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

It is readily seen that when body forces are nonzero ($1 # 0, $2 # 0) the
equations are far more complicated than when body forces are absent. For
the statically determinant case we would probably assume that the material
is at rest so that only the applied air stress is contained in f1 and $2.
However, if we also consider a nonzero velocity field, then $1 and $2 contain
contributions from water drag, Coriolis force, and strength gradients given
by equation (30).
We now return to the governing equations along velocity characteristics
(79), and follow an analogous development. Expansion into components and
use of the new notation provide two simple governing equations:
where the roots are
- sin 2y i d i g
-
1-11 B’ + cos 2y
(94)
These equations are seen to be homogeneous and coefficeints are less complex
than the stress characteristic equations. However, the directions 1-1, depend
on the stress state through both y and B’ and so the difficulties of determining
stress cannot be eliminated.
An important physical property of the velocity field is that no stretching
occurs along velocity characteristic curves. To demonstrate this property
for the AIDJEX plastic model shown for classical plastic models by Hill
(1950), Martin (1975), and others, consider the requirement that at a point
there be no stretching in an arbitrarily chosen direction given by unit
vector
-
where @ indicates the counterclockwise angle between n and the x-axis. If
there is no stretching along this direction, n remains a unit vector and
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