Solutions analytiques de problèmes de contact en grandes déformations

It is essential for an engineer to verify the exactitude of the numerical tools he is using, as it is his duty to ensure that they give the expected solution to a given problem. In a finite-element code, this can be achieved by using analytical solutions when they exist, or by the method of manufactured solutions (MMS). In this work, we propose to extend the MMS to large deformation unilateral contact problems for which, to our knowledge, there exists no simple analytical solutions. We will show how this method can be a very efficient verification tool for the engineer. We will also study the precision and convergence order of different choices of mixed spaces (displacement-contact pressure), on triangular and quadrangular elements.