Volumetric strain as a measure of auxeticity, a case study on polygonprism unit cells
R.G.W. van den Bergh (TU Delft - Mechanical Engineering)
J.L. Herder – Mentor (TU Delft - Mechatronic Systems Design)
P. Roberjot – Mentor (TU Delft - Mechatronic Systems Design)
Jieun Yang – Graduation committee member (TU Delft - Mechatronic Systems Design)
F.G.J. Broeren – Graduation committee member (TU Delft - Precision and Microsystems Engineering)
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Abstract
Auxetic metamaterials are engineered structures commonly characterised by their negative Poisson’s ratio, which indicates transverse expansion when the structure is stretched axially. However, Poisson’s ratio becomes increasingly difficult to apply and interpret for non-cubic unit cells with higher-order symmetry or complex geometries. This limitation contributes to the strong focus on cubic unit cells in current research, despite their limited robustness due to a restricted number of symmetry axes. This study proposes volumetric strain as an alternative and geometry-independent measure of auxeticity. The approach is demonstrated through a case study on non-cubic polygon-prism unit cells generated by in-plane copy rotation. The mechanical behaviour of 2-, 4-, 6-, and 8-fold configurations is analysed using an analytical rigid-body replacement model, finite element simulations, and experimental testing. A Hoberman ring is introduced as an intermediary mechanism to enable uniform multi-directional actuation using a one-dimensional tensile tester. The results show that volumetric strain provides a consistent and robust description of auxetic behaviour across all configurations and modelling approaches. In contrast, Poisson’s ratio exhibits strong sensitivity to small deviations near zero strain and leads to inconsistencies between analytical, numerical, and experimental results. The experimental force–displacement response confirms a linear scaling with the number of bases, while the volumetric strain remains independent of the initial polygonal shape of the unit cell. These findings demonstrate that volumetric strain is a reliable measure of auxeticity for non-cubic unit cells and offers clear advantages for the analysis and experimental validation of complex auxetic geometries. The proposed framework provides a foundation for extending auxetic metamaterial design towards more intricate structures, including spatially copy-rotated unit cells and honeycombs based on Archimedean solids.