Cowin–Mehrabadi Theorem in six dimensions

Abstract

The Cowin–Mehrabadi Theorem concerning normals to the planes of symmetry of an anisotropic material is generalized to six dimensions. Commutation of the reflection matrix with the 6×6 matrix representing the elasticity tensor in the six-dimensional formulation of the elasticity tensor, provides the condition for the existence of a plane of symmetry. This condition implies the existence of at least two isochoric states for every class except the triclinic one. A simple proof is presented of the fact that an axis of symmetry A_n, with n > 4 must be an axis of isotropy.