Do not use the Voigt notation ![edit source]
The projection of second order tensor in the orthonormal base is not the Voigt one. I think it's a better idea to introduce real base.
The stress and strain tensors are now defined by :
Then once constructs the bound matrix in the orthonormal base
the rotation matrix in base.
is the rotation along the axis in the : base
The associated rotation in the base is :
The rotation of a second order tensor is now defined by :
The élasticity tensor in the : is defined in the : by
and is rotated by: