Implementation of the Jäger contact model for discrete element simulations

Abstract

SUMMARYIn 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, Jürgen Jäger developed an efficient approach for computing the full three-dimensional force between identical elastic spheres that have undergone difficult movement sequences (J. Jäger, New Solutions in Contact Mechanics. WIT Press: Southampton, U.K.). This paper presents a complete Jäger 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 Jäger 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.

Multi-directional behavior of granular materials and its relation to incremental elasto-plasticity

“…Such implementations do not permit frictional dissipation in the form of 29 micro-slip and can result in an unfortunate and physically inadmissible infusion of energy during close cycles of contact movement [40]. To avoid these problems, we used the Jäger algorithm for the tangential force, which can model arbitrary sequences of normal and tangential contact movements [39]. With the Cattaneo-Mindlin contacts, the loading simulations were conducted with an inter-particle friction coefficient µ = 0.55, particle shear modulus G = 29 GPa, and Poisson ratio ν = 0.15.…”

Contact Transience during Slow Loading of Dense Granular Materials

“…The assemblies are large enough to capture the average material behavior but sufficiently small to prevent meso-scale localization, such as shear bands. The contact model was a full implementation of a Hertz-Mindlin contact between elasticfrictional spheres by using the Jäger algorithm, which can model arbitrary sequences of normal and tangential contact movements (Kuhn 2011). The simulations were conducted with an inter-particle friction coefficient µ = 0.60, particle shear modulus G = 29 GPa, and Poisson ratio ν = 0.15.…”

Quasi-static incremental behavior of granular materials: Elastic–plastic coupling and micro-scale dissipation

“…The results discussed above are exclusively for axisymmetric triaxial conditions, in which the initial probe state was established with constant-p triaxial compression (ε 11 < 0) and in which the subsequent triaxial probes were conducted with equal lateral strains, dε 22 = dε 33 .…”