Gy. Wei et Sf. Edwards, POISSON RATIO IN COMPOSITES OF AUXETICS, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 58(5), 1998, pp. 6173-6181
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].