Transversely isotropic elasticity

A transversely isotropic material is symmetric with respect to a rotation about an axis of symmetry. For such a material, if $e_{3}$ is the axis of symmetry, then $C$ matrix can be expressed as:

$C$ matrix has following form:

$$C=\begin{bmatrix}C_{11} & C_{12} & C_{13} & 0 & 0 & 0\\ C_{12} & C_{11} & C_{13} & 0 & 0 & 0\\ C_{13} & C_{13} & C_{33} & 0 & 0 & 0\\ 0 & 0 & 0 & \frac{C_{11}-C_{12}}{2} & 0 & 0\\ 0 & 0 & 0 & 0 & C_{44} & 0\\ 0 & 0 & 0 & 0 & 0 & C_{44} \end{bmatrix}$$

info

We need total 5 parameters to describe a transversely isotropic material.