Combined Effect of Load Waviness and Auxeticity on the Shear Deformation in a Class of Rectangular Plates

Abstract

Auxetic materials are solids that exhibit negative Poisson's ratio. Due to its uniqueness, it is expected that auxetic solids and structures manifest certain mechanical responses that are distinct from conventional materials. So far classical plate theory (CPT) has been used to investigate the behavior of thin auxetic plates and, for thick auxetic plates, the first-order shear deformation theory (FSDT) has been recently employed. The third-order shear deformation theory (TSDT) is adopted herein as it employs a realistic transverse shear stress and strain distribution across the plate cross section, and therefore removes the need for a correction factor. The results obtained herein reveal that as a plate material's Poisson's ratio becomes more negative, the plate deflection characteristic mimics that of (a) reduced plate thickness, (b) reduced plate aspect ratio, and (c) reduced load waviness. The results of this investigation support (i) the use of auxetic materials in applications where there is a need to reduce the extent of transverse shear deformation, and (ii) the use of the simpler CPT instead of any shear deformation plate theory if the Poisson's ratio of the plate material is sufficiently negative.