title: Stress field in granular systems: loop forces and potential formulation.
abstract: The transmission of stress through a marginally stable granular pile in two dimensions is exactly formulated in terms of a vector field of loop forces, and thence in terms of a single scalar potential. This leads to a local constitutive equation coupling the stress tensor to fluctuations in the local geometry. For a disordered pile of rough grains this means the stress tensor components are coupled in a frustrated manner. In piles of rough grains with long range staggered order, frustration is avoided and a simple linear theory follows. We show that piles of smooth grains can be mapped onto a pile of unfrustrated rough grains, indicating that the problems of rough and smooth grains may be fundamentally distinct.
authors.affiliation: Department of Physics, University of Warwick, CV4 7AL Coventry, United Kingdom.
authors.forename: Robin C
authors.initials: RC
authors.lastname: Ball
authors.forename: Raphael
authors.initials: R
authors.lastname: Blumenfeld