Three-dimensional finite element computations for frictional contact problems with non-associated sliding rule

This paper presents an algorithm for solving anisotropic frictional contact problems where the sliding rule is non-associated. The algorithm is based on a variational formulation of the complex interface model that combine the classical unilateral contact law and an anisotropic friction model with a non-associated slip rule. Both the friction condition and the sliding potential are elliptical and have the same principal axes but with different semi-axes ratio. The frictional contact law and its inverse are derived from a single non-differentiable scalar-valued function, called a bi-potential. The convexity properties of the bi-potential permit to associate stationary principles with initial/boundary value problems. With the present formulation, the time-integration of the frictional contact law takes the form of a projection onto a convex set and only one predictor–corrector step addresses all cases (sticking, sliding, no-contact). A solution algorithm is presented and tested on a simple example that shows the strong influence of the slip rule on the frictional behaviour