Indeterminacy of a dry friction problem with viscous damping involving stiction

TLDR: In this article, a passage to the limit of the usual friction law for one degree of freedom solid where the dynamical friction coefficient is smaller than the static friction coefficient was studied, and it was shown that this law can lose all predictive power.

Abstract: We study a usual friction law for one degree of freedom solid where the dynamical friction coefficient is smaller than the static friction coefficient. We show that this law can be dangerous, because it can lose all predictive power. We first study a passage to the limit to prove that the limit is strongly depending on the data. We secondly study the obtained limit law, which is written with a non maximal monotone multivalued graph; this property implies that the differential inclusion possesses a set of solutions, whose diameter is too big to know the solution with precision. Moreover, the associated numerical scheme does not have a unique solution.