Improved implicit integrators for transient impact problems––dynamic frictional dissipation within an admissible conserving framework

Abstract

This work presents a frictional extension of an improved conservative integration framework for dynamic contact, extending the details of the frictionless scheme to encompass Coulomb stick/slip friction and the associated conservation/dissipation. It addresses algorithmic details that do not appear in the frictionless context, establishing an appropriate and objective treatment of relative tangential motion that is necessary to rigorously ensure conservation of angular momentum in the fully discrete setting. It also further extends the functionality of a discrete contact velocity term proposed in the frictionless implementation, using it to preserve conservation or dissipation locally as warranted by the frictional model and effectively enabling an enforcement of the contact constraints independent of energy considerations. The result is a robust implicit algorithmic framework for dynamic frictional impact, viable for large deformation analysis, appropriately conservative or dissipative for both stick and slip phenomena on a local scale, and readily extensible to more complex frictional models.