On the Determination of Plane and Axial Symmetries in Linear Elasticity and Piezo-Electricity

Abstract

We formulate necessary and sufficient conditions for a unit vector \(\pmb{\nu }\) to generate a plane or axial symmetry of a constitutive tensor. For the elasticity tensor, these conditions consist of two polynomial equations of degree lower than four in the components of \(\pmb{\nu }\). Compared to Cowin–Mehrabadi conditions, this is an improvement, since these equations involve only the normal vector \(\pmb{\nu }\) to the plane symmetry (and no vector perpendicular to \(\pmb{\nu }\)). Similar reduced algebraic conditions are obtained for linear piezo-electricity and for totally symmetric tensors up to order 6.