POISSON RATIO IN COMPOSITES OF AUXETICS

Mean-field theory of elastic moduli of a two-phase disordered composit e with ellipsoidal inclusions is reviewed together with an indication as to how interactions among inclusions may be taken into account. In the mean-field approximation, the effective Poisson ratio sigma(e) in composites with auxetic inclusions of various shapes such as discs, sp heres, blades, needles, and disks is studied analytically and numerica lly. It is shown that phase properties such as inclusion volume or are a fraction phi and matrix and inclusion Poisson ratios (sigma(m) and s igma) and Young's moduli (E-m and E) have a marked effect on sigma(e). The earlier theoretical findings of the existence of auxeticity windo ws and the widening effect of inclusion-inclusion interactions on the window for delta=E/E-m are reconfirmed for composites of auxetic spher es in both two and three dimensions, with new auxeticity windows disco vered for the other inclusion shapes. For a composite with sigma= -0.8 , sigma(m) = 0.25, and phi=0.4, it is found that the sphere is the mos t sigma(e)-lowering or negative-sigma(e)-producing inclusion shape for delta around 1/2, while disklike inclusions yield a most negative sig ma(e) for delta greater than 1. [S1063-651X(98)03911-7].