Sorting out the elastic anisotropy of transversely isotropic materials

By means of the spectral decomposition of the compliance S and stiffness C tensors for transversely isotropic materials, the elastic loading eigenstates of these anisotropic materials are defined in a simple and efficient manner. It was shown that the necessary parameters for an invariant description of the elastic behavior of transversely isotropic materials are the four eigenvalues, complemented by the eigenangle omega. However, restrictions are imposed on the variational bounds of this parameter, based on the classical thermodynamical requirement for positive definite strain energy density. It is the purpose of this paper to study the influence of the imposed thermodynamic restrictions, along the spectrum of variation of the eigenangle omega, on the type and properties of the corresponding elastic bodies, and describe the limits imposed by the respective values of omega on the elastic properties of anisotropic materials. Based on this study, transversely isotropic media are categorized systematically into four classes, depending on the value of their eigenangle omega, which is sufficient for a monoparametric qualitative characterization of both their elastic properties and their respective toughness.