interpretation of anisotropic invariants

hi all,

both anisotropic invariants I₄ and I₅ are required to fully describe the material response of transversely isotropic materials. The invariant I₄ has a direct interpretation as the square of the stretch in the direction of the fiber but I₅ does not have a similar immediate interpretation. if the direction of the fiber is taken to correspond to the E3 coordinate direction then I₄ =C₃₃^2, while I₅ =C₃₃^2+C₁₃^2+_C23^2 and hence I₅ is a measure of the influence of shear on the  transversely isotropic materials (C_ij is component of the right Cauchy–Green tensor)

Are there better interpretation for I₅ ??

awaiting to reply

thank you 

regards

Davood Taghizadeh