Page 324 - Introduction to Continuum Mechanics

308 The Elastic Solid

where as we already know from Section 5.4, E is Young's modulus , v is the Poisson's ratio
and G is the shear modulus and

The compliance matrix is positive definite, therefore the diagonal elements are all positive,
thus

and

i.e.,

Thus,

5.29 Engineering Constants for Transversely Isotropic Elastic Solid

For a transversely isotropic elastic solid, the symmetric stiffness matrix with five inde-
pendent coefficients can be inverted to give a symmetric compliance matrix with also five
independent constants. The compliance matrix is

t To simplify the notation, we drop the subscript Y from E.