Lobatto-type variational integrators for mechanical systems with frictional contact

Abstract

This paper introduces a family of Lobatto IIIA-IIIB methods for simulating mechanical systems with frictional contact. These methods extend the existing schemes by addressing both bilateral and unilateral constraints, as well as set-valued Coulomb friction. The Lobatto IIIA-IIIB methods presented in this paper make a substantial contribution to the ongoing endeavor of developing event-capturing versions of high-order schemes.By stating a generalized version of the principle of virtual action for nonsmooth mechanical systems, the integrators are derived from an appropriate discretization of it. The discrete contact laws are found by discretizing the impenetrabilty condition as well as the Newton-type frictional impact laws in an event-capturing way. The presented discrete contact laws exhibit no contact penetration and satisfy the involved unilateral constraints both on position and on velocity level. This behavior is showcased using benchmark examples.