9. Conclusion

This test case makes it possible to validate the continuous contact formulation combined with X- FEM in the presence of curved contact surfaces with linear and quadratic meshes, in 2D. In particular, it was able to establish the convergence orders for the continuous contact method combined with X- FEM and to verify a convergence in energy of 1 and in displacement of 2 for linear meshes, of 2 in energy and of 3 in movement for quadratic meshes, for sufficiently rich integration schemes, for sufficiently rich integration schemes, when the contact interface is in accordance with the mesh and the mesh is radiant or not in conformity.