Discrete structures in continuum descriptions of defective crystals

Parry, Gareth P.

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 correspond-ingly general constitutive specification.

Citation

Parry, G. P. (2016). Discrete structures in continuum descriptions of defective crystals. Philosophical Transactions A: Mathematical, Physical and Engineering Sciences, 374(2066), https://doi.org/10.1098/rsta.2015.0172

• Journal Article Type: Article
• Online Publication Date: Apr 28, 2016
• Publication Date: Mar 21, 2016
• Deposit Date: Dec 7, 2015
• Publicly Available Date: Mar 21, 2016
• Journal: Philosophical Transactions of the Royal Society A: Mathematical, Physical & Engineering Sciences
• Print ISSN: 1364-503X
• Electronic ISSN: 1471-2962
• Publisher: The Royal Society
• Peer Reviewed: Peer Reviewed
• Volume: 374
• Issue: 2066
• DOI: https://doi.org/10.1098/rsta.2015.0172
• Keywords: Crystals, defects, Lie groups, discrete structures.
• Public URL: https://nottingham-repository.worktribe.com/output/779779
• Publisher URL: http://rsta.royalsocietypublishing.org/content/374/2066/20150172
• Related Public URLs: http://rsta.royalsocietypublishing.org/content/by/year
• Additional Information: Parry GP. 2016. Discrete structures in continuum descriptions of defective crystals. Phil. Trans. R. Soc. A 374: 20150172.; http://dx.doi.org/10.1098/rsta.2015.0172