Axes and Planes of Symmetry of an An-isotropic Elastic Material

This book deals with necessary and sufficient conditions for the existence of axes and planes of symmetry. We discuss matrix representation of an elasticity tensor belonging to a trigonal, a tetragonal or a hexagonal material. The planes of symmetry of an anisotropic elastic material (if they exist) can be found by the Cowin-Mehrabadi theorem (1987) and the modified Cowin-Mehrabadi theorem proved by Ting (1996). Using the Cowin-Mehrabadi formalism Ahmad (2010) proved the result that an anisotropic material possesses a plane of symmetry if and only if the matrix associated with the material commutes with the matrix representing the elasticity tensor. A necessary and sufficient condition to determine an axis of symmetry of an anisotropic elastic material is given by Ahmad (2010). We review the Cowin-Mehrabadi theorem for an axis of symmetry and develop a straightforward way to find the matrix representation for a trigonal, a tetragonal or a hexagonal material.

Autorentext

Siddra Rana obtained the degree of MPhil in Applied mathematics in 2010 from NUST Pakistan. Presently, she is working as a Lecturer in the Department of Mathematics, University of Wah, Wah cantt. She has taught various courses of Applied Mathematics at the undergraduate and Postgraduate level. Her research interests are in the field of elasticity.