Inverse design of programmable Poisson's ratio and in-plane stiffness for generalized four-fold origami

Abstract

Origami-inspired metamaterials and structures exhibit extraordinary properties, including programmable Poisson's ratio and tunable stiffness. Although some research has achieved the programmability of generalized four-fold origami structures, the proposed formulas of Poisson's ratio and stiffness are complex and difficult to be applied for inverse design of origami engineering. Here, the geometric mechanics of a generalized four-fold origami unit with three angles and two lengths controls are studied. The analytical formulas give a great potential of inverse design for in-plane Poisson's ratio and in-plane stiffness. To realize inverse design, the transcendental equation with uninvertible solution is simplified by polynomial fitting method. Moreover, the results are verified by the classical Miura origami results, the existing Origami Simulator tools and the physical polyethylene models. Finally, to make the proposed inverse design applicable to non-zero thickness origami, it is recommended to adopt carbon fiber reinforced polymer shell as the connection of the panel.