*Article* **In-Plane Mechanical Behavior of a New Star-Re-Entrant Hierarchical Metamaterial**

### **Wenjiao Zhang 1,\*, Shuyuan Zhao 2, Rujie Sun 3, Fabrizio Scarpa 3 and Jinwu Wang 1,\***


Received: 11 May 2019; Accepted: 21 June 2019; Published: 3 July 2019

**Abstract:** A novel hierarchical metamaterial with tunable negative Poisson's ratio is designed by a re-entrant representative unit cell (RUC), which consists of star-shaped subordinate cells. The in-plane mechanical behaviors of star-re-entrant hierarchical metamaterial are studied thoroughly by finite element method, non-dimensional effective moduli and effective Poisson's ratios (PR) are obtained, then parameters of cell length, inclined angle, thickness for star subordinate cell as well as the amount of subordinate cell along *x*, *y* directions for re-entrant RUC are applied as adjustable design variables to explore structure-property relations. Finally, the effects of the design parameters on mechanical behavior and relative density are systematically investigated, which indicate that high specific stiffness and large auxetic deformation can be remarkably enhanced and manipulated through combining parameters of both subordinate cell and parent RUC. It is believed that the new hierarchical metamaterial reported here will provide more opportunities to design multifunctional lightweight materials that are promising for various engineering applications.

**Keywords:** hierarchical; metamaterial; re-entrant structure; auxetic; mechanical behavior
