Abstract
Keywords: spectral decomposition, Nitinol, symmetry group, eigenvalues, eigenvectors
For anisotropic elasticity, the elasticity matrix can be regarded as a symmetric linear transformation on the six-dimensional spaces. In these conditions, the elasticity matrix can be expressed in terms of its spectral decomposition. The structures of the spectral decomposition are determined by the sets of invariant subspaces that are consistent with material symmetry. Eigenvectors are, in part, independent of the values of the elastic constants, but the eigenvalues depend on these values. For the cubic symmetry group of crystallography, the structure of the spectral decompositions is presented. A numerical example for the shape memory alloys named Nitinol is presented.