Simultaneously programmable design of metamaterials with negative Poisson's ratios and nonlinear mechanical responses

Abstract

Auxetic metamaterials exhibit promising applications in flexible electronics, medical devices and aerospace fields by virtue of their excellent fracture resistance, impact resistance and energy absorption capabilities. However, in practical applications, simultaneously and accurately controlling negative Poisson's ratios and nonlinear mechanical responses of auxetic metamaterials remains a significant challenge. To this end, this paper proposes a topology optimization method of auxetic metamaterials under large deformations to achieve simultaneously programmable design in terms of the above two kinds of mechanical behaviors. A hyperelastic material model based on strain energy interpolation is adopted to ensure numerical accuracy and stability during nonlinear topology optimization. A representative volume element, combined with periodic boundary conditions, is employed to simultaneously characterize multiple macroscopic mechanical behaviors of metamaterials under various deformation states. Then, a topology optimization model for programmable auxetic metamaterials under large deformations is constructed. A series of chiral and anti-chiral auxetic metamaterials is designed to achieve target combinations of negative Poisson's ratios and nonlinear mechanical responses. Subsequently, auxetic tubular structures are presented. The results indicate that the proposed method enables the simultaneous programmable design of auxetic metamaterials, thereby paving the way for customized metamaterial design.