A contact-stabilized Newmark method for dynamical contact problems

The numerical integration of dynamical contact problems often leads to instabilities at contact boundaries caused by the non-penetration condition between bodies in contact. Even an energy dissipative modification (see, e.g. (Comp. Meth. Appl. Mech. Eng. 1999; 180:1-26)), which discretizes the non-penetration constraints implicitly, is not able to circumvent artificial oscillations. For this reason, the present paper suggests a contact stabilization in function space, which avoids artificial oscillations at contact interfaces and is also energy dissipative. The key idea of this contact stabilization is an additional L²-projection at contact interfaces, which can be easily added to any existing time integration scheme. In case of a lumped mass matrix, this projection can be carried out completely locally, thus creating only negligible additional numerical cost. For the new scheme, an elementary analysis is given, which is confirmed by numerical findings in an illustrative test example (Hertzian two-body contact).