Patterning origami in nematic elastomer sheets

Nematic elastomers dramatically change their shape in response to actuation by light or heat. In this work, 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 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 multistable, 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.