inequalities

This paper is concerned with asymptotic and monotonicity properties of some parameter-dependent variational inequalities. The main part of the study deals with inequalities modelling friction problems with normal compliance or Tresca’s conditions in which the parameter stands for the friction coefficient. The corresponding inequalities are (generalizations) of variational inequalities of the second kind. We then study an inequality of the first kind representing the elastoplastic torsion problem where the parameter represents the plasticity yield.