Symmetry detection of auxetic behaviour in 2D frameworks
Materials Science
2015-06-16 v1
Abstract
A symmetry-extended Maxwell treatment of the net mobility of periodic bar-and-joint frameworks is used to derive a sufficient condition for auxetic behaviour of a 2D material. The type of auxetic behaviour that can be detected by symmetry has Poisson's ratio -1, with equal expansion/contraction in all directions, and is here termed equiauxetic. A framework may have a symmetry-detectable equiauxetic mechanism if it belongs to a plane group that includes rotational axes of order n = 6, 4, or 3. If the reducible representation for the net mobility contains mechanisms that preserve full rotational symmetry (A modes), these are equiauxetic. In addition, for n = 6, mechanisms that halve rotational symmetry (B modes) are also equiauxetic.
Keywords
Cite
@article{arxiv.1305.5752,
title = {Symmetry detection of auxetic behaviour in 2D frameworks},
author = {H. Mitschke and G. E. Schroeder-Turk and K. Mecke and P. W. Fowler and S. D. Guest},
journal= {arXiv preprint arXiv:1305.5752},
year = {2015}
}