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We consider a class of evolutionary variational inequalities de- pending on a parameter, the so-called viscosity. We recall existence and uniqueness results, both in the viscous and inviscid case. Then we prove that the solution of the inequality involving viscosity converges to the so- lution of the corresponding inviscid problem as the viscosity converges to zero. Finally, we apply these abstract results in the study of two antiplane quasistatic frictional contact problems with viscoelastic and elastic materi- als, respectively. For each of the problems we prove the existence of a unique weak solution; we also provide convergence results, together with their me- chanical interpretation.

A convergence result for evolutionary variational inequalities and applications to antiplane frictional contact problems