Design of auxetic sandwich panel faceplates comprising cellular networks with high stiffness and negative Poisson’s ratio

Abstract

In the present work, a novel design is presented for producing auxetic laminated faceplates for structures that contain auxetic cores in order to produce fully auxetic sandwich structures. The design is based on the use of periodic cellular networks that are embedded in a fibre-reinforced polymer matrix. These networks have a high in-plane negative Poisson’s ratio and a high in-plane stiffness. Two auxetic networks were chosen for this purpose: a classical re-entrant hexagonal network and an anti-tetra chiral auxetic network. The finite elements method was used to model the auxetic network and the faceplate. For the auxetic network, the relative modulus (Es/Em) was investigated to determine its effect on the behaviour of the faceplate. The auxetic behaviour of the faceplate occurs when the auxetic network has a high relative modulus. For example, for a classical re-entrant hexagonal network faceplate, the auxetic behaviour starts to appear when Es/Em > 33, while for an anti-tetra chiral auxetic network faceplate, the auxetic behaviour starts to appear when Es/Em > 24. Analytical expressions for the elastic constants of the faceplates were developed using the representative volume element model (RVE) and a semi-empirical formula of the rule of mixtures (ROMs). The results of the analytical expressions were compared with the finite elements results for various values of the relative density parameter ρ*. The relative density had a significant effect on the elastic constants of the faceplate. The model produced with the representative volume element method had higher values for the elastic constants than did that created with the finite elements model, but the semi-empirical rule of mixtures gave more accurate results for both types of faceplates. A modified design for the classical re-entrant hexagonal network that increases the in-plane stiffness of the auxetic network is presented since it has been found that it plays a major role in producing a high negative Poisson’s ratio. The modified networks are an oval re-entered and a stiffened re-entered network. Experiments were carried out on the oval re-entered faceplates to obtain the in-plane moduli and the Poisson’s ratios. The tested faceplate samples clearly showed auxetic behaviour. A good agreement between the finite elements results and the experimental data was obtained.