Abstract EN:

The purpose of this thesis deals firstly with the analysis of the algebraic problem arising from a two fields mixed formulation (velocity and stress rate fields), and in a second way with the development of an original and very performant structure of the problem issued from the well-known one field displacement (or velocity) formulation. The constitutive laws considered in this work are the incremental ones involving interpolation. The analysis of the two discrete problems allows us to establish a more general theorem that states the equivalence between the two fields formulation and the one field one. Two numerical integration rule criteria are also established and their physical meaning are explained. A lot of algorithms for solving linear or nonlinear systems arising from both finite element formulations (two and single field) are proposed. Their performances are also proved. We ended this work by the presentation of the finite element program which is based upon all these considerations. So it works with the two fields formulation, the single displacement or velocity one and finally it will work simultaneously with both of these approaches (both single and two fields). This thesis is closed by simulations of some mechanical problems.