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

Fig. 1. Yield surface expressed in terms of invariants a1 and
aII. Slope aoII/3o1 = b!(o,, p") is measured by angle 6 so
that b' = tan B. The stretching vector lies at angle 8,
which satisfies 8 - B = 7r/2 when a normal flow rule is
assumed.
If the potential function 11, is set equal to the yield function Cp in this
expression, then the normal flow rule is obtained. Rewriting the flow rule
in terms of the stress invariants gives
where
11, = ll,(uI, aII, p*) is a potential function
o' - = o - - oI & is the stress deviator, and
X 2 0 is a non-negative scalar.
The potential function 11,
is defined independently to describe the response
of the material. If we choose I# to be of the form
119