title: Discrete structures in continuum descriptions of defective crystals.
abstract: I discuss various mathematical constructions that combine together to provide a natural setting for discrete and continuum geometric models of defective crystals. In particular, I provide a quite general list of 'plastic strain variables', which quantifies inelastic behaviour, and exhibit rigorous connections between discrete and continuous mathematical structures associated with crystalline materials that have a correspondingly general constitutive specification.
authors.affiliation: School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK gareth.parry@nottingham.ac.uk.
authors.forename: G P
authors.identifier: http://orcid.org/0000-0001-6256-757X
authors.initials: GP
authors.lastname: Parry
keywords: Lie groups; crystals; defects; discrete structures