Contact rolling and deformation in granular media

The paper considers rotations at different scales in granular materials: the rotations of individual particles, the rolling and rigid-rotation of particle pairs, the rotational interactions of a particle within its cluster of neighbors, and the rotation of material regions. Numerical, Discrete Element Method (DEM) simulations on two- and three-dimensional (2D and 3D) assemblies show that particle rotations are diverse, that they increase with strain until the material begins to soften, and that they are expressed in spatial patterns, even at small strains. The interactions of a pair of particles are a combination of three modes: a contact deformation mode, a contact rolling mode, and a mode of rigid pair motions. Definitions are presented for each mode, including four different definitions of contact rolling. A rolling curl is also defined, which describes the cumulative rolling of neighboring particles around a central particle or sub-region. At a larger scale, material deformation and rotation are measured within small sub-regions of material, and the material deformation can be attributed to separate contributions of contact rolling, contact deformation, and the rigid-rotation of particle pairs. The diversity and extend of contact rolling were measured in 2D and 3D simulations. A dominant rolling pattern was observed, which resembles the interactions of rolling gears. This pattern can extend to distances of at least six particle diameters from a central particle.