Frictional contact of a nonlinear spring

We describe and analyze a frictional problem for a system with a compressed spring which behaves as if it has a spring constant that is negative over a part of its extension range. As a result, the problem has three critical points. The friction is modeled by the Coulomb law. We show that there are three separate stick regions for some values of the parameters, centered on the critical points. We model three other versions of the process. Then we describe a numerical scheme for the models and present a number of computer simulations.