Comptes Rendus
no. 3
Transient rolling friction model for discrete element simulations of sphere assemblies
Matthew R. Kuhn1 
1Department of Civil Engineering, Donald P. Shiley School of Engineering, University of Portland, 5000 N. Willamette Blvd., Portland, OR 97203, USA
Comptes Rendus. Mécanique, Micromechanics of granular materials – A tribute to Ching S. Chang, Volume 342 (2014) no. 3, pp. 129-140

The rolling resistance between a pair of contacting particles can be modeled with two mechanisms. The first mechanism, already widely addressed in the DEM literature, involves a contact moment between the particles. The second mechanism involves a reduction of the tangential contact force, but without a contact moment. This type of rotational resistance, termed creep-friction, is the subject of the paper. Within the creep-friction literature, the term “creep” does not mean a viscous mechanism, but rather connotes a slight slip that accompanies rolling. Two extremes of particle motions bound the range of creep-friction behaviors: a pure tangential translation is modeled as a Cattaneo–Mindlin interaction, whereas prolonged steady-state rolling corresponds to the traditional wheel–rail problem described by Carter, Poritsky, and others. DEM simulations, however, are dominated by the transient creep-friction rolling conditions that lie between these two extremes. A simplified model is proposed for the three-dimensional transient creep-friction rolling of two spheres. The model is an extension of the work of Dahlberg and Alfredsson, who studied the two-dimensional interactions of disks. The proposed model is applied to two different systems: a pair of spheres and a large dense assembly of spheres. Although creep-friction can reduce the tangential contact force that would otherwise be predicted with Cattaneo–Mindlin theory, a significant force reduction occurs only when the rate of rolling is much greater than the rate of translational sliding and only after a sustained period of rolling. When applied to the deviatoric loading of an assembly of spheres, the proposed creep-friction model has minimal effect on macroscopic strength or stiffness. At the micro-scale of individual contacts, creep-friction does have a modest influence on the incremental contact behavior, although the aggregate effect on the assembly's behavior is minimal.

Published online:
DOI: 10.1016/j.crme.2013.03.002
Keywords: Contact mechanics, Granular materials, Rolling, Hertz

Matthew R. Kuhn  1

1 Department of Civil Engineering, Donald P. Shiley School of Engineering, University of Portland, 5000 N. Willamette Blvd., Portland, OR 97203, USA 
Matthew R. Kuhn. Transient rolling friction model for discrete element simulations of sphere assemblies. Comptes Rendus. Mécanique, Micromechanics of granular materials – A tribute to Ching S. Chang, Volume 342 (2014) no. 3, pp. 129-140. doi: 10.1016/j.crme.2013.03.002
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