On the Properties of Anisotropic Engineering Materials Based Upon Orthonormal Representations

Abstract

A decomposition method[5] based upon orthonormal representations is reviewed and improved toexpress any anisotropic engineering tensor showing the effect of the material properties on the structures. A new decomposed form for the stress tensor (example for symmetric second rank tensor) different from the one available in the literature where the engineering understanding is improved, is presented. Numerical examples from different engineering materials serve to illustrate and verify the decomposition procedure. The norm concept of elastic constant tensor and norm ratios are used to study the anisotropy of these materials. It is shown that this method allows to investigate the elastic and mechanical properties of an anisotropic material possessing any material symmetry and determine anisotropy degree of that material. For a material given from an unknown symmetry, it is possible to determine its material symmetry type by this method.