Spatial Coulomb Friction

Abstract

As already discussed in Chapter 1, Coulomb friction does not fit in with the framework of force potentials. Because of its enormous importance for practical applications, however, we will present at least some mathematical formulations of the spatial problem. As we have seen, set-valued force laws may be conveniently stated in terms of complementarities which express the complementary behavior of forces and displacements or velocities, and which finally lead to a linear complementarity problem in standard form as discussed in Chapter 8. Linear complementarity is still available for the planar friction problem and for spatial friction when the friction cone is approximated by a pyramid, as one might easily imagine. If, however, the conic friction law is considered, nonlinearities are involved in the formulation of the complementarity conditions. Thus, one cannot expect linear complementarity to be available. In most cases, this situation is treated with special algorithms such as in [91], [101] and [3], but no formulation as a standard problem is given.