A finite element method for contact/impact

Ideas from the analysis of differential-algebraic equations are applied to the numerical solution of frictionless contact/impact problems in solid mechanics. Index-one and two formulations for dynamic contact-impact within the context of the finite element method are derived. The resulting equations are shown to stabilize the kinematic fields at the contact interface, at the expense of a small energy loss, which is shown to decrease consistently with mesh refinement. This energy dissipation is shown to be necessary for the establishment of persistent contact. A Newmark-type time integration scheme is derived from the proposed formulation, and shown to yield excellent results in modeling the transition to contact/impact. (C) 1998 Elsevier Science B.V. All rights reserved.