Page 326 - Introduction to Continuum Mechanics

310 The Elastic Solid

If TH is the only nonzero stress component, then

and if T 22 is the only nonzero stress component, then

Thus, EI is the Young's modulus in the ej and e 2 directions (i.e., in the plane of isotropy),
v 2i is the Poisson's ratio for the transverse train in the x 2 direction when stressed in the jtj
direction or transverse strain in the jcj direction when stressed in the x 2 direction (i.e.,
Poisson's ratio in the plane of isotropy, v 12 = v 2i) and v 13 is the Poisson's ratio for the
transverse strain in the 63 direction (the axis of transverse isotropy) when stressed in a direction
in the plane of isotropy. We note that since the compliance matrix is symmetric, therefore

23 * 13 -*12
From 2#23 — 7^-, ^E^i — -pr~ and 2E\i - -pr-* it is clear that G\ 2 is the shear modulus
^13 °13 °12
in the plane of transverse isotropy and G\^ is the shear modulus in planes perpendicular to
the plane of transverse isotropy.
Since the compliance matrix is positive definite, therefore, the diagonal elements are
positive definite. That is,

Also,

i.e.,