A non-centrosymmetric square lattice with an axial–bending coupling

Abstract

Metamaterials can enable the design of exotic properties, including the mechanical coupling of different loading modes. Chirality and non-centrosymmetry are known to play essential roles in the rational design of coupling effects. However, there is no theoretical support for the design of coupling behaviors based on the constitutive behavior of lattice structures. Exploring a planar non-centrosymmetric square lattice, we find a novel coupling effect: a compression-induced bending, which a micropolar continuum model can support. Observing the micropolar constitutive equation of a 2D lattice, we find that non-centrosymmetry is necessary but insufficient for designing an axial–bending coupling. The micropolar homogenization is adopted to calculate the material properties of infinite lattices, revealing that the axial-bending coupling coefficient is dependent on the cell size, which is verified by finite element simulations. The axial–bending coupling size effect of finite lattices shows different deformation patterns depending on the cell size and the magnitude of external loading. The novel coupling effect can expand the design space of metamaterials with potential applications in multidirectional mechanical actuators and mechanical logic gates for biomedical, automobile, and aerospace devices.