Negative Poisson's Ratio Behavior Induced by an Elastic Instability

Katia Bertoldi,Tom Mullin,Stephen Willshaw,Pedro M Reis

doi:10.1002/adma.200901956

Abstract

Negative Poisson's ratio behavior has been uncovered in cellular solids that comprise a solid matrix with a square array of circular voids. The simplicity of the fabrication implies robust behavior, which is relevant over a range of scales. The behavior results from an elastic instability, which induces a pattern transformation and excellent quantitative agreement is found between calculation and experiment.

Highlights

The geometric reorganization observed at the instability is both reversible and repeatable and it occurs over a narrow range of the applied load
We show that the pattern transformation leads to unidirectional negative Poisson’s ratio behavior for the 2D structure i.e. it only occurs under compression
The uncomplicated manufacturing process of the samples together with the robustness of the observed phenomena suggests that this may form the basis of a practical method for constructing planar auxetic materials over a wide range of length-scales

Summary

Introduction

We show that the pattern transformation leads to unidirectional negative Poisson’s ratio behavior for the 2D structure i.e. it only occurs under compression. As will be discussed in detail below, above a critical value of compressive nominal strain of εc = -0.047 a transformation to a pattern of alternating, mutually orthogonal ellipses was observed and an example of the resulting pattern switch is shown in Figure 1b where the image was taken at ε = -0.06 nominal strain.

Results

Conclusion