  Anisotropic laminates with a negative Poisson's ratio for at least some
directions are called auxetic. In this paper, we consider the conditions for
optimizing the auxeticity of an orthotropic laminate, namely: for a laminate
composed by a given material, (i) how to obtain the lowest, i.e. the highest
negative, Poisson's ratio and (ii) how to maximize the auxetic zone, i.e. the
set of directions where the Poisson's ratio is negative. It is shown that in
both the cases the optimal solution is found on the boundary of the feasible
domain and in particular that it can be obtained using angle-ply sequences of
identical layers. The polar method with dimensionless moduli is employed for
representing the anisotropic behavior of the laminate, which allows, on the one
hand, to reduce the dimensionality of the problem and, on the other hand, to
have an effective mathematical representation of anisotropy by dimensionless
invariants.
