A micropolar plate model for bending of triangular lattices comprising zigzag beams

Equilateral triangle lattices comprising zigzag beams are a typical kind of periodic structures with chiral unit cells. The in-plane deformation of these materials was believed to exhibit chiral effect, but the out-of-plane bending has never been explored. Here, we develop a continuum model to describe the overall bending behavior of such lattices by homogenizing them as micropolar plates. The governing equations of the plate are derived in an asymptotic way with no need of any ad hoc kinematic assumptions, and the effective elastic parameters are determined analytically from the unit cell by imposing the generalized Hill-Mandel condition. Different from the previous study, we find that there are no chiral effects in both the in-plane and out-of-plane deformations. Moreover, with two examples for unconstrained and constrained bending, we show that the curvature of the lattice can be transformed between anticlastic and synclastic by changing the zigzag angle or the sectional aspect ratio of the beams. The results agree excellent with finite element simulations of the lattice.