You can find principal components and principal directions using closed-form expression in UFL, see dolfiny/invariants.py at master · michalhabera/dolfiny · GitHub
These UFL expression have to be “evaluated” for specific FE functions as input (displacements or stress tensor is your case). In old FEniCS please use project() for this, in FEniCSX use Expressions and interpolation to get the exact point evaluations.