  The problem of obtaining anisotropic auxetic composite laminates, i.e. having
a negative Poisson's ratio for at least some directions, is examined in this
paper. In particular, the possibility of obtaining auxeticity stacking
uni-directional identical plies is considered. It is shown that if the ply is
composed by isotropic matrix and fibers, then it is impossible to obtain
totally auxetic orthotropic laminates, i.e. auxeticity for each direction,
unless at least one among matrix and fibers is auxetic itself. Moreover, it is
shown what are the conditions, in terms of the mechanical properties of the
constituents and of the volume fraction of the fibers, to fabricate
uni-directional plies with which to realize laminates having a negative
Poisson's ratio for some directions. Several existing materials are also
examined. All the analysis is done using the polar formalism, very effective
for the study of plane anisotropic problems.
