  We describe experiments that probe the response to a point force of 2D
granular systems under a variety of conditions. Using photoelastic particles to
determine forces at the grain scale, we experimentally show that disorder,
packing structure, friction and texture significantly affect the average force
response in granular systems. For packings with weak disorder, the mean forces
propagate primarily along lattice directions. The width of the response along
these preferred directions grows with depth, increasingly so as the disorder of
the system grows. Also, as the disorder increases, the two propagation
directions of the mean force merge into a single direction. The response
function for the mean force in the most strongly disordered system is
quantitatively consistent with an elastic description for forces applied nearly
normally to a surface. These observations are consistent with recent
predictions of Bouchaud et al. and with the anisotropic elasticity models of
Goldenberg and Goldhirsch. At this time, it is not possible to distinguish
between these two models. The data do not support a diffusive picture, as in
the q-model. This system with shear deformation is characterized by stress
chains that are strongly oriented along an angle of 45 degrees, corresponding
to the compressive direction of the shear deformation. In this case, the
spatial correlation function for force has a range of only one particle size in
the direction transverse to the chains, and varies as a power law in the
direction of the chains, with an exponent of -0.81. The response to forces is
strongest along the direction of the force chains, as expected. Forces applied
in other directions are effectively refocused towards the strong force chain
direction.
