  Stress transmission inside three dimensional granular packings is
investigated using computer simulations. Localized force perturbation
techniques are implemented for frictionless and frictional shallow, ordered,
granular arrays confined by solid boundaries for a range of system sizes.
Stress response profiles for frictional packings agree well with the
predictions for the semi-infinite half plane of classical isotropic elasticity
theory down to boxes of linear dimensions of approximately forty particle
diameters and over several orders of magnitude in the applied force. The
response profiles for frictionless packings exhibit a transitional regime to
strongly anisotropic features with increasing box size. The differences between
the nature of the stress response are shown to be characterized by very
different particle displacement fields.
