Structure preserving and energy dissipative contact approaches for implicit dynamics

Abstract

In this work, several structure preserving and energy dissipative contact approaches are proposed and evaluated. The time integration schemes considered are general with regard to the version of constraint type, but here the emphasis was on mortar contact. The proposed mortar contact approach conserves both linear and angular momentum for mortar contact in a novel way. The proposed time integration scheme can conserve energy or provide strict contact dissipation. In addition, the proposed scheme enforces both gap constraints and gap velocity constraints (i.e., persistency). Using a midstep time integrator often causes energy dissipation during initial impact, here this energy can be recovered in a novel way. Enforcing the gap velocity constraint mitigates the contact chatter of the contact pressure and nodes in many problems. Whereas some approaches enforce the persistency condition and gap constraints simultaneously during the solution of the equations of motion (EOM) requiring multipliers for both constraints included in the equation set, here the gap constraint is solved through the equations of motion and the persistency condition is satisfied in the time integration scheme by the velocity update after the equations of motion. It is shown that this approach is strictly dissipative in that a plastic contact condition can be achieved. Analogous to a coefficient of restitution for rigid bodies, any dissipated energy can then be returned upon release if energy conservation is desired. Structure preserving methods are good for long-time dynamics simulations and energy conserving and strictly dissipative methods can overcome stability issues associated with standard time integration algorithms such as the Newmark method.