Stable IMEX schemes for a Nitsche-based approximation of elastodynamic contact problems. Selective mass scaling interpretation

We introduce some IMEX schemes (implicit-explicit schemes with an implicit term being linear) for approximating elastodynamic contact problems when the contact condition is taken into account with a Nitsche method. We develop a theoretical and numerical study of the properties of the schemes, especially in terms of stability, provide some numerical comparisons with standard explicit and implicit scheme and propose some improvements to obtain a more reliable approximation of motion for large time steps. We also show how selective mass scaling techniques can be interpreted as IMEX schemes.