Shear Deformation in Rectangular Auxetic Plates

Solids that exhibit negative Poisson's ratio are called auxetic materials. This paper examines the extent of transverse shear deformation with reference to bending deformation in simply supported auxetic plates as a ratio of Mindlin-to-Kirchhoff plate deflection for polygonal plates in general, with special emphasis on rectangular plates. Results for square plates show that the Mindlin plate deflection approximates the Kirchhoff plate deflection not only when the plate thickness is negligible, as is obviously known, but also when (a) the Poisson's ratio of the plate is very negative under all load distributions, as well as (b) at the central portion of the plate when the load is uniformly distributed. Hence geometrically thick plates are mechanically equivalent to thin plates if the plate Poisson's ratio is sufficiently negative. The high suppression of shear deformation in favor of bending deformation in auxetic plates suggests its usefulness for bending-based plate sensors that require larger difference in the in-plane strains between the opposing plate surfaces with minimal transverse deflection.