Finite element analysis of C-shaped auxetic reentrant structure validated experimentally: Insights into buckling and mechanical behavior

This study examines the mechanical behavior of a C-shaped reentrant auxetic cylindrical structure using finite element analysis (FEA) for five unit-cell configurations, with the length and height varied together (l = h) from 8 to 11 mm. Experimental validation was conducted for the 9.5 mm configuration. The results show a gradual decrease in peak force from 870 N at 8 mm to 418 N at 11 mm. For the 9.5 mm configuration, the experimental peak force was 602.8 N, and the force-displacement response agreed reasonably well with the FE predictions before the peak, although differences became more pronounced during post-peak deformation. A similar trend was observed in stiffness, which decreased from 1712.5 N/mm for the 8 mm model to 294.9 N/mm for the 11 mm model. The experimental stiffness at 9.5 mm was 560.0 N/mm. The energy absorbed over the first 4 mm of displacement was 1.87 J in the FE model and 1.13 J in the experiment, indicating that the numerical model overestimated the measured energy absorption. The Poisson's ratio remained negative across the investigated configurations, ranging from −1.21 to −2.12, confirming the auxetic response of the structure. These findings indicate that the reentrant geometry offers potential for vibration-control applications in optical equipment. Nevertheless, its effectiveness within the 10–1000 Hz frequency range remains to be established through dynamic testing. The differences between the numerical predictions and experimental measurements also suggest that material behavior, contact conditions, friction, and mesh convergence warrant further investigation to improve the reliability of the FE model.