Characterization of the anisotropic materials capable of exhibiting an isotropic Young or shear or area modulus

By means of the decomposition of an anisotropic elastic tensor into symmetric traceless tensors, the general intrinsic expressions involving no redundant elastic coefficients are obtained for the orientation distribution functions of the Young, shear and area moduli of an anisotropic material. Necessary and sufficient conditions are established for each of these moduli to be isotropic. It is found that an anisotropic material exhibiting an isotropic Young or shear or area modulus can be only either transversely isotropic or orthotropic.