Summary
There is an ongoing effort to develop nonsmooth versions of high-order schemes for the simulation of mechanical systems with frictional contact. In this paper, we introduce a particular version of the principle of virtual action, which allows to derive a nonsmooth extensions to the Lobatto IIIA-IIIB methods. The discretization is performed using the ideas of Discrete Mechanics. The schemes are derived by pairing the discretization of the principle of virtual action with a discretization of the contact laws that is consistent with the bilateral constraints of the system. Finally, the properties of the presented schemes, e.g., their convergence behavior, are analyzed using a suitable numerical benchmark example.
