Designing hierarchical metamaterials by topology analysis with tailored Poisson's ratio and Young's modulus

In this work, we present an innovative three-dimensional (3D) hierarchical design strategy to systematically summarize the configuration characteristics of existing cellular structures and propose a novel class of mechanical metamaterials based on topology analysis, which have tailored Poisson's ratio and Young's modulus. Theoretical, numerical and experimental analyses were conducted to reveal the basic mechanical properties of the metamaterials. And these results agree very well which validate the correctness of the theories. Samples of the proposed structures made of Nylon were fabricated through 3D printing technology to carry out compression tests and finite element analysis (FEA) were performed to give an insight into the mechanical response. Experimental and numerical results revealed that the proposed 3D second-order hierarchical metamaterials can achieve a series of special combinations of Poisson's ratio in three perpendicular directions. The sign and magnitude of Poisson's ratio can be tailored by appropriately adjusting the first and second order configurations and their geometrical parameters. Meanwhile, systemic analysis and comparison reveal that relative Young's modulus is contingent on deformation pattern, i.e., axial-deformation dominated stiffness is much higher than bending-dominated stiffness. Similar to Poisson's ratio, the magnitude of Young's modulus can be tailored by geometrical parameters and first and second order configurations in a relative large range in the case of given Poisson's ratio (sign and magnitude). This work can provide useful reference for the design, fabrication and analysis of 3D metamaterials with novel properties and functions, particularly with auxetic behavior, which are promising in some technical applications.