Junction mechanics governing effective Poisson's ratio and stress concentration in re-entrant auxetic lattices

초록

Auxetic unit-cells achieve a negative Poisson's ratio primarily through the rotation of inclined members, especially in the well-known re-entrant unit-cell. The junctions linking their members are typically considered just geometric connections, but their local geometry can affect stress concentration and the structure's effective response. This study examines how junction design affects auxetic deformation and stress concentration while the main unit-cell parameters are held fixed. Solid (S), open circular (OC), open square (OS), and open auxetic (OA) junction types were fabricated from thermoplastic polyurethane (TPU) using fused filament fabrication and tested under quasi-static uniaxial tension with digital image correlation. Finite element simulations evaluated structural deformation, stress distribution, and junction rotation. For the largest junction, S increased the magnitude of effective Poisson's ratio (EPR) by 151% compared with the reference re-entrant unit-cell. However, this improvement was accompanied by increases of 39% in specimen mass and 224% in maximum von Mises stress. At the same junction size, OC increased the EPR magnitude by 72%, with limited mass and maximum von Mises stress increases to 14% and 23%, respectively. The magnitude of EPR decreased by 36%, 14%, 33% and 29% when the junction size was scaled down from the largest to the smallest for S, OC, OS and OA, respectively. These results show how the junction design controls the auxetic response, stress concentration, and mass, all of which are important consideration in lightweight structures.

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