Shear deformation in thick auxetic plates

Abstract

This paper aims to understand the effect of auxeticity on shear deformation in thick plates. Three models for the shear correction factor of plates as a function of Poisson’s ratio were proposed: an analytical model, a cubic fit model and a modified model. Of these three, the cubic fit model exhibits the best accuracy over the entire range of Poisson’s ratio from −1 to 0.5. The extent of shear deformation is herein investigated using the example of uniformly loaded circular plates. It was found that the maximum deformation of such plates based on Mindlin theory approximates to those according to Kirchhoff theory when the Poisson’s ratio of the plate material is highly negative. When the Poisson’s ratio of the plate material is −1 and the edge of the plate is simply supported, the calculation of the maximum deflection by Mindlin theory simplifies into that by Kirchhoff theory. These results suggest that auxeticity reduces shear deformation in thick plates, permitting the use of classical plate theory for thick plates only if the plate material is highly auxetic.