  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.
