A hybrid finite element formulation for large-deformation contact mechanics

As is well-known, displacement-based finite elements are prone to the ‘locking’ problem. Thus, employing them for solving contact mechanics problems involving thin structures and almost incompressible materials might require a significant amount of computational effort. Hybrid elements which are based on a two-field Hellinger–Reissner variational principle are known to provide an effective remedy for this locking problem associated with displacement based elements. In this work, we employ the hybrid finite element methodology along with the mortar method towards developing an efficient and robust finite element contact strategy for frictionless two dimensional and axisymmetric problems. The proposed contact formulation can effectively model the contact interaction of thin as well as thick geometries as well as contact between bodies made of almost incompressible materials. Further, for accurate estimation of the contact pressure, a new projection technique is proposed. We demonstrate the excellent coarse mesh accuracy of the proposed formulation through various examples.