Direct measurement of negative Poisson ratios of auxetic materials via the impulse excitation technique (IET)

Abstract

The direct measurement of Poisson ratios via the impulse excitation technique (IET) is based on determining the frequency ratio between the resonant frequencies of flexural and torsional vibrations of circular discs. However, the direct measurement of negative Poisson ratios, which occur in auxetic materials, has been impeded until now by the absence of numerical values of Martinček’s solution for frequency ratios smaller than 1.35, because the relevant ASTM standards have not considered the possibility of negative Poisson ratios so far. Here we provide this missing link by reconsidering Martinček’s solution and presenting the necessary values in the forms of graphs and fit relations from which the Poisson ratio, including negative ones (down to −0.273), can be determined from frequency ratios down to 1.1 for a wide range of specimen aspect ratios (down to 4).