Application of the discrete null space method to domain decompositionand large deformation contact problems

Abstract

AbstractWe aim at the development of energy consistent ‘mechanical’ integrators for the differential‐algebraic equations (DAEs) associated with the contact problems under consideration. First steps towards the energy consistent time integration of frictionless dynamic contact problems can be found in the works by Laursen & Chawla [4], Armero & Petöcz [1] and Laursen & Love [5]. Energy consistent mechanical integrators have been recently developed for DAE‐formulations of constrained mechanical systems (e.g. Gonzalez [3]). These works are based on the direct discretization of the underlying DAEs leading to a saddle point system to be solved in each iteration of the iterative solution procedure. Due to the presence of Lagrange multipliers this approach leads to a large number of unknowns and potential conditioning problems. To remedy these drawbacks the discrete null space method (Betsch [2]) has been recently developed. We apply the discrete null space method to both domain decomposition in the framework of nonlinear elastodynamics and large deformation contact problems. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)