OGS
[tag] local_coordinate_system

A local coordinate system used for tensor transformations.

It offers a simple way for input of anisotropic tensors w.r.t. a coordinate system. The basis vectors form a transformation matrix $$R = (e_0, e_1, e_2)$$. For a given anisotropic tensor $$A$$ parameter with the corresponding [tag] use_local_coordinate_system the tensor is rotated according to the formula: $$A' = R\cdot A\cdot R^T$$.

For computations in transverse isotropic material models, we can create a coordinate system with only one base, where the last base is explicitly given. The other bases are set as implicit and computed from the given base as follows:

• For a 2D coordinate system, the unit vector orthogonal to the given base is used as the first base,
• For a 3D coordinate system, the given base vector, unit_direction, is set as the third base, $${\vec e}_2$$. An arbitrary unit vector orthogonal to $${\vec e}_2$$ is selected as the second base $$e_1$$, and the first base $${\vec e}_0$$ is calculated as $${\vec e}_0 = {\vec e}_1 \times {\vec e}_2$$.