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3D auxetic mechanical metamaterials: an analytical, numerical, and experimental study

Metamaterials are man-made rationally-designed structures that present unprecedented mechanical properties not found in nature. One of the most common metamaterials are Auxetics which demonstrate negative Poisson’s ratio (NPR) behavior that is very beneficial for biomedical and engineering applications. In this study, a specific type of auxetic metamaterial structure namely idealized 3D re-entrant structure is studied analytically, numerically, and experimentally. The noted structure is constructed of three types of struts: one loaded purely axially, and two loaded simultaneously flexurally and axially which are inclined and are spatially defined by angles θ and φ). Analytical relationships for elastic modulus, yield stress, and Poisson’s ratio of the 3D re-entrant unit cell based on two well-known beam theories namely Euler-Bernoulli and Timoshenko theories are derived. Moreover, two numerical approaches one based on beam elements and the other based on volumetric elements are implemented. Moreover, several specimens are additively manufactured and tested under compression. The analytical results had good agreement with volumetric numerical model and experimental results. Moreover, the effect of various geometrical parameters on the mechanical properties of the structure was studied and the results demonstrated that angle θ (related to tension-dominated struts) has the most effect on the sign of the Poisson’s ratio and its extent, while angle φ (related to compression-dominated struts) has minimal effect on Poisson’s ratio. However, the struts corresponding to φ angle provide strength and stiffness for the structure. The results also demonstrated that the structure could have zero Poison’s ratio for a specific range of θ and φ angles. Finally, a lightened re-entrant structure is introduced and its results are compared to those of the idealized 3D re-entrant structure.