Directional Auxetic Behavior of Mechanical Metamaterials: Material-Dependent and Geometry-Driven Mechanisms

Mechanical metamaterials derive their unconventional properties from geometry rather than composition, enabling phenomena such as negative Poisson's ratio and tunable stiffness. This study presents a systematic finite element analysis of three canonical auxetic topologies-re-entrant, chiral, and anti-chiral lattices-subjected to uniaxial loading in two orthogonal directions. Four engineering metals (steel, copper, aluminum, titanium) were analyzed to evaluate how material stiffness interacts with geometry in defining auxetic response. A detailed mesh-convergence and sensitivity analysis ensured numerical reliability and isolation of geometric effects within the linear-elastic regime. The results reveal three distinct mechanisms: (i) material-sensitive auxeticity in re-entrant lattices, which achieved the most extreme negative Poisson's ratios (ν < -2.0) but with strong dependence on stiffness; (ii) directional auxeticity in chiral lattices, which exhibited negligible response under X-loading but significant negative values (ν ≈ -0.5) under Z-loading; and (iii) geometry-dominated auxeticity in anti-chiral lattices, which remained robust and nearly material-independent (ν ≈ -1.2). This comparative framework clarifies the balance between geometry- and material-driven mechanisms, extending prior single-material or single-geometry studies. The findings provide design guidelines for selecting auxetic topologies depending on whether robustness, tunability, or maximum auxetic effect is required, with direct implications for protective equipment, aerospace structures, and biomedical scaffolds.