Page 321 - Introduction to Continuum Mechanics
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Constitutive Equation for a Transversely isotropic Linearly Elastic Material 305
The addition of Eq. (viii) and Eq. (ix) gives
and Eq. (ix) then gives
Thus, the number of independent coefficients reduces to 5 and we have for a transversely
isotropic elastic solid with the axis of symmetry in the 63 direction the following stress strain
laws
and in contracted notation, the stiffness matrix is
In the above reduction of the elastic coefficients, we demanded that every Sp plane be a
plane of material symmetry so that Eqs. (i) must be satisfied for all ft. Equivalently, we can
demand that the elastic coefficients C,yi/ be the same as C,y/y for all ft and achieve the same
reductions.
The elements of the stiffness matrix satisfy the conditions:
