Kirigami-inspired metamaterials for programming constitutive laws: Mixed-mode multidirectional auxeticity and contact-induced stiffness modulation

Stress-strain constitutive relations and Poisson’s ratios are fundamental properties of naturally occurring materials, based on which their mechanical applications can be designed. The lack of tailorability and restricted margin for such critical properties severely limit the bounds of achievable multi-functional engineering designs using conventional materials. Through analytical and numerical analyses, supported by elementary-level physical experiments, we have proposed a kirigami-inspired hybrid metamaterial with programmable deformation-dependent stiffness and mixed-mode multidirectional auxeticity. The metamaterial can transition from a phase of low stiffness to a contact induced phase that brings forth an extensive rise in stiffness. Uniform and graded configurations of multi-layer tessellated material are developed to modulate the constitutive law of the metastructure with augmented programmability in two- and three-dimensional spaces. The proposed metamaterial will lead to extreme lightweight functional designs for impact resistance, shape morphing, multidirectional deformation, vibration and wave propagation control, where the capabilities of intrinsic material can be most optimally exploited.