Interlocking hexagons model for auxetic behaviour

A 2D 'Rough Particle' model consisting of interlocking hexagons is reported. Analytical expressions for the in-plane Poisson's ratios and Young's moduli due to particle translation along the geometrically matched male and female interlocks are derived for the model. The dependency of the mechanical properties on each of the model (geometrical and stiffness) parameters is provided, and it is shown that the assembly of interlocking hexagons deforming by particle translation along the interlocks displays auxetic (negative Poisson's ratio) behaviour. The model predictions are compared with experimental mechanical properties for auxetic polypropylene (PP) films and fibres. The model predicts the experimental Poisson's ratio values very well (model: nu(xy) = -1.30, nu(yx) = -0.77; experiment (PP films): nu(||) = -1.12, nu(perpendicular to) = -0.77). The model generally overestimates the Young's moduli of the films, but is in reasonable agreement with the axial Young's modulus of the fibres.