Numerical modeling of contact problems with the finite element method utilizing a B-Spline surface for contact surface smoothing

Abstract The basic aim of this work is to present a method to treat structural mechanics problems dealing with tridimensional contact and large elastic deformations. The formulation presented in this article offers a B-Spline based discretization for the contact surface, which solves the continuity problems presented by the classic Lagrangian contact element formulation. A B-Spline surface is utilized to discretize the contact surface, and the B-Spline basis functions are used to distribute the contact forces between the contact surfaces nodes. The finite element utilized is an 8-node hexahedron, and the formulation is continuum mechanics based, written in the current configuration, utilizing a neo-Hookean material model. The contact restrictions are enforced by the augmented Lagrangian method.