Symmetry detection of auxetic behaviour in 2D frameworks
Mitschke, H., Schröder-Turk, G.E., Mecke, K., Fowler, P.W. and Guest, S.D. (2013) Symmetry detection of auxetic behaviour in 2D frameworks. Europhysics Letters, 102 (6).
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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.
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