Formulation and analysis of conserving algorithms for frictionless dynamic contact/impact problems Original Research Article

This paper presents the formulation of conserving time-stepping algorithms for frictionless dynamic contact of solids. A new class of finite element methods is proposed for the solution of these problems that exhibit the same conservation laws as the underlying continuum dynamical system. The proposed methods are based on a penalty regularization of the constrained contact problem, and lead to full conservation of the total energy of the system (including the regularization penalty potential) during persistent contact, and restoration of the original energy upon release. Both linear and angular momenta are conserved by the scheme. Furthermore, the newly developed methods have the ability to enforce the associated constraints in the velocity besides the impenetrability constraint in the displacements, while preserving the conservation/restoration properties of the final numerical scheme. A modification of these schemes is described that assures positive energy dissipation if desired (even in the highly nonlinear setting of contact/impact problems), leading to contact schemes with high-frequency energy dissipation. Representative numerical simulations are presented illustrating the performance of the proposed numerical schemes.