Shear Deformation in Rectangular Auxetic Plates

Abstract

S h ear D efo rm atio n in R ectan g u lar A uxetic P latesSolids that exhibit negative Poisson's ratio are called auxetic materials. This paper examines the extent of transverse shear deformation with reference to bending deforma tion 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 o f 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.

Static and dynamic analyses of auxetic hybrid FRC/CNTRC laminated plates

“…A number of studies have been dedicated to these structures. Particularly, investigations were made to study the bending [10,11], dynamic [12,13], and buckling behavior [13][14][15] of these structures. However, in these researches [10][11][12][13][14][15], the value of the negative Poisson's ratios (NPRs) for estimating the effect of auxetic feature on the mechanical behavior of a plate is based on an assumption.…”

Refined shear correction factor for very thick simply supported and uniformly loaded isosceles right triangular auxetic plates

“…A number of these investigations that consider lateral deformation of auxetic plates typically adopt Classical Plate Theory (CPT), which neglects the effect of shear deformation. Recently the First-order Shear Deformation Theory (FSDT) has been adopted for the analysis of auxetic plates [50][51][52][53]. Arising from the assumption of constant shear strain (and hence constant shear stress) across the plate thickness, a shear correction factor is required due to the parabolic shear stress distribution.…”