Design optimization of modified re-entrant auxetic metamaterials reinforced with asymmetric edge cells for crushing behavior using the Taguchi method

This work describes the compressive failure behavior and optimization of modified hierarchical re-entrant auxetic metamaterials reinforced with asymmetrical edge cells. The mechanical behavior of these metamaterials is parametrized against the width, thickness and angles of the cells. A Taguchi design (L27 (3(boolean AND)13)) has been performed to determine the effect of the eight geometric factors on the maximum compressive strength (specific strength), mean crushing force (MCF), specific energy absorption (SEA) and Poisson's ratio of the metamaterials. An analysis of variance (ANOVA) has been also performed to find out the relative significance and contribution percentage of each parameter from a statistical standpoint. The results show that the cell wall angle between the lateral and inclined ribs of the re-entrant unit cells has the largest effect on the compressive strength and absorbed energy of the structure that exhibits a percent variation of 82.5%, 30.0%, 85.9% and 75.1% in specific strength, MCF, SEA and Poisson's ratio, respectively. Moreover, the size of slot width and thickness, especially in the inclined struts, have a considerable effect on the mechanical performance compared to the angle of asymmetrical cells. Lastly, two samples from the optimization design table showing the best and worst mechanical responses are manufactured by using 3D printing and are tested under compression loading. The effects of the design factors on the deformation mechanisms and mechanical responses have been discussed by comparing the experimental and FE simulation results. The results show that the deformation mechanism of the asymmetrical unit cells and inclined struts play a key role in the resistance of the structures under compressive loads.