Unimode metamaterials made from rotating rigid triangles are analysed mathematically for their mechanical and thermal expansion properties. It is shown that these unimode systems exhibit positive Poisson's ratios irrespective of size, shape and angle of aperture, with the Poisson's ratio exhibiting giant values for certain conformations. When the Poisson's ratio in one loading direction is larger than +1, the systems were found to exhibit the anomalous property of negative linear compressibility along this direction, that is, the systems expand in this direction when hydrostatically compressed. Also discussed are the thermal expansion properties of these systems under the assumption that the units exhibit increased rotational agitation once subjected to an increase in temperature. The effect of the geometric parameters on the aforementioned thermo-mechanical properties of the system, are discussed, with the aim of identifying negative behaviour.
years, it has been possible to note an emergence of promising directions of studies that address the possibility of observing these effects. In fact, one of the most interesting directions of studies related to this topic are mechanical metamaterials, [3,[28][29][30][31][32] that is, structures that can exhibit counterintuitive mechanical behavior based primarily on their design. Mechanical metamaterials are known for their ability to exhibit counterintuitive mechanical properties such as auxetic behavior, [33][34][35][36][37][38][39][40] negative stiffness [2,41] and negative compressibility [42,43] that are essential in many industries. However, in a vast majority of cases, standard mechanical metamaterial proved insufficient while searching for structures capable of exhibiting versatile deformation patterns. This in turn led to intensive studies devoted to hierarchical mechanical metamaterials, [44][45][46] that is, structures composed of elements having their own geometry that normally can deform irrespective of the rest of the system.Despite the large popularity of hierarchical mechanical metamaterials, it is a relatively new thread in the field of mechanical metamaterials. It seems that some of the first studies devoted to this topic were published by Gatt et al. [45] and Cho et al. [46] where the famous hierarchical rotating square system was proposed. In the following years, it was demonstrated [45][46][47][48][49] that this structure can exhibit tunable auxetic behavior where the extent of auxeticity depends on the relative rate of the deformation of hierarchical levels constituting the system. Recently, it was also reported that the design of the hierarchical square system can be modified in order to change its characteristic. [4,[50][51][52][53] Similar studies based primarily on the extent of the observed auxeticity were also conducted for structures based on rotating rectangles [54] as well as re-entrant and other honeycombs. [54][55][56][57][58] Even though the concept of hierarchical mechanical metamaterials proved to be very popular and resulted in numerous publications, it is possible to note that the hierarchical structures proposed up to date normally share several limitations. First, most of the known hierarchical mechanical metamaterials are designed in a way where their different hierarchical levels correspond either to the same deformation mechanism or to structures having very similar Poisson's ratio. Hence, the possible range of the resultant auxetic behavior is relatively small and may prove to be insufficient in the case of applications where functional materials must significantly change their mechanical response. Another limitation of the already reported hierarchical metamaterials is the fact that in a vast majority of cases, their ability to exhibit the tunable mechanical behavior Shape morphing and the possibility of having control over mechanical properties via designed deformations have attracted a lot of attention in the materials community and led to a variety of applications w...
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