A rotation-based approach to third medium contact regularization

The third medium contact method utilizes a fictitious “third” medium to implicitly model contact interactions. When contact occurs, the fictitious medium is severely deformed which necessitates numerical regularization to ensure numerical stability. Ultimately, this regularization should promote good element quality but otherwise not interfere with the modeling of the contact mechanics. One approach penalizes both stretch and rotational deformation modes using the displacement Hessian which requires higher order elements. Another approach introduces additional degrees of freedom to penalize an approximation of the rotation gradient which drastically increases the system size. We propose a new regularization based on an approximation of the rotation gradient in the fictitious medium, which does not penalize stretch deformation modes and can be used with first-order elements. The efficacy of our method is exemplified using several numerical examples including benchmark tests, an investigation of parasitic forces in the third medium and a novel application to general loading condition.