for dij

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].