Résumé
The work presented in this document are related to three different themes. The first theme "Numerical approach for non convexity and instabilities in mechanics" is a continuation of work begun during my thesis and made mainly with P. Alart (LMGC). The second theme "Inverse Methods in Mechanics" is the result of a collaboration with Giuseppe Geymonat (LMGC), and François Hild (LMT Cachan) on a problem of identification of parameters associated with mechanical equations. The last theme deals with more mathematical investigations.