Quadratic invariants of elastic moduli

Abstract

A quadratic invariant is defined as a quadratic form in the elements of a tensor that remains invariant under a group of coordinate transformations. It is proved that there are seven quadratic invariants of the 21-element elastic modulus tensor under SO(3) and 35 under SO(2). This answers some open questions raised by Ting and Ahmad in this journal. © The author 2007. Published by Oxford University Press; all rights reserved.