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

ate of deformation, we have normalized p such that D; + D:=
= 1 and each of
the six examples then corresponds to a different ratio of shearing to dilating,
measured by 8. The stretching invariants are presented in the first two
columns of Table 1. The normalized principal values to be used in Figure 5
appear in columns 3 and 4; and y, the orientation of p, appears in column 5.
The angle 8 is given in column 6. For the yield surface presented in Figure
5 (we have chosen an arbitrary but representative curve) the stress states
needed to induce each of the stretchings are shown. These principal values
are given in column 7 and 8 of Table 1. For the normal flow rule the princi-
pal directions of D and o are aligned. The tangent to the yield curve is
., .,
given in column 9. Orientation of the characteristic directions is described
in column 10. Finally, in column 11, we state which part of Figure 5 gives
the proper graphic description.
Results are understood most simply if the reader assumes that a normal
flow rule is applicable SO that stress and velocity characteristics coincide.
However, for the more general non-normal flow rule, the results describe
either the stress characteristics or the velocity characteristics, but not
both. To visualize the stress characteristics, select the example according
to the value of 6 associated with either the stress or the stretching state.
For a specific flow rule, 8 and (3 are known for each stress state so that
both pairs of characteristics may be superposed to visualize the complete
set of characteristic directions.
In Figure 5a isotropic contracting is presented. For this case no real
characteristic directions exist because 8 > 3~14. Uniaxial contracting is
shown in Figure 5b, One real characteristic direction exists and it is
oriented parallel to the directions of the larger principal stress. For this
case we could envision that ridges form along the characteristic directions
to allow the deformation to occur. The ridges are orthogonal to the direction
of maximum normal stress. We must remember that this model does not
describe the fornation of a single ridge which must form along an existing
lead, but instead represents the average of an isotropic field of ridges.
However, it is doubtful that the analysis is valid for this condition in
any case. When ridging occurs we expect a hardening model rather than an
ideal plastic model to be required. A hardening plastic model has not been
134