To model cohesionless granular flow using
continuum theory, the usual approach is to assume
the cohesionless CoulombMohr yield condition.
However, this yield condition assumes that the
angle of internal friction is constant, when
according to experimental evidence for most
powders the angle of internal friction is not
constant along the yield locus, but decreases for
decreasing normal stress component
from a maximum value of
. For this reason, we consider here the more
general yield function which applies for
shearindex granular materials, where the angle
of internal friction varies with
. In this case, failure due to frictional slip
between particles occurs when the shear and
normal components of stress
and satisfy the socalled Warren Spring equation
, where
, and are positive constants which are referred to as
the cohesion, tensile strength and shearindex
respectively, and experimental evidence indicates
for many materials that the value of the
shearindex lies between 1 and 2. For many materials, the
cohesion is close to zero and therefore the
notion of a cohesionless shearindex granular
material arises. For such materials, a continuum
theory applying for shearindex cohesionless
granular materials is physically plausible as a
limiting ideal theory, and any analytical
solutions might provide important benchmarks for
numerical schemes. Here, we examine the
cohesionless shearindex theory for the problem
of gravity flow of granular materials through
twodimensional wedgeshaped hoppers, and we
attempt to determine analytical solutions.
Although some analytical solutions are found,
these do not correspond to the actual hopper
problem, but may serve as benchmarks for purely
numerical schemes. The special analytical
solutions obtained are illustrated graphically,
assuming only a symmetrical stress distribution.
