Large Deflection of Circular Auxetic Membranes Under Uniform Load

Abstract

Currently, available results for the large deflection of circular isotropic membranes are valid for Poisson's ratio of 0.2, 0.3, and 0.4 only. This paper explores the deflection of circular membranes when the membrane material is auxetic, i.e., when they possess negative Poisson's ratio and compared against conventional ones. Due to the multistage calculations involved in the exact method, a generic semiempirical model is proposed to facilitate convenient and direct computation of the membrane deflection as a function of the radial distance; additionally, a specific semiempirical model is given to provide a more accurate maximum deflection. Comparison of deflection distributions verifies the validity of the semiempirical model visأ vis the exact model. The deflection of circular membrane increases with the diminishing effect as the Poisson's ratio of the membrane material becomes more negative.