Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Continuum mechanics of line defects in liquid crystals and liquid crystal elastomers

Authors: Amit Acharya and Kaushik Dayal
Journal: Quart. Appl. Math. 72 (2014), 33-64
MSC (2010): Primary 76A15
DOI: https://doi.org/10.1090/S0033-569X-2013-01322-X
Published electronically: November 13, 2013
MathSciNet review: 3185131
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Abstract: This paper generalizes the Ericksen-Leslie continuum model of liquid crystals to allow for dynamically evolving line defect distributions. In analogy with recent mesoscale models of dislocations, we introduce fields that represent defects in orientational and positional order through the incompatibility of the director and deformation `gradient' fields. These fields have several practical implications: first, they enable a clear separation between energetics and kinetics; second, they bypass the need to explicitly track defect motion; third, they allow easy prescription of complex defect kinetics in contrast to usual regularization approaches; and finally, the conservation form of the dynamics of the defect fields has advantages for numerical schemes.

We present a dynamics of the defect fields, motivating the choice physically and geometrically. This dynamics is shown to satisfy the constraints, in this case quite restrictive, imposed by material-frame indifference. The phenomenon of permeation appears as a natural consequence of our kinematic approach. We outline the specialization of the theory to specific material classes such as nematics, cholesterics, smectics and liquid crystal elastomers. We use our approach to derive new, non-singular, finite-energy planar solutions for a family of axial wedge disclinations.

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Additional Information

Amit Acharya
Affiliation: Civil and Environmental Engineering, Carnegie Mellon University
Email: acharyaamit@cmu.edu

Kaushik Dayal
Affiliation: Civil and Environmental Engineering, Carnegie Mellon University
Email: kaushik@cmu.edu

DOI: https://doi.org/10.1090/S0033-569X-2013-01322-X
Keywords: Liquid crystals, disclinations, Ericksen-Leslie theory
Received by editor(s): February 23, 2012
Published electronically: November 13, 2013
Article copyright: © Copyright 2013 Brown University
The copyright for this article reverts to public domain 28 years after publication.

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