Poisson's ratio flow diagrams, that is, the Poisson's ratio versus the
fiber fraction, are obtained numerically for hexagonal arrays of elas
tic circular fibers in an elastic matrix. High numerical accuracy is a
chieved through the use of an interface integral equation method. Ques
tions concerning fixed point theorems and the validity of existing asy
mptotic relations are investigated and partially resolved. Our finding
s for the transverse effective Poisson's ratio, together with earlier
results for random systems by other authors, make it possible to formu
late a general statement for Poisson's ratio flow diagrams: For compos
ites with circular fibers and where the phase Poisson's ratios are equ
al to 1/3, the system with the lowest stiffness ratio has the highest
Poisson's ratio. For other choices of the elastic moduli for the phase
s, no simple statement can be made. (C) 1996 American Institute of Phy
sics.