Hierarchical tessellation enables programmable morphing matter

Shape-morphing materials offer feasible pathways for mimicking adaptive biological organisms that can transform between various morphologies. However, existing morphing strategies through pre -arranged localized strain and/or cut/fold patterns have a limited range of achievable geometries, and the morphed structures usually have low stiffness due to the intrinsic softness of underlying materials. To address these challenges, we propose an inverse -design framework via tessellating target 3D geometries at two different levels: kirigami tessellation at the global level and particle tessellation at the local level, referred as "hierarchical tessellation."Upon actuation, general 3D geometries such as varying curvature and asymmetry, and tunable stiffness can be reversibly achieved by assembling rigid tessellated building blocks from a 2D surface. We demonstrate its applications with an interactive lamp, a protective rescue channel, and the smart actuation with electrothermal actuators. Our framework provides guidelines for designing programmable matter with high morphing capabilities and respectable mechanical robustness for multiscale applications.