Comptes Rendus
Transient rolling friction model for discrete element simulations of sphere assemblies
Comptes Rendus. Mécanique, 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
     author = {Matthew R. Kuhn},
     title = {Transient rolling friction model for discrete element simulations of sphere assemblies},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {129--140},
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     year = {2014},
     doi = {10.1016/j.crme.2013.03.002},
     language = {en},
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Matthew R. Kuhn. Transient rolling friction model for discrete element simulations of sphere assemblies. Comptes Rendus. Mécanique, Volume 342 (2014) no. 3, pp. 129-140. doi : 10.1016/j.crme.2013.03.002.

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