AIDJEX Bulletin #40 - Polar Science Center - University of Washington

Since small changes in the yield surface may change the system of equations
from hyperbolic to elliptic, it is of interest to know what the
corresponding change in the actual stress state will be. Hodge (1950) has
shown that a small change in a von Mises yield surface produces small changes
in the stress field in the problem of an expanding circular hole in a plate,
while for a notched bar in tension the stress state does not vary smoothly as
the system goes from hyperbolic to elliptic.
Problems in the plasticity of soils are solved by using a Coulomb yield
function. They differ from metals problems where the materials are typically
assumed incompressible. De Jong (1959) and Haithornwaite (1963) have argued
that if this is to be the case, then a non-normal flow rule must be used.
At the same time, Saint-Venant's hypothesis that the principal directions of
the stress and strain tensors coincide is found to give unrealistic results.
The alternative, formulated by Shield (1955) and Jenike (1961), is to allow
the cohesion of the soil to be a function of density and to allow workhardening.
Spencer (1964) obtains equations governing the velocity field for an
incompressible material, but does not integrate along the characteristic
directions. Likewise, Morrison and Richmond (1976) extend Spencer's result
to include body forces and solve the problem of gravity flow through a
restricting channel. This solution, as with all solutions in soils plasticity,
is for a state of plane strain. When the Coulomb yield criterion is
used the possibility of non-real characteristic roots does not occur, so the
equations are always hyperbolic. The problem of repeated characteristic
roots is not encountered, either.
Recently, Sodhi (1977) has taken the plane strain solution of Morrison
and Richmond (1976) and applied it to the flow of pack ice througharestricting
channel. By correlating lead directions in the icepackwithcharacteristic
directions, he predicts the conditions required for ice breakout to occur
and, by measuring the relative orientation of leads through a point, deduces
the cohesive strength of the ice cover. This model differs both in the
yield surface and the flow rule from the AIDJEX plastic model and the results
are not applicable to our work.
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