Abstract
Non-uniform director fields in flat, responsive, glassy nematic sheets lead to the induction of shells with non-trivial topography on the application of light or heat. Contraction along the director causes metric change, with, in general, the induction of Gaussian curvature, that drives the topography change. We describe the metric change, the evolution of the director field, and the transformation of reference state material curves, e.g. spirals into radii, as curvature develops. The non-isometric deformations associated with heat or light change the geodesics of the surface, intriguingly even in regions where no Gaussian curvature results.
Highlights
Nematic solids elongate or contract along their preferred direction, the director n, in response to heat, light, pH change, and solvent uptake
The evolution of the shape of a nematic surface upon stimulation is governed by the metric induced by local deformations encoded by the director field
The director field itself evolves during this process and undergoes local rotations with respect to material lines across the evolving surface
Summary
Nematic solids elongate or contract along their preferred direction, the director n, in response to heat, light, pH change, and solvent uptake. Deformations are simple locally, if the director field n(r) is non-uniform in the plane of a sheet-like sample, it will in general be driven to develop Gaussian curvature (GC) to avoid expensive distortion from the new, natural contracted/ elongated state. We will show that the rotations induced can be compounded, even when the ls are large We show this property by a general argument based on a pair of successive finite deformations. (3) We consider geodesics on cones that result from the response of circular, radial or, in general, logarithmic spiral director distributions. They are different from those of cones that are more conventionally constructed from flat sheets. The curves in the flat space that are geodesics in the target space differ, even though both types of cones have zero Gaussian curvature, except at their tips
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