Negative Poissonʹs ratios in cellular foam materials

Materials with negative Poissonʹs ratios (auxetic) get fatter when stretched and thinner when compressed. This paper discusses a new explanation for achieving auxetic behaviour in foam cellular materials, namely a ‘rotation of rigid units’ mechanism. Such auxetic cellular materials can be produced from conventional open-cell cellular materials if the ribs of cell are slightly thicker in the proximity of the joints when compared to the centre of the ribs with the consequence that if the conventional cellular material is volumetrically compressed (and then ‘frozen’ in the compressed conformation), the cellular structure will deform in such a way which conserves the geometry at the joints (i.e. behave like ‘rigid units’) whilst the major deformations will occur along the length of the more flexible ribs which form ‘kinks’ at their centres as a result of the extensive buckling. It is proposed that uniaxial tensile loading of such cellular systems will result auxetic behaviour due to re-unfolding of these ‘kinks’ and re-rotation of the ‘rigid joints’.