Alternative Definition of Particle Rolling in a Granular Assembly

The paper presents a definition of rolling between a pair of two-dimensional or three-dimensional particles with a compliant contact. The definition of rolling movement is based upon the shapes of the objects’ surfaces as described with differential geometry. A pseudoinverse of the surface curvatures is used for producing a rolling vector that is tangent to the two objects at their contact. Matrix expressions are presented for the efficient computation of the vector. The rolling vector is objective and is independent of the reference points that are used to track the particle motions. The definition of rolling is applied in a discrete element method simulation of the triaxial compression of three large, dense cubic assemblies: one packing of spherical particles and two packings of nonspherical particles. At small strains, particle rolling was slightly less with the nonspherical particles, but the packing with the greatest coordination number had much less rolling.