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Cowin-Mehrabadi Theorem in six dimensions

Ahmad F.

Archives of Mechanics

2010

Vol. 62, nr 3

215-222

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 An, with n > 4 must be an axis of isotropy.