The Tensorial Anisotropy Index A  extends the Zener ratio for fully anisotropic materials and overcomes the limitation of the AU that is designed for materials exhibiting internal symmetries of elastic crystals, which is not always observed in multi-component composites. It takes into consideration all the 21 coefficients of the fully anisotropic stiffness tensor and covers the directional differences among the stiffness tensor groups.
It is composed of two major parts and , the former referring to components existing in cubic tensor and the latter in anisotropic tensor so that   This first component includes the modified Zener ratio and additionally accounts for directional differences in the material, which exist in orthotropic material, for instance. The second component of this index  covers the influence of stiffness coefficients that are nonzero only for non-cubic materials and remains zero otherwise.
where  is the coefficient of variation for each stiffness group accounting for directional differences of material stiffness, i.e. In cubic materials each stiffness component in groups 1-3 has equal value and thus this expression reduces directly to Zener ratio for cubic materials.
The second component of this index <math>
A^A