DESIGN OF ENERGY CONSERVING ALGORITHMS FOR FRICTIONLESS DYNAMIC CONTACT PROBLEMS

This paper proposes a formulation of dynamic contact problems which en ables exact algorithmic conservation of linear momentum, angular momen tum, and energy in finite element simulations. It is seen that a Lagra nge multiplier enforcement of an appropriate contact rate constraint p roduces these conservation properties. A related method is presented i n which a penalty regularization of the aforementioned rate constraint is utilized. This penalty method sacrifices the energy conservation p roperty, but is dissipative under all conditions of changing contact s o that the global algorithm remains stable. Notably, it is also shown that augmented Lagrangian iteration utilizing this penalty kernel repr oduces the energy conserving (i.e. Lagrange multiplier) solution to an y desired degree of accuracy. The result is a robust, stable method ev en in the context of large deformations, as is shown by some represent ative numerical examples. in particular, the ability of the formulatio n to produce accurate results where more traditional integration schem es fail is emphasized by the numerical simulations.