  In three-dimensional discrete element method (DEM) simulations, the particle
motions within a granular assembly can produce bewildering sequences of
movements at the contacts between particle pairs. With frictional contacts, the
relationship between contact movement and force is non-linear and
path-dependent, requiring an efficient means of computing the forces and
storing their histories. By cleverly applying the principles of Cattaneo,
Mindlin, and Deresiewicz, Jurgen Jager developed an efficient approach for
computing the full three-dimensional force between identical elastic spheres
that have undergone difficult movement sequences (J. Jager, New Solutions in
Contact Mechanics. WIT Press: Southampton, U.K.). This paper presents a
complete Jager algorithm that can be incorporated into DEM codes and also
describes three special provisions for DEM simulations: (1) a method for
handling particle pairs that undergo complex tumbling and twirling motions in
three-dimensions; (2) a compact data structure for storing the loading history
of the many contacts in a large assembly; and (3) an approximation of the Jager
algorithm that reduces memory demand. The algorithm addresses contact
translations between elastic spheres having identical properties, but it does
not resolve the tractions produced by twisting or rolling motions. A
performance test demonstrates that the algorithm can be applied in a DEM code
with modest increases in computation time but with more substantial increases
in required storage.
