A mortar segment-to-segment contact method for large deformation solid mechanics

Abstract

Contact modeling is still one of the most difficult aspects of non-linear implicit structural analysis. Most 3D contact algorithms employed today use node-on-segment approaches for contacting dissimilar meshes. Two pass node-on-segment contact approaches have the well known deficiency of locking due to over-constraint. In this work, we develop and demonstrate a segment-to-segment contact approach based on the mortar method. By eliminating the over-constraint, this method appears to be much more robust than the node-on-segment approach. Furthermore, node-on-segment approaches suffer when individual nodes slide out of contact at contact surface boundaries or when contacting nodes slide from facet to facet. This causes jumps in the contact forces due to the discrete nature of the constraint enforcement and difficulties in convergence for implicit solution techniques. These jumps in forces are avoided in the segment-to-segment approach, since penetration is measured by the occluded weighted volume which varies smoothly with perturbations. Until now, all mortar schemes have been developed for small deformation/sliding and have mainly been applied on flat surfaces. Here we will present the integration scheme and the linearization approach used for handling the contact surface integrals in the event of large sliding. The schemes are designed to conserve linear momentum and can be applied to arbitrarily curved 3D surfaces. Although expensive, our numerical examples demonstrate that the approach is far more robust than even smoothed node-on-segment contact techniques. That is, problems previously not solvable with node-on-segment can now be solved with our segment-to-segment contact.