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**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 nË†a are the three principal directions of the Cauchy stress tensor. Then, the normal traction, Ïƒoct, on this plane is

obtained using (4.5) and the spectral representation for the Cauchy stress (4.16). Similarly, the shear traction, Ï„oct 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.

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