Rolling friction of a viscoelastic sphere on a rigid plane in finite deformation

In this work, we study the mechanism of rolling friction that controls the movement of a viscoelastic sphere under large nonlinear deformations over a rigid plane. The study is based on a three-dimensional continuous model formulated in referential coordinates, assuming a Saint Venant–Kirchhoff material with Newtonian internal friction and complemented by appropriate boundary conditions at the contact interface. The model is discretized spatially using finite elements, and its subsequent evolution from initial conditions is followed over time. Several additional numerical experiments, designed with the aid of dimensional analysis, investigate the dependence of the rolling friction coefficient (RFC) on model parameters such as rolling velocity, contact load, and material properties. The results show that the RFC is approximately proportional to the contact load and sphere size and increases linearly with rolling velocity. In contrast to previous studies, the model shows that the RFC increases with the Poisson’s ratio.