Significance of cell number on the bulk elastic properties of auxetic reentrant lattices

Auxetics are characterized by a negative Poisson's ratio, expanding/contracting in tension/compression. Given this behavior, they are expected to possess high shear, fracture and indentation resistance, and superior damping. The lack of natural isotropic auxetics promoted an effort to design structures that mimic this behavior, e.g. reentrant model. This last is based on honeycombs with inverted protruding ribs. Commonly, this model is employed in lattices and has been thoroughly studied in terms of mechanical properties and deformation behavior. Given that the amount of cells has an influence in the overall internal structural behavior, there seems to be an absence of data that determines the minimum number of cells for such structure to present internal static bulk properties. Recurring to FEA, this study determines the minimum number of cells to obtain an overall face constrained auxetic lattice with internal bulk elastic behavior, namely in terms of normalized Young's modulus and Poisson's ratio. It is shown that adding reentrant cells increases the Poisson's ratio on an exponential rise to maximum function, reducing the normalized Young's modulus on an exponential decay function. Fundamentally, a minimum number of 13 cells per row to obtain an internal bulk behavior in lattices with constrained faces.