Variational and numerical approach to a steady-state rolling problem

A steady-state rolling problem with rigid–plastic, incompressible material and nonlocal Coulomb-contact friction condition is considered. The corresponding primal, penalty and regularized penalty variational formulations are presented and studied. It is shown that the solutions of the penalty and regularized penalty variational problems converge to the solutions of the primal and penalty variational problems, when the penalty and regularization parameters tend to zero. The finite-element approximation of the regularized penalty problem is presented and analysed. An algorithm, combining the finite-element method with convergent successive iterations method of secant-modulus is proposed and applied to solve an illustrative example.