Micropolar modeling for bending shape of 2D lattices: The case of equilateral triangular cell structure

Abstract

It was found recently that the bending shape of a 2D lattice may be substantially influenced by the height-to-width ratio of the constituent beams. To capture such an unusual effect, we focus on 2D lattices with equilateral triangular cell structure and formulate a continuum model by homogenizing them to transversely isotropic micropolar plates. The governing equations are derived along a new routine without introducing any ad hoc kinematic assumptions, and the effective elastic parameters are achieved from a scheme based on the generalized Hill-Mandel condition. Our model contains the displacement and microrotation components of the mid-plane as six independent unknowns. To highlight the crucial role of the beam cross-section geometry, two illustrative examples are solved analytically, and the predictions are validated by discrete finite element simulations.