A New Regularization of Coulomb Friction

We present a new regularization of Coulomb’s law of friction that permits a straight-forward incorporation of frictional forces within existing numerical simulations. Similar to existing regularizations, the proposed modification to Coulomb friction leads to a continuous representation of friction and does not require the identification of transitions between slip and stick. However, unlike more common regularizations, the current reformulation maintains a structure at zero contact velocity that is identical to the classical, discontinuous form of Coulomb friction. The implementation of this regularization is presented through two examples in which slip-stick motion induced by sliding friction is of primary importance. The first is a simple one degree-of-freedom system and illustrates the existence of nontrivial equilibrium states. The second example is a multi-degree-of-freedom system in which the present model provides a computationally efficient scheme for simulating the dissipation arising from sliding friction. For systems in which slip-stick transitions are important the proposed regularization provides a computationally efficient scheme to obtain time-accurate simulations.