  Under external perturbations, inter-particle forces in disordered granular
media are well known to form a heterogeneous distribution with filamentary
patterns. Better understanding these forces and the distribution is important
for predicting the collective behavior of granular media, the media second only
to water as the most manipulated material in global industry. However, studies
in this regard so far have been largely confined to granular media exhibiting
only geometric heterogeneity, leaving the dimension of mechanical heterogeneity
a rather uncharted area. Here, through a FEM contact mechanics model, we show
that a heterogeneous inter-particle force distribution can also emerge from the
dimension of mechanical heterogeneity alone. Specifically, we numerically study
inter-particle forces in packing of mechanically heterogeneous disks arranged
over either a square or a hexagonal lattice and under quasi-static isotropic
compression. Our results show that, a hexagonal packing exhibit a more
heterogeneous inter-particle force distribution than a square packing does. For
both packing lattices, preliminary analysis shows the consistent coexistence of
outliers (i.e., softer disks sustaining larger forces while stiffer disks
sustaining smaller forces) in comparison to their homogeneous counterparts,
which implies the existence of nonlocal effect. Further analysis on the portion
of outliers and on spatial contact force correlations suggest that the
hexagonal packing shows more pronounced nonlocal effect over the square packing
under small mechanical heterogeneity. However, such trend is reversed when
assemblies becomes more mechanically heterogeneous. Lastly, we confirm that, in
the absence of particle reorganization events, contact friction merely plays
the role of packing stabilization while its variation has little effect on
inter-particle forces and their distribution.
