Tunable prestressed metamaterials: Mimicking Poisson’s ratio through geometric stiffness

Abstract

Conventional mechanical metamaterial typically locks its material properties, including the Poisson’s ratio, to a particular shape of the cell structures. Here we integrate traditional shape-determined auxetic metamaterials with prestressed states, developing metamaterials with identical shapes but varied or even opposite Poisson’s ratios. Motivated by the use of geometric stiffness in slender components to mimic the elastic response of planar components, we propose an equivalent planar element and equivalent constitutive matrix for lattice structures derived from the weak form of governing equations. This equivalent constitutive matrix integrates both the contribution of component rotation and prestress. Equivalent Poisson’s ratios for individual slender components and commonly employed frames, with or without prestress, are exhibited. Guided by this approach, we design both isotropic and quasi-anisotropic metamaterials constructed from prestressed, self-equilibrated lattice cell structures. These materials, possessing identical configurations, present varying or even opposing Poisson’s ratios, consistent with the predictions made by the equivalent constitutive matrices. This influence of pre-stress on the material’s Poisson’s ratio is confirmed through numerical simulations and supported by experimental proof-of-concept.