Spectral decomposition of the linear elastic tensor for trigonal symmetry; classification of symmetry restrictions for arbitrary point groups

Abstract

The linear compliance tensor for trigonal symmetry has four different eigenvalues, two of which have multiplicity 1, the others multiplicity 2. They and the corresponding eigenvectors have been calculated in terms of the seven parameters of the corresponding Voigt matrix. Necessary and sufficient conditions have been derived for these components to guarantee positive eigenvalues and thus a positive strain energy. The hierarchy of restrictions on the linear elastic tensors that follow from Neumann's principle for arbitrary point groups in three dimensions has been established for the standard choice of the Cartesian coordinate system, as well as in coordinate-independent form.