THE BIPOTENTIAL METHOD - A CONSTRUCTIVE APPROACH TO DESIGN THE COMPLETE CONTACT LAW WITH FRICTION AND IMPROVED NUMERICAL ALGORITHMS

Nowadays, the concept of convex potential of dissipation is a powerful tool customarily used to model the constitutive dissipative laws. Unf ortunately, it fails when applied to Coulomb's dry friction contact, w hich is shown in this paper by checking the cyclic monotony condition. Next, a new approach, the bipotential method, is presented and succes sfully applied to the contact law. This enables us to write it in a co mpact form and to uncover an implicit normality rule structure. The ad vantages of the new approach are numerous, among which is emphasized a pretty extension of the calculus of variation. Two minimum principles of the so-called bifunctional are presented for contact problems. Nex t, the bipotential method can be qualified as constitutive in the sens e that it suggests improved numerical algorithms. In particular, it is proved that the complete contact law can be rewritten as a projection equation onto Coulomb's cone. Numerical examples show the feasibility of the algorithm and the computer time reduction with respect to othe r previous numerical approaches. (C) 1998 Elsevier Science Ltd. All ri ghts reserved.