Encoding of direct 4D printing of isotropic single-material system for double-curvature and multimodal morphing

The ability to morph flat sheets into complex 3D shapes is extremely useful for fast manufacturing and saving materials while also allowing volumetrically efficient storage and shipment and a functional use. Direct 4D printing is a compelling method to morph complex 3D shapes out of as-printed 2D plates. However, most direct 4D printing methods require multi-material systems involving costly machines. Moreover, most works have used an open-cell design for shape shifting by encoding a collection of 1D rib deformations, which cannot remain structurally stable. Here, we demonstrate the direct 4D printing of an isotropic single-material system to morph 2D continuous bilayer plates into doubly curved and multimodal 3D complex shapes whose geometry can also be locked after deployment. We develop an inverse-design algorithm that integrates extrusion-based 3D printing of a single-material system to directly morph a raw printed sheet into complex 3D geometries such as a doubly curved surface with shape locking. Furthermore, our inverse-design tool encodes the localized shape-memory anisotropy during the process, providing the processing conditions for a target 3D morphed geometry. Our approach could be used for conventional extrusion-based 3D printing for various applications including biomedical devices, deployable structures, smart textiles, and pop-up Kirigami structures.