The maximal number of degenerate directions for non-piezoelectric media of trigonal symmetry

TL;DR

This paper demonstrates that it is possible to construct a positively defined elastic constant matrix for trigonal media with exactly 16 degenerate directions, advancing understanding of wave propagation in such materials.

Contribution

It introduces a method to construct specific elastic matrices for trigonal media with a precise number of degenerate directions, which was previously unknown.

Findings

Existence of a positively defined elastic matrix with 16 degenerate directions.

Explicit construction method for such matrices.

Enhanced understanding of wave degeneracies in trigonal media.

Abstract

We show that one can construct positively defined matrix of elastic constants representing medium of trigonal symmetry for which exactly 16 distinct degenerate directions exist.