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

This paper presents a new time-stepping algorithm for frictional contact problems that exhibits unconditional positive energy dissipation. More specifically, the proposed scheme preserves a priori stability estimates of the continuum problem for both frictionless and frictional contact, leading to improved numerical stability properties in particular. For the normal contact component, the algorithm exhibits full energy conservation between released states, 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 regularization 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 assumed. Complete analyses of these considerations, as well as a detailed description of their finite element implementation, are included in the general finite deformation range. Representative numerical simulations are presented to assess the performance of the newly proposed methods.