3D Hyperbolic Kirigami Metamaterials With Tunable Auxeticity and Multistability.

Kirigami mechanical metamaterials provide exceptional tunability in mechanical properties and morphing capabilities, exhibiting great potential for deployable and actuatable devices. However, most kirigami structures can only deform freely within a 2D plane, with limited out-of-plane deformability, making them inadequate for constructing periodic objects with arbitrary 3D shapes. Here, a novel class of 3D mechanical metamaterials with hyperbolic kirigami tessellations has been developed. By projecting hyperbolic kirigami templates onto three types of triply periodic minimal surfaces, candidate structures are developed with remarkable properties. An extreme negative Poisson's ratio of -1 and tunable mechanical multistability are uncovered through theoretical analysis, numerical simulations, and experiments thanks to the flexible kirigami geometry. Notably, the structure achieves a maximum volume expansion of up to 488% during auxetic morphing. Furthermore, programmable morphing behaviors are demonstrated through voxelated assemblies of kirigami unit cells with varying geometrical parameters. The novel design strategy presented in this work based on hyperbolic kirigami tessellations opens up new avenues toward auxetic and multistable mechanical metamaterials with broad applications spanning shape-morphing architectures, deployable space structures, and soft machines.