Gaussian curvature from flat elastica sheets

Abstract

We discuss methods of reversibly inducing non-developable surfaces from flat sheets of material at the micro-scale all the way to macroscopic objects. We analyse the elastic ground states of a nematic glass in the membrane approximation as a function of temperature for disclination defects of topological charge +1. An aim is to show that by writing an appropriate director field into such a solid, one could create a surface with Gaussian curvature, dynamically switchable from flat sheets while avoiding stretch energy. In addition to the prospect of programmable structures, such surfaces offer actuation via stretch in thin systems since when illumination is subsequently removed, unavoidable stretches return.

Shape control of active surfaces inspired by the movement of euglenids

“…This mechanism can be relevant for thin films made of nematic glasses or elastomers (Modes et al, 2011). By choosing p 0 and q 0 so that they form a 45 angle with s 0 and m 0 , it is easy to see that U 2 is only equivalent to Eq.…”

“…In these and most references, the non-uniformity in the deformation is accomplished by patterning non-uniform swelling or nematic director fields, see also e.g. Modes et al (2011), and applying a uniform stimulus, although it has also been accomplished by non-uniform illumination (Camacho-Lopez et al, 2004). Such programmed NEPs can therefore execute predefined shape changes, although the path between configurations can present significant variability (Kim et al, 2012).…”

Programmed morphing of liquid crystal networks

“…10). At higher strains, the number of buckles can increase, leading to a more crumpled anticone [31].…”

Angular deficits in flat space: remotely controllable apertures in nematic solid sheets

“…In the simple case of a +1 azimuthal defect, where the integral curves of the texture are concentric circles, a thin sheet of nematic glass will become conical upon heating (figure 1c) or anti-conical upon cooling (figure 1d) [5,6]. These cones represent point sources of Gaussian curvature and are robustly confined to an area of the defect comparable with the sheet thickness for any appreciable strain [7], as a result of the stretch cost in the elastic energy strongly outweighing simple bend penalties and the according material desire to concentrate the Gaussian curvature at the defect. One moves beyond single cones or anti-cones in a constructionist manner by restricting the full space of nematic textures to those that are piece-wise constant [8], or perhaps include arcs of +1 disclination textures, so long as the regions of constant director are patched together along rank-1 connected boundaries [9].…”