| The mechanical contact is the problem of solids mechanics that presents the most difficult nonlinearity. The good resolution of the frictional contact problem is disrupted by the nonlinearity and the non differentiability of the contact's equations (stick/unstick and the initiation of sliding). Until now, no method could be used to resolve all contact problems. This work is focused on the methods of calculation of the mechanical contact in a more general way. It could be separated in two parts.;The first one concerns the creation of the systems of equations and the algorithm of resolution. The methods more used are the Penalty Method and Lagrangian Augmented Method. Although these methods are simple, they are very difficult to use because the choice of the value of penalty coefficients (normal and tangential). For this reason, a new method, the "Lagrangian Augmented Adapted Method" is proposed. This new method is based on the Lagrangian Augmented Method and on the adaptation of the penalty coefficients. With it, the user does not need to choose the value of penalty coefficients. In addition, this method has the speed of the Penalty Method and the reliability of the Lagrangian Augmented Method.;The second part of this work deals with the calculation of the mechanical contact under a spatial discretization. The method more used is the "Point-Surface" Method. The contact is calculated between every point of one surface and the other surface. This method has many limits, as the representativeness and the regularity of the solution when the boundaries are deformable and irregular. Many researches are done on another method, the "Surface-Surface" Method based on the Mortar Element Method. The mechanical contact is calculated on each node of one surface in function of the two surfaces. With this method the solution is more regular and reliable. But the calculation of the mechanical contact is more difficult, so it can not be used to the three dimensional problems. An adaptation of this method has been proposed to the two and three dimensional problems.;All these methods are tested on some academics and industrials multi-physical problems. |
