Discrete structures in continuum descriptions of defective crystals-Reference-Cited by-同舟云学术

Discrete structures in continuum descriptions of defective crystals

Published:2016-04-28 Issue:2066 Volume:374 Page:20150172
ISSN:1364-503X
Container-title:Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
language:en
Short-container-title:Phil. Trans. R. Soc. A.

Author:

Parry G. P.^ORCID

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.

Funder

EPSRC

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Link

https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.2015.0172

Reference26 articles.

1. A proposal for a continuum theory of defective crystals

2. Elastic invariants in continuously defective crystals;Davini C;Atti dell’Istituto di Meccanica Teorica ed Applicata,1984

3. Sur l’equilibre et le mouvement d’un systeme de points materials sollecites par d’attraction ou de repulsion mutuelle;Cauchy AL;Ex. Math.,1828

4. Bilby BA. 1960 Continuous distributions of dislocations. In Progress in solid mechanics vol. 1 (ed. I Sneddon) pp. 331–400. Amsterdam The Netherlands: North-Holland.

Cited by 5 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. ALMOST ABELIAN LIE GROUPS, SUBGROUPS AND QUOTIENTS;Journal of Mathematical Sciences;2022-08-27

2. The structure of almost Abelian Lie algebras;International Journal of Mathematics;2022-06-23

3. A Kinematics of Defects in Solid Crystals;Advances in Mechanics and Mathematics;2020

4. Connection and curvature in crystals with non-constant dislocation density;Mathematics and Mechanics of Solids;2018-08-06

5. Geometrical Structure of Two-Dimensional Crystals with Non-Constant Dislocation Density;Journal of Elasticity;2016-12-07