On the relative motions of two rigid bodies at a compliant contact: Application to granular media

We consider the relative motions of a pair of discrete three-dimensional particles that share a common contact point. The contact interactions are characterized by three independent motions: rigid movement, translational deformation, and rotational (rolling and twisting) deformation. The rigid motions are non-objective but satisfy a weakened objectivity condition; whereas, the two types of deformation are objective. Three types of rolling motions are discussed: all are objective and two are independent of the choice of the reference points at which the particle motions are measured. To aid in implementation, tensor and matrix descriptions are provided for each type of motion.