The Cowin–Mehrabadi theorem for an axis of symmetry

The well-known Cowin–Mehrabadi Theorem deals with necessary and sufficient conditions for a normal n to a symmetry plane. Necessary conditions require that n be a common eigenvector of Cijkk, Cikjk and Cijklnjnl. It is shown that a vector parallel to an axis of symmetry must also satisfy these conditions. An axis of rotational symmetry is also a normal to a plane of symmetry except in the case of a trigonal material. Being a common eigenvector of Cijkk and Cikjk belonging to a nondegenerate eigenvalue guarantees it to be an axis of symmetry.