Using an Anti-Relaxation Step to Improve the Accuracy of the Frictional Contact Solution in a Differential Variational Inequality Framework for the Rigid Body Dynamics Problem

Systems composed of rigid bodies interacting through frictional contact are manifest in several science and engineering problems. The number of contacts can be small, such as in robotics and geared machinery, or large, such as in terramechanics applications, additive manufacturing, farming, food industry, and pharmaceutical industry. Currently, there are two popular approaches for handling the frictional contact problem in dynamic systems. The penalty method calculates the frictional contact force based on the kinematics of the interaction, some representative parameters, and an empirical force law. Alternatively, the complementarity method, based on a differential variational inequality (DVI), enforces non-penetration of rigid bodies via a complementarity condition. This contribution concentrates on the latter approach and investigates the impact of an anti-relaxation step that improves the accuracy of the frictional contact solution. We show that the proposed anti-relaxation step incurs a relatively modest cost to improve the quality of a numerical solution strategy which poses the calculation of the frictional contact forces as a cone-complementarity problem.