Metabeams with intrinsic tension-rotation and tension-shear-rotation couplings for tailoring auxeticity

Negative Poisson's ratios commonly arise from internal rotational mechanisms. However, conventional honeycombs generally remain non-auxetic because their ligaments behave as classical beams with largely decoupled axial, shear, and rotational responses. Here, antichiral and chiral metabeams containing periodically embedded rotating bodies are introduced to encode element-level tension-rotation coupling (TRC) and tension-shear-rotation coupling (TSRC), respectively. Using these metabeams as structural building blocks, two complementary classes of mechanical metastructures are developed. First, metabeams are embedded into conventional antichiral and chiral honeycombs, tailoring the magnitude and sign of their effective Poisson's ratios. Second, metabeams are incorporated into conventional hexagonal honeycombs, where inclined ligaments are represented by complete stiffness matrices. Closed-form relationships between Poisson's ratio and stiffness coefficients are derived, identifying the axial-shear stiffness term as the key governing parameter and demonstrating sign reversal to negative Poisson's ratios even under positive skew angles. A deformation-competition perspective further elucidates how rotation of main rings, TRC/TSRC-induced metabeam deformations and direct bending of metabeams jointly govern auxeticity in these metastructures. Overall, this work establishes an element-level coupling strategy for programmable auxeticity and presents metabeams as mechanically interpretable building blocks for lightweight, functionally tunable mechanical metamaterials.