  A simple model is developed to predict the complex mechanical properties of
carbon nanotube sheets (buckypaper) [Hall \textit{et al.}, \textit{Science}
\textbf{320} 504 (2008)]. Fabricated using a similar method to that deployed
for making writing paper, these buckypapers can have in-plane Poisson's ratios
changed from positive to negative, becoming auxetic, as multiwalled carbon
nanotubes are increasingly mixed with single-walled carbon nanotubes. Essential
structural features of the buckypapers are incorporated into the model:
isotropic in-plane mechanical properties, nanotubes preferentially oriented in
the sheet plane, and freedom to undergo stress-induced elongation by both angle
and length changes. The expressions derived for the Poisson's ratios enabled
quantitative prediction of both observed properties and remarkable new
properties obtainable by structural modification.
