 Orientation averaging of an axisymmetric stresslet

The angular factor of an axial stresslet is linear in the symmetric traceless rank-two tensor $\mathbf{ee}-I/3$. Hence averaging a collection of directors amounts to averaging this tensor. For uniformly distributed in-plane directions, $⟨\mathbf{ee}⟩=(I-\mathbf{nn})/2$, so $⟨S(\mathbf{ee}-I/3)⟩=-(S/2)(\mathbf{nn}-I/3)$. The averaged director is normal to the plane and its signed strength is reversed and halved.