This thesis concerns the study of the yield criterion of the porous materials using the homogeneization, the limit analysis and the interior point optimization. The yield criterion of a porous material using Gurson's model, the most widely accepted for such materials in elasto-platic codes, is investigated. The Gurson model idealizes the porous material as a single cavity in a homothetic cell composed of a rigid plastic Mises material, called the Representative Volume Element (RVE) in the following. In this model, the cavities don't have any interactions or coalescence. Then we use the two limit analysis approaches, via a discretization of the model in finite elements. They lead to non-linear optimization problems, solved either by two commercial (???j'ai change le "cormmecial")codes, XA or MOSEK, both optimization codes based on so-called interior point methods. For porous materials with cylindrical cavities, the Gurson criterion appears to be insufficient. In the generalized plane strain case, an analytical expression of this true criterion must take the form of a function of the loading parameters, at least in a three-dimensional representation. Conversely, for a porous material with spherical cavities, a full 3D model is worked out. The Gurson approach is slightly improved and, for the first time, it is validated by our rigorous static and kinematic approaches. The study of a RVE with 35 cylindrical random cavities confirms a bimodal criterion in generalized plane strain. In plane stress loading, the RVE is not representative. A nonlinear interior point method for solving stress based upper bound problems is proposed. To solve the problem, we used a convex optimizer, written on Matlab, developed at CORE (Centre of Operation Research and Econometrics) of Louvain la Neuve in Belgium. Assuming a linear, continuous or discontinuous virtual velocity field, the method appears to be efficient and general. This method is straightforward, needing only the yield criterion as information on the material
