Negative Mechanical Characteristics of Self‐Similar Star‐Like Hinged Grilles

Ferroelastic textures called star patterns are transformable into grilles whose rigid bars replace domain boundaries and are connected with hinges at their junctions. The grilles show several levels of self‐similarity. Exact formulae for the scaling factors as functions of the shape and number N of the arms are provided. The minimal dynamic model of such systems involves force constants at only one level (generation) of self‐similarity. The minimal set of force constants ensures stability of the stars with N = 2 and N = 3. At N = 4 the minimal model exhibits exactly one mode of zero frequency. The reaction of the four‐arm star to a tensile stress applied at the level of the force constants depends on the self‐similarity scaling factor and on the separation between the applied stress and the generation where the observation is made. In some regions of these parameters the reaction is analogous to auxetics but it also shows negative tensile characteristics, that is, a shrinking in the direction of the stress axis. With increasing distance from the external perturbation toward outer generations of self‐similarity the system shows a surprisingly fast restoration of the symmetry broken by the stress.