@article{1214659ad0264a4482a282f0ee825bf9,
title = "Disordered auxetic networks with no reentrant polygons",
abstract = "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.",
author = "Hagh, {Varda F.} and Michael Thorpe",
note = "Funding Information: We acknowledge useful discussions with Sidney Nagel, Andrea Liu, Louis Theran, and Mahdi Sadjadi. The work at Arizona State University is supported by the National Science Foundation under Grant No. DMS 1564468. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation Grant No. ACI-1548562. Funding Information: We acknowledge useful discussions with Sidney Nagel, Andrea Liu, Louis Theran, and Mahdi Sadjadi. The work at Arizona State University is supported by the National Science Foundation under Grant No. DMS 1564468. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation Grant No. ACI-1548562. Publisher Copyright: {\textcopyright} 2018 American Physical Society.",
year = "2018",
month = sep,
day = "24",
doi = "10.1103/PhysRevB.98.100101",
language = "English (US)",
volume = "98",
journal = "Physical Review B",
issn = "2469-9950",
publisher = "American Physical Society",
number = "10",
}