Design of isotropic 2D chiral metamaterials based on monohedral pentagonal tessellations

A novel class of transversely-isotropic metamaterials with the potential to exhibit a wide range of Poisson’s ratios and stiffnesses is proposed in this work. These metamaterials, which also have the potential to exhibit auxetic behaviour, are formed through the chiralisation of 2D monohedral Euclidean pentagonal tessellations. Through Finite Element simulations and experimental testing on additively manufactured prototypes, we show that these systems can exhibit Poisson’s ratios which encompass the entire range of transverse isotropicity, i.e. +1 to -1, and that the mechanical properties of these structures can be tailored considerably through variation of the geometric parameters without a loss of global symmetry and isotropy. The level of versatility observed in these new metamaterials exceeds by far that which is commonly found in traditional and well-known isotropic auxetic systems such as hexachiral honeycombs. In addition, analytical expressions pertaining to the geometric limits which define the realisability of this new class of auxetic metamaterials have also been derived and presented. The findings of this work demonstrate that pentagonal tessellations have considerable potential for the development of novel metamaterials and that the geometric constraints associated with transverse isotropy need not necessarily be an insurmountable barrier for the design of metamaterials with tailorable and versatile mechanical properties.