M.Sc Thesis

M.Sc StudentVictor Salit
SubjectShear Modulus Change in Thin-Walled Structures by
Introduction of Negative Poisson's Ratios
DepartmentDepartment of Aerospace Engineering
Supervisor Professor Emeritus Weller Tanchum


Poisson's ratio (PR) is defined as the negative ratio between the lateral and longitudinal strain due to application of load in the longitudinal direction. In isotropic homogeneous materials, PR may vary in the range 0.5 to -1. Whereas, contraction of a specimen in the lateral direction, when stretching it in the longitudinal is a well known and recognized behavior that is associated with positive PR's, expansion of a specimen in the lateral direction when stretching it longitudinally is counterintuitive and barely experienced. Such behavior, associated with negative PR's, is called auxetic. According to classical elasticity theory, an auxetic behavior should be accompanied by sharp increase in shear stiffness. This could lead to weight reduction of shear panel structural elements and other types of thin-walled structural members.

Motivated by this assumption of potential structural benefit and the fact, that currently available auxetic materials (mostly honeycombs, foams and polymers), are not suitable for thin-walled structural applications, this study undertook to look into two main issues: 1) feasibility of inducing auxetic behavior into thin-walled structures and 2) in case it is possible, would it indeed lead to shear stiffness enhancement.

In this study, geometry of a membrane, which by itself is a naturally occurring thin-walled auxetic material, was chosen as an initial geometric model. It was represented by three successive mechanical models: a rigid rods fishnet, a flexible stripes fishnet and as continuous surface. After performing a set of surface manipulations the feasibility issue was examined. Then, to address the second issue, a parametric study was performed.

The results obtained in this study indicated that on the one hand the effective elastic properties, E* and G* of the proposed auxetic surfaces, are lower than those of the material the surface are fabricated from, E* ~ 1% of the material elastic modulus and G* ~ 80% of its shear modulus. This decrease appears to be due to the significant flexibility, which is added to the surface containing bends. On the other hand, the properties that were obtained for the proposed surfaces are much higher than those observed for other available auxetics like honeycombs, foams and polymers. Another advantage of the proposed surfaces is continuity of the material, as compared with cellular auxetics.