Mixed‐Mode Multidirectional Poisson's Ratio Modulation in Auxetic 3D Lattice Metamaterials

Abstract

If a conventional material is compressed in one direction, it tries to expand in the other two perpendicular directions and vice versa, indicating a positive Poisson's ratio. Recently auxetic materials with negative Poisson's ratios, which can be realized through artificial microstructuring, are attracting increasing attention due to enhanced mechanical performances in multiple applications. Most of the proposed auxetic materials show different degrees of in‐plane auxeticity depending on their microstructural configurations. However, this restricts harnessing the advantages of auxeticity in 3D systems and devices where multidirectional functionalities are warranted. Thus, there exists a strong rationale to develop microstructures that can exhibit auxeticity both in the in‐plane and out‐of‐plane directions. Herein, generic 3D connected double loop (3DCDL) type periodic microstructures are proposed for multi‐directional modulation of Poisson's ratios. Based on the bending dominated behavior of elementary beams with variable curvature, mixed‐mode auxeticity following the framework of multimaterial unit cells is demonstrated. The proposed 3DCDL unit cell and expanded unit cells formed based on their clusters are capable of achieving partially auxetic, purely auxetic, purely nonauxetic and nullauxetic behavior. Comprehensive numerical results are presented for the entire spectrum of combinations concerning the auxetic behavior in the in‐plane and out‐of‐plane directions including their relative degrees.