Morphable architected materials with topologically variable and volumetric reconfiguration

Morphable architected materials enable tunable mechanical and functional properties through geometry rather than material composition. However, existing morphing strategies are largely limited to one- or two-dimensional transformations, preserve topology during deformation, and often rely on material-level phase changes for shape retention, restricting volumetric tunability, structural stiffness, and material choice. Here, we present a general inverse design framework for topologically variable and volumetric morphing of 3D architected materials with shape locking capabilities. The proposed approach enables reversible morphing between flat two-dimensional configurations and a wide range of three-dimensional curvilinear and polyhedral geometries-including shapes with different Euler characteristics-while remaining functionally bistable, with stable undeployed and deployed configurations. The framework combines volumetric mapping of bistable modular origami unit cells with kinematic constraints for flat foldability and kinetic constraints that induce structural bistability, achieving shape locking through mechanical instability rather than material phase transitions. Volumetric morphing further enables access to a previously unexplored materials design space, allowing a single architected material to exhibit widely tunable bulk and shear moduli and programmable structural responses. This work establishes a unified paradigm for inverse-designed morphable architected materials and the energy-efficient fabrication of complex 3D structures.