A segment-to-segment mortar contact method for quadratic elements and large deformations

This paper describes a new extension of mortar based, segment-to-segment algorithms for large deformation contact analysis, permitting their use when quadratic interpolations are used in the underlying finite element method. The work builds upon results previously described by Puso and Laursen [M.A. Puso, T.A. Laursen, A mortar segment-to-segment contact method for large deformation solid mechanics, Comput. Methods Appl. Mech. Engrg. 193 (2004) 601–629; M.A. Puso, T.A. Laursen, A mortar segment-to-segment frictional contact method for large deformations, Comput. Methods Appl. Mech. Engrg. 193 (2004) 601–629], where methods were developed for quasistatic and implicit dynamic analysis in the context of linear element interpolations. Here, we see that many algorithmic ideas from the linear case can be adopted for use with quadratic elements along with different alternative interpolations of the mortar (contact) multipliers. The result is a class of methods appropriate for use for either mesh tying, true large sliding simulation (frictionless or frictional) and readily admits mixing of element types. Several numerical examples are given to demonstrate the effectiveness of the approach.