2013/05/24 by H. Mitschke, Holger Mitschke, G. E. Schroeder-Turk +7 · 25 citations
Engineering · Mathematics · Medicine · Physics and Astronomy · #Advanced Materials and Mechanics #Automotive and Human Injury Biomechanics #Auxetics #Cellular and Composite Structures #Condensed matter physics #Geometry #Global symmetry #Mathematics #Physics #Poisson distribution #Poisson's ratio #Quantum mechanics #Rotational symmetry #Spontaneous symmetry breaking #Symmetry (geometry) #Symmetry breaking #Symmetry group #Symmetry operation #Thermodynamics #cond-mat.mtrl-sci
paper · pdf · doi:10.1209/0295-5075/102/66005
published in Europhysics Letters (EPL) 102(6), 66005 (Institute of Physics)
arxiv created 2013/05/24 · openalex publication_date 2013/06/01 · arxiv updated 2015/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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. © EPLA, 2013.