Response of a hexagonal granular packing under a localized overload:   effects of pressure
  We study the response of a two-dimensional hexagonal packing of rigid, frictionless spherical grains due to a vertically downward point force on a single grain at the top layer. We use a statistical approach, where each configuration of the contact forces is equally likely. We find that the response is double-peaked, independantly of the details of boundary conditions. The two peaks lie precisely on the downward lattice directions emanating from the point of application of the force. We examine the influence of the confining pressure applied to the packing. 
S. Ostojic and D. Panja