The dip under the heap

Yet unsolved is the correct description of the distribution of static forces in a granular system submitted to an arbitrary load. A paradigmatic example for this has been the minimum in the pressure exerted on the basal plane by a heap exactly below its apex. With Jan Hemmingsson and Stéphane Roux we have studied various cellular automata describing the transfer of forces along the direction of gravity and obtained the dip under the heap.

The figure shows the network of forces inside a 2d heap obtained by Jan Hemmingsson using the cellular automaton described in our paper (J. Physique I, 7 , 291-302 (1997))

It is interesting that one can obtain exact results for the stress distribution in small piles despite the non-linear nature of no-tension in the contacts. This has been done in two dimensions for several piles in the paper with Gadi Oron published in Phys. Rev. E Vol. 58, p.2079-2089 (1998) which shows that the pressure distribution on the bottom very much depends on the orientation of the heap packing and the nature of the bottom plate. In three dimensions one finds similar results only that the system sizes studied are not as big as in two dimensions as discussed in a paper published in Physica A Vol.265, p.336-343 (1999)