In this paper, we compare four algorithms solving the quasi-static contact between one elastic body and one rigid obstacle in two dimensions. With the Coulomb’s law of friction, this example exhibits multiple solutions if the friction coefficient is larger than 3. After describing the numerical methods tested in this paper, we study the influence of the parameters of the algorithms on the nature of the obtained solution at convergence. On this academic example, we also compute two existing criteria on the uniqueness of the solution. Finally, for friction coefficient larger than 3, we compute a new sliding solution and observe that not all approaches are able to find it.
Valentine Rey (Sat,) studied this question.