A new class of fully history-dependent variational-hemivariational inequalities with application to contact mechanics

In this paper, we consider the behaviour of solutions to a class of fully history-dependent variational-hemivariational inequalities with respect to the perturbation of the data. First, the existence and uniqueness of the solution to a class of fully history-dependent variational-hemivariational inequalities is obtained by using a fixed point theorem. Second, we obtain continuous dependence result of solutions with respect to all the data of variational-hemivariational inequalities. Meanwhile, the convergence results of the solutions for the special case of abstract variational inequalities are also given. Finally, to illustrate our main results, we consider a class of viscoelastic contact problem with a long memory. By using our abstract result, we get the continuous dependence of the solutions to frictional contact problem with respect to all the data.