ABSTRACT
Now assume that we want to describe the dielectric displacement in the 1 direction that results from an applied shear stress about the 3 direction (CT6 orCT12= o-2i). We may write the full-and reduced-notation expressions as:
D] = dU2<r\2 + ¿121021 (A12)
And because of the symmetry of stress, we may write that
dijic = dikj (A14)
and thus,
We could go through additional examples to show that, in general, for the normal stresses, the d coefficients in the reduced notation are equal in magnitude to those of the full notation, while for the shear stresses, the d coefficients in the reduced notation are a factor of 2 greater than those used in the full notation. We may state this mathematically as:
dij = dijk when, for am n = 1, 2, or 3; and (A 16)
For the relationship between the full-and reduced-notation description of mechan-
ical behavior, the reader is referred to Nye [39].