Theoretical modeling of the effective elastic constants of a sinusoidal anti-tetra-missing rib auxetic honeycomb

Anti-tetra missing rib auxetic honeycombs represent a typical class of auxetic metamaterials exhibiting pronounced negative Poisson’s ratio (NPR) effect. Conventional straight-ligament designs tend to incur stress concentrations at local nodes, whereas wavy configurations can effectively alleviate this issue. To elucidate the intrinsic relationship between microscopic geometric features and macroscopic mechanical properties, and to provide theoretical guidance for parameter-oriented structural design, this study develops an analytical model for the equivalent Poisson’s ratio and elastic modulus of a sinusoidal anti-tetra-missing rib honeycomb (SATMRH) based on the energy method within the small-deformation framework. Finite element (FE) simulations are conducted to validate the analytical formulations. The results show that the proposed model agrees well with the numerical predictions and accurately captures the influence of geometric parameters on the macroscopic equivalent mechanical properties. Moreover, it is revealed that the structure maintains a nearly constant negative Poisson’s ratio of approximately –0.65, regardless of geometric variations, allowing stiffness tuning without sacrificing auxeticity. This work offers reliable theoretical support for the structural design and performance tailoring of ligament-based anti-chiral auxetic metamaterials.