Computational model for 3‐D contact problems with friction based on the penalty method

A model based on the penalty method for 3‐D contact problems with friction is proposed. The friction forces are assumed to follow the Coulomb law, with a slip criterion treated in the context of a standard return mapping algorithm. Consistent linearization of the field equations is performed which leads to a fully implicit scheme with non‐symmetric tangent stiffness which preserves asymptotic quadratic convergence of the Newton‐Raphson method. Numerical results are obtained for some representative examples and compared with existing solutions.