  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.
