Presentation and comparison of selected algorithms for dynamic contact based on the Newmark scheme

The straightforward application of classical time discretization schemes to dynamic contact problems often leads to instabilities at the contact boundary. These show up as artificial oscillations in the contact stresses and displacements at the contact boundary, or an uncontrollable behavior of the total energy. During the last years, several new discretization schemes for contact problems have been developed, which are designed to avoid an instable behavior of the discrete evolution. As a matter of fact, many of these methods are based on one of the most popular time discretization schemes in structural dynamics, the Newmark scheme. Here, we present these algorithms in a consistent notation and discuss the advantages and disadvantages of the respective approaches. Our unifying presentation allows furthermore for a deeper insight into the causes of the instabilities, providing physical as well as formal explanations for an instable behavior of the discrete evolutions. Numerical examples in 3D illustrate the effects of the different methods.