We are interested in the stress distribution in static granular matter. Experiments have found a minimum of the vertical normal stress beneath the apex of a sandpile.
Because of the indeterminacy of static friction force even in the simplest sandpile and the ensuing absence of a constitutive relation between stress and strain (Hooke's law) there is no closed set of equations. Continuum theories, trying to describe the "dip", have to make assumptions on the existence of constitutive relations among the components of the stress tensor itself.
Because it is difficult to measure the stress in real sandpiles, we have done numerical simulations. The simulation is done by a 2-dimensional molecular-dynamics code using polygonal particles. We investigate the dip's dependence on construction history and examine to what extent the different assumptions are justified.