Smooth doubly curved origami shells with reprogrammable rigidity

Abstract

Origami tessellations can transform flat sheets into curved yet inherently compliant surfaces that only approximate curvature and are unable to reconcile a fundamental trade-off among load-bearing capacity, curvature precision, and stiffness reprogrammability. We resolve this conflict by introducing a tileable crease pattern that folds into smooth, doubly curved shapes, enabling structural locking with minimal sagging under load. Solving an inverse problem, we compute fold patterns that match prescribed smooth surfaces with double, variable, and constant curvature. By strategically embedding tendons with varying pre-tension, we demonstrate reversible transformations from ultrasoft, formless states into rigid, load-bearing structures with in-situ tunable stiffness spanning orders of magnitude. This work unlocks a paradigm for folding doubly curved origami metamaterials, enabling flat-pack transport and scalable deployment of smooth, load-bearing shells.