A novel centresymmetric honeycomb composite structure Abderrezak Bezazi a, * ,1 , Fabrizio Scarpa a,1 , Chrystel Remillat b a Multidomain Cellular Solids Laboratory, Department of Mechanical Engineering, University of Sheﬃeld, Mappin Street, S1 3JD, UK b Department of Aerospace Engineering, The University of Bristol, Queen’s Building, BS8 2QL Bristol, UK Abstract In this paper analytical and ﬁnite element (FE) simulations are carried out to calculate the in-plane PoissonÕs ratio and YoungÕs mod- uli of a new centresymmetric honeycomb conﬁguration under uniaxial loading. Opposite to similar re-entrant honeycomb structures studied in the past, the new re-entrant unit cell topology takes into account possible manufacturing constraints typical of production routes like Resin Transfer Moulding (RTM) or Rapid Prototyping (RP). The results obtained through the analytical and FE analysis show a signiﬁcant decrease of the PoissonÕs ratio for the internal cell angle between 20° and +20° compared to the classical re-entrant conﬁgurations exhibited in literature. The results also show that the presence of edge corners in the unit cell honeycomb conﬁguration gives rise to a cellular structure with enhanced ﬂexibility compared to the classical centresymmetric one. The results obtained by the ana- lytical model show good agreement with the Gibson and Ashby rib-bending model when the honeycomb conﬁguration reduces to the theoretical layout without modiﬁcations due to manufacturing constraints. Ó 2005 Elsevier Ltd. All rights reserved. Keywords: Auxetic; Honeycomb; Mechanical properties; YoungÕs moduli; PoissonÕs ratio; Finite element; Analytical model 1. Introduction Honeycomb core materials have been produced in vari- ous forms and developed for a range of applications, using in general a hexagonal cell shape for optimum eﬃciency, being relatively simple to manufacture and ideal for the construction of ﬂat sandwich panels. A disadvantage of the hexagonal cell honeycomb is the anticlastic or sad- dle-shaped curvature assumed during bending because of the eﬀective in-plane positive PoissonÕs ratios. Anticlastic curvature constitutes a serious production problem for radome structures. In fact, curved or dome-shaped sand- wich panels are commonly produced by forcing a sheet of honeycomb into the desired shape, causing local crush- ing of the cells, or by machining a block to the required proﬁle, with additional costs involved. However, if the eﬀective PoissonÕs ratio is made negative by altering the cell shape domed or sinclastic curvatures can be achieved naturally. The negative PoissonÕs ratio (NPR), or auxetic, characteristic is due to the re-entrant shape of the honey- comb unit cell. The value of the in-plane PoissonÕs ratio is determined by the cell geometry alone whereas the stiﬀness in bending of the sheet of honeycomb is related to the mechanism by which the individual cells deform, which in turn, is determined by the material properties of the cell wall material. Gibson and Ashby [1] developed a seminal model that successfully predicts PoissonÕs ratio for macro- scopic honeycombs, assuming small deformation by ﬂex- ure. Masters and Evans [2] have proposed also a theory for general honeycombs where hinging and stretching mechanisms, combined with wall ﬂexure, describe the linear elastic properties of these cellular solids. Both Gibson and Ashby [1] and Masters and Evans [2] approaches are able to model re-entrant centresymmetric honeycomb structures, with negative internal cell angles, 0263-8223/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruct.2005.09.035 * Corresponding author. Address: Laboratoire de Me ´canique & Struc- tures (LMS), BP 401, Universite ´ 08 Mai 1945, Guelma 24000, Algeria. Tel.: +213 37 21 58 50; fax: +213 37 20 72 68. E-mail addresses: ar_bezazi@yahoo.com, a.bezazi@sheﬃeld.ac.uk (A. Bezazi). 1 Tel.: +44 114 222 78 48; fax: +44 114 222 78 90. www.elsevier.com/locate/compstruct Composite Structures 71 (2005) 356–364