Kirigami-Inspired Three-Dimensional Metamaterials with Programmable Isotropic and Orthotropic Thermal Expansion

Mechanical metamaterials with specifically designed cells can provide unusual thermal expansion properties for diverse applications. Limited by very few available cell topologies and complicated non-linear structural deformation, most existing thermal expansion metamaterials can only achieve orthogonally isotropic negative/zero/positive thermal expansion (NTE/ZTE/PTE) within a mild range, especially the 3D ones. Here, based on one-degree-of-freedom kirigami polyhedrons proposed with a kinematic design strategy, a family of 3D isotropic and orthotropic metamaterials capable of programmable NTE, PTE, and even ZTE over ultra-wide range is developed. Incorporating bi-material strips as creases for isotropic polyhedrons, NTE and PTE metamaterials with coefficients of thermal expansion (CTEs) ranging from -2354.3 to 3006.7 ppm/°C are designed and programmed by the theoretical model. Meanwhile, isotropic ZTE metamaterials are constructed by either homogeneous tessellation of ZTE cells or hybrid tessellation of NTE and PTE cells. Furthermore, by allowing distinct geometric parameters in the three orthogonal directions of the kirigami polyhedrons while preserving the kinematic motion, orthotropic metamaterials, in which each of the three directions can be assigned with an independently programmed NTE, ZTE, or PTE, are also achieved. This study paves a novel pathway for the development of thermal expansion metamaterials with potential applications for space optical systems, MEMS, and so on.