I.4.6.10 Rotations of vectorial and tensorial Results

Two singleton methods can be used to rotate tensorial or vectorial Results considering a non-symmetric tensor Result:

• “directRotation” has two Result arguments $Q$ and $R$, and returns a new result “$R$” obtained by rotation of $R$ considering that $Q$ is an orthogonal tensor.

• “inverseRotation” has two Result arguments $Q$ and $R$, and returns a new result “$R$” obtained by inverse rotation of $R$ considering that $Q$ is an orthogonal tensor.

More precise information about the rotations is given in section X.B.6. In both cases, it is the responsibility of the user to verify that $Q$ is orthogonal. (No check done by FeResPost.) $R$ can be scalar, vectorial or tensorial. (Scalar Results are not modified by the method.)

Tensorial Result $Q$ can be replaced by a vectorial Result $r$. Then, the methods convert this vectorial Result into an orthogonal rotation tensor $R$ according to Rodrigue’s rotation formula presented in section X.B.7. Note however that according to the expressions in sections X.B.6 and X.B.7, $R=QT$. However, the rotation can easily be inverted using argument $-r$ instead of $r$. (One can also switch “directRotation” and “inverseRotation”, of course.)