Enhancing the Mechanical Properties of Auxetic Metamaterials by Incorporating Nonrectangular Cross Sections into Their Component Rods: A Finite Element Analysis

Abstract

Herein, four prevalent architectures of metamaterials, namely, the arc‐star, star, reentrant, and antichiral models, are examined to study the effects of the cross‐sectional shapes of component rods on the stiffness and Poisson's ratios of the materials. Four differently sized cross sections of rods are designed, and two types of cross‐sectional geometries—square and I‐shaped—are adopted. Aspect ratios of 0.5, 0.75, and 1 are considered for the I‐shaped cross‐sectional models. A total of 64 metamaterial models are analyzed. The results show that the stiffness and negative Poisson's ratios of the metamaterials depend primarily on their architectures. For example, the antichiral model exhibits approximately 13 times more stiffness than its arc‐star counterpart. The cross‐sectional geometries of the component rods also play an essential role in the mechanical behaviors of the metamaterials. For instance, the antichiral architecture, which consists of bars with an I‐shaped section that has a width‐to‐height ratio of 0.5, has an elastic modulus 9 times greater than that of the model composed of bars with a square cross section. This study shows that it is possible to design metamaterials several times stronger simply by changing the shape of the cross section of their constituent elements without compromising on their lightweight property.