Rate-dependent projection operators for frictional contact constraints

We develop rate-dependent regularization approaches for three-dimensional frictional contact constraints based on the Kelvin and Maxwell viscoelastic constitutive models. With the present regularization schemes, we aim to provide a basis to better model friction and to stabilize the contact analysis while keeping the contact model as simple as possible. The key feature of the regularization approaches, implemented using an implicit time integrator, is that one can recover in the limit the widely used rate-independent elastoplastic regularization framework without encountering numerical di culties. Intermediate contact tractions are de ned in terms of the relative displacement, the relative velocity, and the regularization parameters. The projection operators operate on the intermediate tractions and yield contact tractions that satisfy all the discretized contact constraints. The use of projection operators allows a systematic implementation of the present regularization schemes. Through numerical simulations, we observed that the Maxwell-type regularization e ectively avoids convergence problems, even for relatively large time step sizes, while the Kelvin-type regularization does not