Effective behavior of nematic elastomer membranes

We derive the effective energy density of thin membranes of liquid crystal elastomers as the Gamma-limit of a widely used bulk model. These membranes can display fine-scale features both due to wrinkling that one expects in thin elastic membranes and due to oscillations in the nematic director that one expects in liquid crystal elastomers. We provide an explicit characterization of the effective energy density of membranes and the effective state of stress as a function of the planar deformation gradient. We also provide a characterization of the fine-scale features. We show the existence of four regimes: one where wrinkling and microstructure reduces the effective membrane energy and stress to zero, a second where wrinkling leads to uniaxial tension, a third where nematic oscillations lead to equi-biaxial tension and a fourth with no fine scale features and biaxial tension. Importantly, we find a region where one has shear strain but no shear stress and all the fine-scale features are in-plane with no wrinkling

Programming complex shapes in thin nematic elastomer and glass sheets

Nematic elastomers and glasses are solids that display spontaneous distortion under external stimuli. Recent advances in the synthesis of sheets with controlled heterogeneities have enabled their actuation into non-trivial shapes with unprecedented energy density. Thus, these have emerged as powerful candidates for soft actuators. To further this potential, we introduce the key metric constraint which governs shape changing actuation in these sheets. We then highlight the richness of shapes amenable to this constraint through two broad classes of examples which we term nonisometric origami and lifted surfaces. Finally, we comment on the derivation of the metric constraint, which arises from energy minimization in the interplay of stretching, bending and heterogeneity in these sheets

Chandra observation of the Galactic supernova remnant CTB 109 (G109.1-1.0)

Context: We study the X-ray emission of the Galactic supernova remnant (SNR) CTB 109 (G109.1-1.0), which is well-known for its enigmatic half-shell morphology both in radio and in X-rays and is associated with the anomalous X-ray pulsar (AXP) 1E2259+586. Aims: We want to understand the origin of the X-ray bright feature inside the SNR called the Lobe and the details of the interaction of the SNR shock wave with the ambient interstellar medium (ISM). Methods: The Lobe and the northeastern part of the SNR were observed with Chandra ACIS-I. We analysed the spectrum of the X-ray emission by dividing the entire observed emission into small regions. The X-ray emission is best reproduced with one-component or two-component non-equilibrium ionisation models depending on the position. In the two-component model one emission component represents the shocked ISM and the other the shocked ejecta. Results: We detect enhanced element abundances, in particular for Si and Fe, in and around the Lobe. There is one particular region next to the Lobe with a high Si abundance of 3.3 (2.6 - 4.0) times the solar value. This is the first, unequivocal detection of ejecta in CTB 109. Conclusions: The new Chandra data confirm that the Lobe was created by the interaction of the SNR shock and the supernova ejecta with dense and inhomogeneous medium in the environment of SNR CTB 109. The newly calculated age of the SNR is t ~ 1.4 x 10^4 yr.Comment: Accepted for publication in A&A. 9 pages, 10 figure

Patterning nonisometric origami in nematic elastomer sheets

Nematic elastomers dramatically change their shape in response to diverse stimuli including light and heat. In this paper, we provide a systematic framework for the design of complex three dimensional shapes through the actuation of heterogeneously patterned nematic elastomer sheets. These sheets are composed of \textit{nonisometric origami} building blocks which, when appropriately linked together, can actuate into a diverse array of three dimensional faceted shapes. We demonstrate both theoretically and experimentally that: 1) the nonisometric origami building blocks actuate in the predicted manner, 2) the integration of multiple building blocks leads to complex multi-stable, yet predictable, shapes, 3) we can bias the actuation experimentally to obtain a desired complex shape amongst the multi-stable shapes. We then show that this experimentally realized functionality enables a rich possible design landscape for actuation using nematic elastomers. We highlight this landscape through theoretical examples, which utilize large arrays of these building blocks to realize a desired three dimensional origami shape. In combination, these results amount to an engineering design principle, which we hope will provide a template for the application of nematic elastomers to emerging technologies

Actuation of thin nematic elastomer sheets with controlled heterogeneity

Nematic elastomers and glasses deform spontaneously when subjected to temperature changes. This property can be exploited in the design of heterogeneously patterned thin sheets that deform into a non-trivial shape when heated or cooled. In this paper, we start from a variational formulation for the entropic elastic energy of liquid crystal elastomers and we derive an effective two-dimensional metric constraint, which links the deformation and the heterogeneous director field. Our main results show that satisfying the metric constraint is both necessary and sufficient for the deformation to be an approximate minimizer of the energy. We include several examples which show that the class of deformations satisfying the metric constraint is quite rich