  We study the relationship between the granular contact angle distribution and
local particle friction on the macroscopic friction and bulk modulus in
non-cohesive disk packings. Molecular dynamics in two dimensions are used to
simulate uniaxial loading-unloading cycles imposed on the granular packings.
While macroscopic Mohr-friction depends on the granular pack geometric details,
it reaches a stationary limit after a finite number of loading-unloading cycles
that render well-defined values for bulk modulus, grain coordination, porosity,
and friction. For random packings and for all polydispersities analyzed, we
found that as inter-particle friction increases, the bulk modulus for the limit
cycle decreases linearly, while the mean coordination number is reduced and the
porosity increased, also as approximately linear functions. On the other hand,
the macroscopic Mohr-friction increases in a monotonous trend with
inter-particle friction. The latter result is compared to a theoretical model
which assumes the existence of sliding planes corresponding to definite
Mohr-friction values. The simulation results for macroscopic friction are well
described by the theoretical model that incorporates the local neighbour angle
distribution that can be quantified through the contact angle entropy. As local
friction is increased, the limit entropy of the neighbour angle distribution is
reduced, thus introducing the geometric component to granular friction.
Surprisingly, once the limit cycle is reached, the Mohr-friction seem to be
insensitive to polydispersity as has been recently reported.
