FLEXURAL RIGIDITY OF THIN AUXETIC PLATES

Abstract

The influence of auxeticity on the mechanical behavior of isotropic plates is considered herein by evaluating the plate flexural rigidity as the Poisson's ratio changes from 0.5 to -1. Since the change in plate's Poisson's ratio is followed by a change in at least one of the three moduli, any resulting change to the plate flexural rigidity is only meaningful when at least one of the moduli is held constant. This was performed by normalizing the plate flexural rigidity by a single modulus, a square root of two moduli product, or a cube root of three moduli product to give a dimensionless plate flexural rigidity. It was found that the plate flexural rigidity decreases to a minimum as the plate Poisson's ratio decreases from 0.5 to 0 when only the Young's modulus is held constant. Thereafter the plate flexural rigidity increases with the plate auxeticity. Results also reveal that when only the shear modulus or when the bulk modulus is held constant, the plate flexural rigidity decreases or increases, respectively, with the plate auxeticity. Intermediate trend in the plate flexural rigidity is observed when the product of two moduli is held constant. When the product of all three moduli is held constant, the plate flexural rigidity increases with the plate auxeticity, and the change is especially drastic when the plate Poisson's ratio is near to the upper and lower limits of Poisson's ratio for isotropic solids. Results from this work are useful for structural designers to control the flexural rigidity of plate made from auxetic materials.