Quadratic invariants of elastic moduli
arXiv:cond-mat/0612506 · doi:10.1093/qjmam/hbm007
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 7 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 (1987) and Ahmad (2002).
20 pages