In the computational mechanics software (Abaqus, Ansys, Comsol, etc), Voigt notation is always used to represent a symmetric tensor by reducing its order.

Now I would ask How can we get the Voigt Notation from second order tensor or fourth order tensor in a very efficient way in Mathematica.

e.g. second order tensor: Array[Subscript[a, ## & @@ Sort[{##}]] &, {6, 6}] // MatrixForm

PS: ‘(Manual) using hand writing’ is not a good way.

Reference Links: https://en.wikipedia.org/wiki/Voigt_notation