Meta-structure with stable isotropic negative Poisson’s ratio based on the cube-framework stacked by Kirigami units

Negative Poisson’s ratio (NPR) metamaterials have excellent mechanical properties due to auxetic characteristics. However, the existing anisotropic NPR structures lead to non-uniform enhancement that limits their applications. Thus, a meta-structure with isotropic NPR is proposed here, in which Kirigami units is stacked in three-axis symmetrical cube-frameworks. The stable NPR is related to the degradability of the Hessian matrix in Hilbert-Einstein action of the Kirigami unit. With such structures, the specific modulus of thermoplastic polyurethane (TPU), silica gel, and acrylonitrile-butadiene-styrene (ABS) increase by 907.6%, 610.9%, and 210.5%, respectively. Finite element analysis further proves that improvement is associated with face constraint effects, which is from a moderate modulus of materials. Meanwhile, the isotropic meta-structures are introduced into anti-collision beams, energy-absorbing boxes, and protective helmets, proving their excellent application potential.