A novel monoclinic auxetic metamaterial with tunable mechanical properties

Abstract

Missing rib auxetics with a reinforced central core may have tunable negative Poisson's ratios (NPRs) and other mechanical parameters. In analogy with the other enhanced missing rib configurations (e.g., enhanced hexa-, anti-tri- and anti-tetra-missing rib honeycombs), a novel enhanced tetra-missing rib honeycomb metamaterial is proposed in this work. Similar as the classical tetra-chiral honeycomb, the proposed enhanced tetra-missing rib honeycomb metamaterial also exhibits monoclinic property, i.e., undergoing coupled shearing and stretching/shrinking under monotonic tension/compression. To facilitate the understanding of the underlying microstructural mechanisms, a theoretical model under the infinitesimal deformation assumption is developed by a simple energy-based approach. The obtained analytical solutions are validated by systematic finite element (FE) analyses conducted for a unit-cell with periodic boundary conditions, and elucidate different roles of the microstructural geometry on the effective mechanical properties of the proposed metamaterial. It is shown that the proposed metamaterial exhibits tailorable Poisson's ratios (from -1 to 0) as well as elastic (over five orders of magnitude) and shear moduli (over four orders of magnitude) in wide ranges. Compared with the previously developed enhanced anti-tetra-missing rib honeycomb, which has the same building block as the proposed design in this paper, the stiffness of the present design is improved remarkably with the same geometrical parameters owing to its monoclinic property. The improvement can even reach two orders of magnitude in some cases. Uniaxial tensile experimental tests and finite-size FE simulations for the proposed metamaterial structures consisting of an array of unit-cells are also performed to validate the theoretical and FE results obtained from the unit-cell analyses.