On the adaptive finite element method of steady-state rolling contact for hyperelasticity in finite deformations Original Research Article

In this paper, we present an adaptive finite element method for steady-state rolling contact in finite deformations along with a residual based a posteriori error estimator for rolling contact problem with Coulomb friction. A general formulation of rolling contact geometry is derived from the point of view of differential geometry. Solvability conditions for the rolling contact problems are discussed. We use Newtonʹs method to solve variational equations derived from a penalty regularization of the finite element approximation of the rolling contact problem. We provide a numerical example to illustrate the method.