#1587 Implement a new orthogonal policy for the fiber direction.
This can be used to define fibers in a plane orthogonal to a given direction. This useful for analytical meshes where defining fiber vectors can result in singuliar fields near some special points (for instance the poles of a sphere). The implementation to define fibers in a plane orthogonal to a fiber direction along the radial direction of a sphere is as follows:
\underline{\underline{T}}= \underline{\underline{Id}} - \underline{e_r} \otimes \underline{e_r}
\\
\begin{pmatrix}
T_1 & \\
T_2 & \\
T_3 & \\
T_4 & \\
T_5 & \\
T_6 &
\end{pmatrix}_{(\underline{e_x},\underline{e_y},\underline{e_z})}
= \begin{pmatrix}
1 & \\
1 & \\
1 & \\
0 & \\
0 & \\
0 &
\end{pmatrix}_{(\underline{e_x},\underline{e_y},\underline{e_z})}
-
\begin{pmatrix}
\left(\underline{e_r} \cdot \underline{e_x}\right)^2 & \\
\left(\underline{e_r} \cdot \underline{e_y}\right)^2 & \\
\left(\underline{e_r} \cdot \underline{e_z}\right)^2 & \\
\left(\underline{e_r} \cdot \underline{e_x}\right) \left(\underline{e_r} \cdot \underline{e_y}\right) & \\
\left(\underline{e_r} \cdot \underline{e_y}\right) \left(\underline{e_r} \cdot \underline{e_z}\right) & \\
\left(\underline{e_r} \cdot \underline{e_x}\right) \left(\underline{e_r} \cdot \underline{e_z}\right) &
\end{pmatrix}_{(\underline{e_x},\underline{e_y},\underline{e_z})}
I_4^{\perp} = \underline{\underline{T}} : \underline{\underline{C}} = \textrm{Tr} ( \underline{\underline{T}} \cdot \underline{\underline{C}} ) = \begin{pmatrix}
C_{11} & C_{22} & C_{33} & C_{12} & C_{23} & C_{13}
\end{pmatrix}
\begin{pmatrix}
T_1 & \\
T_2 & \\
T_3 & \\
2 T_4 & \\
2 T_5 & \\
2 T_6 &
\end{pmatrix}
\\
\frac{\partial I_4^{\perp}}{\partial \underline{\underline{C}}} = \underline{\underline{T}}
Edited by DIAZ Jerome