1. Introduction

For the treatment of the touch-friction problem, there is a significant difference between the so-called « discrete » formulations and the so-called « continuous » formulation. The implementations in the calculation codes are based on models such as those developed by Hallquist [], Alart and Curnier [], Laursen and Simo ([]).

The two essential objects of this document are, on the one hand, the description of the derivation of contact elements from a mixed variational formulation of a contact problem between three-dimensional, deformable solids undergoing large transformations, and, on the other hand, the detail of the resolution strategy.

This document progressively builds the touch-friction problem implemented in Code_Aster under the name of « continuous method for touch-friction » activatable via the keyword FORMULATION =” CONTINUE “in DEFI_CONTACT, initially proposed by Ben-Dhia and Zarroug [].

An extensive bibliography can be found at the end of the document. In particular, the four theses defended on the subject by M.Zarroug [], C.Zammali [], M.Torkhani [] and D.Kudawoo [].