  We investigate the Green function of two-dimensional dense random packings of
grains in order to discriminate between the different theories of stress
transmission in granular materials. Our computer simulations allow for a
detailed quantitative investigation of the dynamics which is difficult to
obtain experimentally. We show that both hyperbolic and parabolic models of
stress transmission fail to predict the correct stress distribution in the
studied region of the parameters space. We demonstrate that the compressional
and shear components of the stress compare very well with the predictions of
isotropic elasticity for a wide range of pressures and porosities and for both
frictional and frictionless packings. However, the states used in this study do
not include the critical isostatic point for frictional particles, so that our
results do not preclude the fact that corrections to elasticity may appear at
the critical point of jamming, or for other sample preparation protocols, as
discussed in the main text. We show that the agreement holds in the bulk of the
packings as well as at the boundaries and we validate the linear dependence of
the stress profile width with depth.
