Variable stiffness and zero Poisson's ratio of the butterfly-shaped mechanical metamaterial

Abstract

Based on the requirements of the low tangential stiffness and the high normal stiffness in the deformed wing skin structure, a butterfly-shaped mechanical metamaterial (BSM) with variable stiffness zero Poisson's ratio is constructed. The analytical expressions for Poisson's ratio, tangential stiffness, and normal stiffness are derived using the energy method. Through numerical simulation and experimental analysis, it is verified that the structure has an equivalent Poisson's ratio close to 0. Moreover, the excellent characteristics of low tangential equivalent stiffness and relatively high normal stiffness are fundamentally different from the low in-plane stiffness and high out-plane stiffness of traditional honeycomb structures. Specifically, in terms of the tangential stiffness, it can maintain low stiffness over a longer deformation range and has the variable stiffness characteristics and a similar pattern to spring series parallel connection; In terms of the normal stiffness, its stiffness is much higher than the tangential low stiffness. These characteristics enable the structure to deform with high efficiency and avoid out-plane warping during deformation. It is possible that this structure with excellent performance serves as the skin material for the deformed aircraft wing.