An adaptive finite element method for contact problems in finite elasticity

We consider a mortar finite element method for 3D finite deformation frictionless contact problems proposed by Popp et al. (Popp, Gitterle, Gee, & Wall 2010) in a version enabling error estimation and mesh adaptivity. Contact of elastic bodies made of hyperelastic nearly incompressible materials is considered. Mixed formulation of finite elasticity with contact is approximated with hexahedral elements. The contact problem is transformed into an equality constrained nonlinear problem which is solved by the Newton-Raphson method. Error estimation and adaptivity of finite element meshes is used to reduce the error of approximation.