Stresses on a Octahedral plane
Consider now a tetrahedron element similar to that of figure 4.5 with a plane equally inclined to the principal axes. Hence, its normal is given by
where nˆa are the three principal directions of the Cauchy stress tensor. Then, the normal traction, σoct, on this plane is
obtained using (4.5) and the spectral representation for the Cauchy stress (4.16). Similarly, the shear traction, τoct on this plane is
Figure 4.5: Eight octahedral planes equally inclined to the principal axes.
From the definition of principal invariants for stress (4.15) it is easy to verify that
Using the above formula one can compute the octahedral normal and shear traction for stress tensor represented using some arbitrary basis.