A study of negative Poissonʹs ratios in auxetic honeycombs based on a large deflection model

Materials or structures that contract in the transverse direction under uniaxial compression, or expand laterally when stretched are called to have negative Poissonʹs ratios. A theoretical approach to predict negative Poissonʹs ratios of auxetic honeycombs has been developed, which is based on the large deflection model. The equations of the deflection curves of the inclined member of the re-entrant cell, strains and Poissonʹs ratios of auxetic honeycombs in two orthogonal directions have been derived. The deformed shapes of the inclined member of the re-entrant cell are calculated. The negative Poissonʹs ratios of auxetic honeycombs are no longer a constant at large deformation. They vary significantly with the strain. The effect of the geometric parameters of the cell on the Poissonʹs ratios is analyzed.