Materials Science and Engineering A 423 (2006) 214–218 Negative Poisson’s ratios in cellular foam materials Joseph N. Grima a,∗ , Ruben Gatt a , Naveen Ravirala b , Andrew Alderson b , K.E. Evans c a Department of Chemistry, University of Malta, Msida MSD 06, Malta b Centre for Materials Research and Innovation, University of Bolton, Bolton BL3 5AB, UK c Department of Engineering, University of Exeter, Exeter EX4 4QF, UK Received 21 July 2005; accepted 29 August 2005 Abstract Materials with negative Poisson’s 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’. © 2006 Published by Elsevier B.V. Keywords: Auxetic; Foams; Negative Poisson’s ratios; Mechanical properties 1. Introduction Materials with negative Poisson’s ratios (auxetic) [1] exhibit the unusual property of becoming fatter when stretched and thin- ner when compressed. This unusual property was first reported in 1944 when iron pyrites single crystals were described as having a negative Poisson’s ratio, a phenomenon, which was regarded as an anomaly and attributed to twinning defects [2]. Since then, and most particularly in the last two decades, auxetic behaviour was predicted, discovered, or deliberately introduced in various materials ranging from molecular level systems (e.g. nanos- tructured and liquid crystalline polymers [1,3–7], metals [8], silicates [9,10] and zeolites [11]) to microstructured materials such as foams [12–15] and microstructured polymers [16–18]. Various auxetic structures have also been proposed including re-entrant [19–21] and chiral honeycombs [22–24] and models based on rigid ‘free’ molecules [25–27]. In all of these systems, the negative Poisson’s ratios are a consequence of the way that the geometry of the structure (the nano/microstructure in the ∗ Corresponding author. Tel.: +356 23402274; fax: +356 21330400. E-mail address: joseph.grima@um.edu.mt (J.N. Grima). case of materials) changes when uniaxial mechanical loads are applied. Auxetic materials are known to exhibit various enhanced physical characteristics over their conventional counterparts ranging from increased indentation resistance [28,29] to improved acoustic damping properties [30,31]. These enhanced characteristics make auxetic materials perform better in many practical applications. A class of auxetics, which has attracted considerable atten- tion in recent years is that of auxetic foams (see Fig. 1). These foams were first manufactured by Lakes [12] and can be pro- duced from commercially available conventional foams through a process involving volumetric compression, heating beyond the polymer’s softening temperature and then cooling whilst remain- ing under compression. For example, Smith et al. [15] report that they convert samples of commercially available reticulated 30 ppi polyurethane foams (‘Filtren’ by Recticel Ltd.) which originally exhibited Poisson’s ratio of ca. +0.85 for loading in the ‘rise direction’ to an auxetic form which exhibits Poisson’s ratios of ca. -0.60 trough a process of compression in volume by ca. 30%, heating at 200 ◦ C and then cooling in the compressed shape. 0921-5093/$ – see front matter © 2006 Published by Elsevier B.V. doi:10.1016/j.msea.2005.08.229