Carl D. Modes

Gaussian curvature from flat elastica sheets

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.

Curvature in nematic elastica responding to light and heat

Nematic elastic bodies can develop a gradient of response to heat, light and other stimuli. They then bend and develop curvature in a complex manner depending on director field distributions, on whether they are monodomain or polydomain structures and on linear or nonlinear light absorptive processes. In each case, we derive the general weak response where bend in each direction is treated independently of that in others. In a subsequent paper, we address the reverse phenomenon, that is of strong spontaneous distortion leading to curvature suppression.

Disclination-mediated thermo-optical response in nematic glass sheets

Nematic solids respond strongly to changes in ambient heat or light, significantly differently parallel and perpendicular to the director. This phenomenon is well characterized for uniform director fields but not for defect textures. We analyze the elastic ground states of a nematic glass in the membrane approximation as a function of temperature for some disclination defects with an eye toward reversibly inducing three-dimensional shapes from flat sheets of material, at the nanoscale all the way to macroscopic objects, including nondevelopable surfaces. The latter offers a paradigm to actuation via switchable stretch in thin systems.

Blueprinting nematic glass: systematically constructing and combining active points of curvature for emergent morphology.

Much recent progress has been made in the study of nematic solids, both glassy and elastomeric, particularly in the realm of stress-free, defect-driven deformation in thin sheets of material. In this paper we consider a subset of texture domains in nematic glasses that are simple to synthesize, and explore the ways that these simple domains may be compatibly combined to yield analogs of the traditional smooth disclination defect textures seen in standard liquid crystals. We calculate the deformation properties of these constructed textures, and show that, subject to the compatibility constraints of the construction, these textures may be further combined to achieve shape blueprinting of three-dimensional structures from flat sheets.

Suppression of curvature in nematic elastica

Nematic elastic bodies can develop a gradient of response to heat, light and other stimuli. They then bend and develop curvature in a complex manner. Using the results for a general weak response derived in the preceding paper, we solve for strong spontaneous distortion where bend in one direction causes stretch in another direction if that too is bending, and vice versa. Since stretch is elastically expensive, it can cause suppression of one of the bends (we determine which), thus eliminating Gaussian curvature. This is the spontaneous distortion equivalent of the classical Lamb calculation of the anti-clastic suppression when large distortions are imposed in classical elastica. In practice, spontaneously deforming nematic solids, e.g. in actuation, are in this strong bend limit.

Responsive nematic solid shells: Topology, compatibility, and shape

Nematic solids, both glassy and elastomeric, with defects in the director field can attain stress-free Gaussian curvature from an initially flat state. In this letter we show how the intrinsic curvature and/or the global topology of the initial reference state interacts with the curvature arising from the spontaneously strained nematic director field. In particular, locally compatible mechanical deformations due to the director can be globally incompatible in certain topologies.

Shape-programmable materials

Inspired by the insights of mathematician Carl Friedrich Gauss, scientists are engineering hydrogels and liquid-crystal-containing polymers that change from flat to curved in response to heat and other stimuli.

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

Recent attention has been given to the realization of angular deficits and surpluses in the local ground-state geometry of thin sheets of nematic solids as out-of-plane deformations. Such systems exhibit conical or anti-conical curvature sites, or possibly arrays of such polyhedral corners, in order to satisfy the materials spontaneous strain-generated metric requirements. Here, we turn the angular deficit requirement on its head, and show theoretically and experimentally that by appropriately altering the topology of the initially flat sheet—for example, by cutting it in carefully chosen regions—the same angular deficits and surpluses may manifest simply in-plane by changing the geometry of the cut region. Such a mechanism offers a route to apertures or arrays of apertures that may be reversibly opened and closed by applying spontaneous strain with heat, light or chemical potential.

The activated morphology of grain boundaries in nematic solid sheets

We review the current understanding of stress-free, defect-driven deformations in thin sheets of nematic solids, from simple, isolated cone-forming +1 disclination defects to more complicated textures constructed from simple building-block domains. Further, by building from these textures we may investigate the effect that grain boundaries of various types have on the material deformation, leading to faceted tubes in some cases and lines of Gaussian curvature, instead of points, in others.