Coulomb friction with rolling resistance as a cone complementarity problem

Coulomb friction model with unilateral contact is a basic, but reliable, to represent the resistance sliding between solid bodies. It nowadays well-known that this can be formulated as second–order cone complementarity problem, or equivalently, variational inequality. In article, enriched take into account rolling, also known rolling friction. Introducing cone, an extended Coulomb's and its dual, formulation of problem shown equivalent standard resistance. Based on formulation, maximum dissipation principle bi-potential function are derived. Several iterative numerical methods based projected fixed point iterations for inequalities block-splitting techniques given. The efficiency these strongly relies computation projection onto cone. original closed-form formula abilities illustrated examples single sphere plane, evolution spheres piles under gravity.