  The recent development of modular origami structures has ushered in a new era
for active metamaterials with multiple degrees of freedom (multi-DOF). Notably,
no systematic inverse design approach for volumetric modular origami structures
has been reported. Moreover, very few topologies of modular origami have been
studied for the design of active metamaterials with multi-DOF. Herein, we
develop an inverse design method and reconfigurable algorithm for constructing
3D active architected structures - we synthesize modular origami structures
that can be volumetrically mapped to a target 3D shape. We can control the
reconfigurability by reconstructing the topology of the architected structures.
Our inverse design based on volumetric mapping with mobility control by
topology reconstruction can be used to construct architected metamaterials with
any 3D complex shape that are also transformable with multi-DOF. Our work opens
a new path toward 3D reconfigurable structures based on volumetric inverse
design. This work is significant for the design of 3D active metamaterials and
3D morphing devices for automotive, aerospace, and biomedical engineering
applications.
