Coupled Treatment of Frictional Contact Problems in a Reduced System and Applications in Large Deformation Context

Abstract

In many metal forming processes and other industrial applications such as joint problems, two or more bodies come into contact with friction and they may undergo large deformation. In such processes nonlinearities arise in geometry, constitutive relation as well as variable contact and friction conditions. Since these nonlinearities make it hard to solve such problems, in particular the contact nonlinearities are non-smooth, a reliable and efficient solution algorithm is necessary. In the literature, large deformation contact problems with friction have almost exclusively been treated by penalty methods (Hallquist, 1983; ANSYS, 1993). Much information points to the fact that the penalty methods have some drawbacks concerning numerical stability and precision, in particular for friction simulation. By means of a theory called ISM (Implicit Standard Materials), De Saxce and Feng (1991) propose an augmented Lagrangian formulation in which, the unilateral contact and the friction are coupled. The frictional contact problem is treated by solving a reduced system. The aim of the present paper is to constitute a brief outline and an extension of previous research in large deformation context and to present some computational examples of nonlinear analysis of contact problems.