Tessellated tubular metamaterials with programmable poisson’s ratio and chirality

Tubular metamaterials exhibit exotic mechanical properties, including negative Poisson’s ratio (NPR), zero Poisson’s ratio (ZPR), and chirality induced by geometrical configurations rather than intrinsic material properties. However, existing tubular designs strongly depend on ad hoc modifications of known structural internal units, limiting systematic exploration of design space. This paper presents a generalized geometric method for designing tessellated tubular metamaterials by mapping two-dimensional polygonal tessellations onto tubular surfaces through a linear coordinate transformation. The method enables independent tuning of internal unit geometry and alignment direction. Finite element simulations using Timoshenko-beam elements, which are validated by solid elements and experiments, evaluate the axial compression and torsional response of the resulting metamaterials with hexagonal, quadrilateral, and pentagonal tessellations. The results demonstrate that the proposed framework generates tubular metamaterials exhibiting NPR, ZPR, and chiral deformation behaviors. The in-plane Poisson’s ratio and alignment direction of units govern the resulting Poisson’s ratio and chirality. A previously unreported hybrid chiral-undulated deformation is identified in the design space of quadrilateral units. Moreover, a hexagonal tubular metamaterial exhibits torsion up to 17.029 ∘ under 1 % compression, exceeding previously reported values. This approach expands the design space of tubular metamaterials and offers a unified geometric foundation for producing programmable mechanical properties. • A unified geometric framework converts 2D tessellations into tubular metamaterials. • Shape and alignment of units tailor Poisson’s ratio and chiral behaviors. • 2D compression–shear coupling yields axial–torsional coupling in tubular metamaterials. • Hybrid chiral-undulated mode is discovered in a previously unexplored design space. • The framework provides general design principles for programmable tubes.