Metric theory of nematoelastic shells

TL;DR

This paper develops a theoretical framework for understanding how nematoelastic shells reshape into cone or anticone forms during nematic-isotropic transitions, influenced by topological defects and doping, with implications for material design.

Contribution

It introduces a metric theory linking shell shape to nematic order parameters, accounting for defect cores and doping effects, advancing the understanding of nematoelastic shell morphologies.

Findings

Shell shape depends on topological defects and doping.

Anticones have an even number of radial creases.

Curvature singularity is resolved by nematic order decay.

Abstract

We consider three-dimensional reshaping of a thin nematoelastic film upon nematic-isotropic transition in the field of a charge one topological defect, leading to either cone or anticone (d-cone) shells. The analysis is based on the relation between the shell metric and the tensor order parameter under the assumption of no elastic deformation and volume change. The shape of the shell can be modified by doping, creating cones with curved generatrices. Anticones necessarily have an even number of radial creases. The curvature singularity at the apex is resolved due to decay of the nematic order parameter at the defect core.