Harmonic Decomposition of Elastic Constant Tensor and Crystal Symmetry

Abstract

This paper presents a new outlook on harmonic decomposition method for elastic constant tensor. Harmonic decomposition method is developed in such a way that it is applied to anisotropic engineering materials exhibiting different crystal symmetry. The explicit results for each crystal symmetry types are presented. Numerical examples serve to illustrate and verify the developed method. This new representation of elastic constant tensor is compared with other theories such as orthogonal and non-orthogonal irreducible decompositions in literature. The results demonstrate that there are significant relationships between harmonic, non-orthogonal irreducible and orthogonal irreducible decomposition methods. While in harmonic and non-orthogonal irreducible decomposition methods, decomposition of total scalar part is not orthogonal. It is proposed that it is possible to make these parts orthogonal to each other.