Disordered auxetic networks with no reentrant polygons

It is widely assumed that disordered auxetic structures (i.e., structures with a negative Poisson's ratio) must contain reentrant polygons in two dimensions (2D) and reentrant polyhedra in 3D. Here, we show how to design disordered networks in 2D with only convex polygons. The design principles used allow for any Poisson's ratio -1<ν<1/3 to be obtained with a prescriptive algorithm. By starting from a Delaunay triangulation with a mean coordination (z)≃6 and ν≃0.33 and removing those edges that decrease the shear modulus the least, without creating any reentrant polygons, the system evolves monotonically towards the isostatic point with (z)≃4 and ν≃-1.