Finite element analysis of three-dimensional contact and impact in large deformation problems

An algorithm that models three-dimensional contact with friction, including cases where large deformations occur is proposed. The algorithm is an extension to three-dimensions of an algorithm for contact previously proposed by Ponthot and Hogge [1]. The present algorithm can be used in implicit or explicit codes, when contact between a rigid and a deformable body or among deformable bodies (multibody contact) is to be determined. The penalty method is used as the contact-friction formulation. Constitutive relations for contact-friction and integration of these relations in a corotational reference system are detailed. In order to provide a good convergence rate, the contact-friction stiffness matrices used are consistent with the time integration process. A simple and fully explicit form was obtained for these matrices. For contact problems involving rigid and deformable bodies, interpenetrations are detected using an iterative procedure. For frictionless multibody contact, a new element that simplifies the gap calculation, eliminating iterative procedures, is proposed. Comparison with benchmark results and the solution of practical examples demonstrate the effectiveness of the algorithm. (C) 1998 Elsevier Science Ltd. All rights reserved.