Proportional Paths, Barodesy, and Granular Solid Hydrodynamics
  Propotional paths as summed up by the Goldscheider Rule (GR) -- stating that given a constant strain rate, the evolution of the stress maintains the ratios of its components -- is a characteristics of elasto-plastic motion in granular media. Barodesy, a constitutive relation proposed recently by Kolymbas, is a model that, with GR as input, successfully accounts for data from soil mechanical experiments. Granular solid hydrodynamics (GSH), a theory derived from general principles of physics and two assumptions about the basic behavior of granular media, is constructed to qualitatively account for a wide range of observation -- from elastic waves over elasto-plastic motion to rapid dense flow. In this paper, showing the close resemblance of results from Barodesy and GSH, we further validate GSH and provide an understanding for GR. 
Yimin Jiang and Mario Liu
cond-mat.soft