Reprogrammable curved-straight origami: Multimorphability and volumetric tunability

Existing origami patterns can transform flat sheets into curved surfaces or be stacked into volumetric lattices with tunable properties. Their folded surfaces, however, cannot morph into other rigid states, and their three-dimensional (3D) tessellations allow stiffness tuning only through large size variations, causing abrupt shifts in stiffness and affecting other properties such as relative density. These limitations hinder their use as reprogrammable structural materials in real-life applications. Here, we introduce a reprogrammable origami integrating curved and straight bistable creases to address both challenges: attaining rigidity while allowing reversible remorphability into numerous load-bearing shapes and generating 3D curved-plate lattices, delivering in a prescribed configuration of fixed dimensions continuously tunable elastic moduli spanning two orders of magnitude. Leveraging curved origami theories, differential geometry, paperboard models, and experiments, we construct the folded pattern, formulate its geometric mechanics, and quantify its mechanical performance. Our approach provides a versatile platform for multifunctional metamaterials, enabling adaptive and resilient materials in aerospace, biomechanics, and soft robotics.