It was noted that, within the context of a continuum theory of crystals which contained defects, the elastic scalar invariants were functions - of the lattice vectors and their spatial gradients - which remained invariant under elastic changes of state. In particular, the lattice components of the dislocation density tensor were typical of elastic scalar invariants of the first order. That is, any such invariant which depended upon just the lattice vectors and their first spatial gradient was found to be a function of those components. A representation theorem for elastic scalar invariants of arbitrary finite order was proved.

Elastic Scalar Invariants in the Theory of Defective Crystals. G.P.Parry, M.Silhavy: Proceedings of the Royal Society A, 1999, 455[1992], 4333-46