Elastic scalar invariants in the theory of defective crystals
- 8 December 1999
- journal article
- research article
- Published by The Royal Society in Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Vol. 455 (1992) , 4333-4346
- https://doi.org/10.1098/rspa.1999.0503
Abstract
In the context of a continuum theory of crystals with defects, the elastic scalar invariants are functions of the lattice vectors and their spatial gradients which remain invariant under elastic changes of state. In particular, the lattice components of the dislocation density tensor are prototypical of elastic scalar invariants of the first order, in the sense that any such invariant which depends just on the lattice vectors and their first spatial gradient turns out to be a function of those components. More generally, a representation theorem for elastic scalar invariants of arbitrary finite order is proven.Keywords
This publication has 10 references indexed in Scilit:
- Equivalence, Invariants and SymmetryPublished by Cambridge University Press (CUP) ,1995
- Material Symmetry in Solid CrystalsPublished by Springer Nature ,1995
- Uniform rearrangement in defective crystalsProceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 1992
- On a class of invariant functionalsProceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 1992
- Equilibrium configurations of defective crystalsArchive for Rational Mechanics and Analysis, 1992
- A complete list of invariants for defective crystalsProceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 1991
- On defect-preserving deformations in crystalsInternational Journal of Plasticity, 1989
- A proposal for a continuum theory of defective crystalsArchive for Rational Mechanics and Analysis, 1986
- Applications of Lie Groups to Differential EquationsPublished by Springer Nature ,1986
- Allgemeine Kontinuumstheorie der Versetzungen und EigenspannungenArchive for Rational Mechanics and Analysis, 1959