MECHANICAL MODELLING OF ENHANCED HEXA-MISSING RIB CHIRALAUXETIC META-MATERIALS

In a previous work, the authors proposed novel enhanced hexa-missing rib chiral auxetic meta-materials (with straight ligaments and wavy ligaments), exhibiting tunable negative Poisson’s ratio and elastic modulus . The previous work, however, was limited in the finite element (FE) analysis. To facilitate the understanding of the underlying microstructure-property relationship and further provide guidelines of meta-material designs to yield target mechanical parameters, a mechanics model under infinitesimal deformation framework was developed by a simple energy-based approach. The considered chiral auxetic honeycombs consist of a set of zigzag ligaments, which can be assumed as simple supported Euler-Bernoulli beams. Therefore, the strain energy of an arbitrary shaped Euler-Bernoulli beam with concentrated forces and moments subjected to the end is derived firstly. Then, theoretical formulations of the effective Poisson’s ratio and elastic modulus for the enhanced hexa-missing rib chiral auxetics are further formulated with considering the equilibrium condition and displacement consistent condition. It is found that the theoretical formulations have a succinct form only if the length ratio between the outer and inner part of the zigzag ligaments is 2:1. To facilitate the application of the theoretical formulations, A graphical user interface (GUI) is developed based on MATLAB so that the effective Poisson’s ratio and elastic modulus of a specific design can be obtained directly by simply inputting the corresponding independent geometric parameters. The obtained analytic solutions, as compared with systematic FE calculations (conducted on one unit-cell with considering periodic boundary condition), elucidated different roles of the microstructure geometry on the effective mechanical parameters of the considered auxetic honeycombs. Results show that a wide range of targeted mechanical parameters can be obtained by adjusting the geometrical structure.