The treatment of the locking phenomenon for a general class of variational inequalities

We present the analysis of a class of variational inequalities depending on a small nonnegative parameter in a singular way, for which direct numerical approximation yield a numerical locking phenomenon. It consists in extending some robust approaches to variational inequalities, mainly, conforming and nonconforming methods. We give general sufficient conditions on the discrete problem insuring a uniform convergence relatively to the small parameter, and consequently avoiding numerical locking.