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 nontrivial 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.

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 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 the nonisometric origami building blocks actuate in the predicted manner, and that the integration of multiple building blocks leads to complex, yet predictable and robust, shapes. We then show that this experimentally realized functionality enables a rich design landscape for actuation using nematic elastomers. We highlight this landscape through 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 provides a template for the programming of arbitrarily complex three dimensional shapes on demand.

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