A new dissipative time-stepping algorithm for frictional contact problems:formulation and analysis

This paper presents a new time-stepping algorithm for frictional contact pr oblems that exhibits unconditional positive energy dissipation. More specif ically, the proposed scheme preserves a priori stability estimates of the c ontinuum problem for both frictionless and frictional contact, leading to i mproved numerical stability properties in particular. For the normal contac t component, the algorithm exhibits full energy conservation between releas ed stales, while the energy does not increase over its initial value due to the enforcement of the normal contact constraint during persistent contact . A penalty regularization is considered to this purpose. A new regularizat ion of the stick conditions is considered for the frictional part. The new scheme is shown rigorously to exhibit positive energy dissipation like the continuum physical problem in this frictional case. Coulomb friction is ass umed. Complete analyses of these considerations, as well as a detailed desc ription of their finite element implementation are included in the general finite deformation range. Representative numerical simulations are presente d to assess the performance of the newly proposed methods. (C) 1999 Elsevie r Science S.A. All rights reserved.