  Granular Solid Hydrodynamics (GSH) is a broad-ranged continual mechanical
description of granular media capable of accounting for static stress
distributions, yield phenomena, propagation and damping of elastic waves, the
critical state, shear band, and fast dense flow. An important input of GSH is
an expression for the elastic energy needed to deform the grains. The original
expression, though useful and simple, has some draw-backs. Therefore, a
slightly more complicated expression is proposed here that eliminates three of
them: (1) The maximal angle at which an inclined layer of grains remains stable
is increased from $26^\circ$ to the more realistic value of $30^\circ$.
(2)Depending on direction and polarization, transverse elastic waves are known
to propagate at slightly different velocities. The old expression neglects
these differences, the new one successfully reproduces them. (3) Most
importantly, the old expression contains only the Drucker-Prager yield surface.
The new one contains in addition those named after Coulomb, Lade-Duncan and
Matsuoka-Nakai -- realizing each, and interpolating between them, by shifting a
single scalar parameter.
