An Accurate Design Equation for the Maximum Deflection in a Class of Auxetic Sectorial Plates

Abstract

Auxetic materials are solids that exhibit negative Poisson's ratio. The effect of material auxeticity (i.e., negativity of Poisson's ratio) is investigated herein on the maximum deflection of sectorial plates with Simply‐Supported straight edges and Free curve edge (SSF). To aid the designer, an accurate and conveniently executable semi‐empirical model has been developed herein, which is valid for the entire range of Poisson's ratio of isotropic solids and for the plate's sectorial angle from 30 to 90 degrees. Results from exact solution reveal that the maximum deflection reduces sharply with the reduction of Poisson's ratio from positive to mildly negative, but deflection reduction is marginal when the sectorial plate's Poisson's ratio changes from moderately negative to highly negative value. It is therefore suggested that (a) the use of auxetic materials is useful to limit the extent of SSF sectorial plate deflection, and that (b) the use of the developed semi‐empirical model herein as a design equation gives greatly simplified but highly accurate maximum deflection prediction for SSF plates made from both conventional (positive Poisson's ratio) and auxetic (negative Poisson's ratio) materials.

An Anisotropic Auxetic 2D Metamaterial Based on Sliding Microstructural Mechanism

“…The extent of anisotropy increases when the array goes to the extremes, thereby leading to extreme negative Poisson’s ratios. The results from this paper, in conjunction with earlier works on auxetic beams [40,41], auxetic rods [42,43,44], auxetic plates [45,46,47,48,49,50,51,52], auxetic shells [53,54], auxetic composites [55,56,57,58,59,60,61,62] and 2D metamaterial structures [63,64], would avail more design options for the engineer in developing novel load bearing materials and structures.…”

Auxetics and Other Systems of Anomalous Characteristics

“…In his paper An accurate design equation for the maximum defl ection of SSF sectorial plates made from auxetic materials Lim [20] explores the interlink between auxeticity and mechanics of plates and solids. He examines the relation between Poisson's ratio of isotropic 3D material systems and maximum defl ection of sectorial plates with Simply-Supported straight edges and Free curve edge (SSF).…”

Auxeticity of Concentric Auxetic-Conventional Foam Rods with High Modulus Interface Adhesive

“…It has also been found that novel properties, distinct from conventional or auxetic materials, arise when a composite structure is made from both conventional and auxetic materials. In addition to a recent comprehensive survey of auxetic materials and structures [ 37 ], the reader is also referred to a recent focus issue on “auxetics and other systems of anomalous characteristics” [ 38 , 39 , 40 , 41 , 42 ], as well as papers in this special issue [ 43 , 44 , 45 , 46 , 47 , 48 ].…”