Coulomb frictional contact by explicit projection in the cone for finite displacement quasi-static problems

We propose, in this paper, a distinct perspective on the solution of the Coulomb frictional contact problem. By combining the prediction/correction method for the contact force vector with the correction step being a cone projection and writing the friction cone surface in the quadratic form, we directly calculate the contact force. The distance along the friction cone normal is determined by solving a nonlinear problem in closed form. Numerical advantages of this projection are apparent for large values of friction coefficient. Six problems previously indicated as difficult to solve by the node-to-segment discretization and the operator split algorithm are here solved with the new projection algorithm. Discretization follows node-to segment and node-to-face derivations with gap vector defined in a global frame (without tangential and normal decomposition). In addition, we provide source codes for the 2D and 3D contact cases.