Micropolar modeling of a typical bending-dominant lattice comprising zigzag beams

Abstract

Within the framework of micropolar theory, we have studied the continuum homogenization procedure of a typical kind of planar chiral structures, in which each two neighboring joints interact through a zigzag beam. Both the triangular and square lattices are taken as the demonstrating examples. Usage of zigzag beams makes the lattices bending-dominant, and thus calls for micropolar theory to predict the constitutive behaviors. According to the equivalence of microstructure- and continuum-level strain energies, the micropolar-type elastic stiffness constants are expressed in terms of the microstructural geometric and material parameters. By considering uniaxial tension, Young's modulus and Poisson's ratio are determined in an analytical form. Particularly, for square lattices, there arises a strong coupling between stretch and shear, meaning that the lattice under uniaxial tension is subject to a shearing deformation along the direction perpendicular to the tension, and vice versa. The theoretical results are validated by comparing with finite element simulations and experiments done on 3D printed specimens. We have also analyzed the influences of microstructural geometric parameters on the homogenized Young's modulus and Poisson's ratio. Furthermore, in this study the micropolar characteristic lengths are given explicitly in terms of microstructural parameters, providing the convenience and guidance of tuning the related size effects.