A unified morphomechanics theory framework for both Euclidean and non-Euclidean curved crease origami

Abstract

Conventional curved crease origami exhibits only Euclidean metrics at the crease, where the surfaces on either side should consistently display convexity on one side and concavity on the other, unfavorably leading to restricted morphologies. Herein, we focus on a special type of origami: non-Euclidean curved crease origami. Additionally, we establish a morphomechanics framework that facilitates the morphology calculation for curved crease origami with arbitrary crease metrics. Specifically, starting with a unified geometric description, it is demonstrated that this non-Euclidean curved crease origami exhibits a broader range of unique morphologies: the convexity and concavity of surfaces can be globally consistent, globally opposite, or vary locally. Additionally, we propose two in-situ reconfiguration strategies: adjusting the folding angle or modifying the sections corresponding to specified angles. Existing calculation methods for designated deployment paths are extended to include non-Euclidean curved crease origami, emphasizing the role of the interfering section in determining deformation limits. Most importantly, we develop a new discrete developable patch model, enabling accurate calculation of the morphology of both Euclidean and non-Euclidean curved crease origami under free deployment paths. Both theoretical and physical models demonstrate the exclusive advantages of complex and diverse morphologies of non-Euclidean curved crease origami, which can be interconverted through two independent reconfiguration strategies. This work broadens the design scope of curved crease origami and provides a systematic framework for subsequent design and theoretical analysis, offering insights for future morphological calculations and active morphology control.