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Non-Euclidean surfaces are ubiquitous in numerous engineering fields, such as automotive, aerospace, and biomedical engineering domains. Morphing origami has numerous potential engineering applications, including soft robots, mechanical metamaterials, antennas, aerospace structures, and biomedical devices, owing to its intrinsic morphing features from two-dimensional (2D) planes to three-dimensional (3D) surfaces. However, the current one-dimensional (1D) hinge deformation-driven transformation of foldable origami with rigid or slightly deformable panels cannot achieve a 3D complex and large curvilinear morphing. Moreover, most active origami structures use thin hinges with soft materials on their creases, thus resulting in a lower load capability. This study proposes a novel origami morphing method that demonstrates large free-form surface morphing, e.g., Euclidean to non-Euclidean surface morphing with shape-locking. We embedded tensorial anisotropic stress in origami panels during the extrusion-based 3D printing of shape memory polymers. The extrusion-based 3D printing of isotropic shape memory polymers can produce tensorial anisotropic stress in origami panels during fabrication, which can realize large non-Euclidean surface morphing with multiple deformation modes. The connecting topology of the origami unit cells influences the global morphing behavior owing to the interaction of the deformation of adjacent panels. Non-Euclidean morphing integrated with four-dimensional (4D) printing can provide multimodal shape locking at material and structural levels. The non-Euclidean surface morphing caused by tensorial residual stress in the panel during 3D printing expands the design space of origami and kirigami structures.

The morphing of 3D structures is suitable for i) future tunable material design for customizing material properties and ii) advanced manufacturing tools for fabricating 3D structures on a 2D plane. However, there is no inverse design method for topologically variable and volumetric morphing or morphing with shape locking, which limits practical engineering applications. In this study, we construct a general inverse design method for 3D architected materials for topologically variable and volumetric morphing, whose shapes are lockable in the morphed states, which can contribute to future tunable materials, design, and advanced manufacturing. Volumetric mapping of bistable unit cells onto any 3D morphing target geometry with kinematic and kinetic modifications can produce flat-foldable and volumetric morphing structures with shape-locking. This study presents a generalized inverse design method for 3D metamaterial morphing that can be used for structural applications with shape locking. Topologically variable morphing enables the manufacture of volumetric structures on a 2D plane, saving tremendous energy and materials compared with conventional 3D printing. Volumetric morphing can significantly expand the design space with tunable physical properties without limiting the selection of base materials.

Future active metamaterials for reconfigurable structural applications require fast, untethered, reversible, and reprogrammable (multimodal) transformability with shape locking. Herein, we aim to construct and demonstrate a magneto-thermomechanical tool that enables a single material system to transform with untethered, reversible, low-powered reprogrammable deformations and shape locking via the application of magneto-thermomechanically triggered prestress on a shape memory polymer and structural instability with asymmetric magnetic torque. We demonstrate the mutual assistance of two physics concepts - magnetic control combined with the thermomechanical behavior of shape memory polymers, without requiring new materials synthesis and high-power energy for reprogramming. Our approach can open a new path of active metamaterials, flexible yet stiff soft robots, and multimodal morphing structures, where we can design them in reversible and reprogrammable ways.