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Continuum Mechanics of Line Defects in Liquid Crystals and Liquid Crystal Elastomers

Amit Acharya's picture

Amit Acharya and Kaushik Dayal

 (To appear in Quarterly of Applied Mathematics)

This paper presents a generalization of traditional continuum approaches to liquid crystals and
liquid crystal elastomers 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

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 materialframe
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 aproach to derive new, non-singular,
finite-energy planar solutions for a family of axial wedge disclinations.

PDF icon LCE-defect.pdf576.88 KB


Amit Acharya's picture

The solution for a family of planar finite-energy wedge disclinations in nematics has been added to the revised paper in the main post. To our knowledge, this is the first derivation of finite-energy planar wedge disclination solutions for nematics in the literature.

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