Disordered auxetic networks with no re-entrant polygons

Abstract

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

arXiv comment5 pages, 4 figures

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Cited by in corpus (4)

• Free-then-freeze: transient learning degrees of freedom for introducing function in materials
• Realizing negative Poisson's ratio in unstressed spring networks
• The Ideal Glass and the Ideal Disk Packing in Two Dimensions
• Realizations of Isostatic Material Frameworks