4.1.1.2 Orthotropic Materials

1. When specifying local as the material axis type, the value is interpreted as a list of three local element node numbers. When specifying zero for all three, the default (1,2,4) is used.

   <mat_axis type="local">0,0,0</mat_axis>
   

2. When using the vector type, you need to define the two generator vectors $a$ and $d$ . These are specified as child elements of the mat_axis element:

   <mat_axis type="vector">
     <a>1,0,0</a>
     <d>0,1,0</d>
   </mat_axis>
   

3. When using the angle type, you need to define the two angles $\theta$ and $\varphi$ in degrees. These are specified as child elements of the mat_axis element:

   <mat_axis type="angles">
     <theta>0</theta>
     <phi>90</phi>
   </mat_axis>
   

   The material axes $\left\{ \mathbf{e}_{r},\mathbf{e}_{\theta},\mathbf{e}_{\varphi}\right\}$ are related to the global Cartesian basis (or local element axes) $\left\{ \mathbf{e}_{1},\mathbf{e}_{2},\mathbf{e}_{3}\right\}$ via $$\begin{aligned}\mathbf{e}_{r} & =\cos\theta\sin\phi\,\mathbf{e}_{1}+\sin\theta\sin\phi\,\mathbf{e}_{2}+\cos\phi\,\mathbf{e}_{3}\\ \mathbf{e}_{\theta} & =-\sin\theta\,\mathbf{e}_{1}+\cos\theta\,\mathbf{e}_{2}\\ \mathbf{e}_{\varphi} & =-\cos\theta\cos\phi\,\mathbf{e}_{1}-\sin\theta\cos\phi\,\mathbf{e}_{2}+\sin\phi\,\mathbf{e}_{3} \end{aligned} \,.$$