**4. Conclusions**

A novel hierarchical metamaterial with tailorable mechanical properties was proposed using re-entrant planar lattice structure with star-shaped subordinate cell. The effective non-dimensional moduli and Poisson's ratio in plane were simulated by FE homogenization firstly, then the influences of the geometric parameters on mechanical behavior and relative density were studied in detail. It was found that the new hierarchical metamaterial can obtain large variations and control of the design of the in-plane mechanics through the variations of parameters for both the re-entrant RUC and star subordinate cell. Comparing with conventional re-entrant honeycomb, the novel star-re-entrant metamaterial has enhanced mechanical properties of specific stiffness and auxeticity accounting for its hierarchical porosity as well as multilevel tunable parameters. In addition, the new auxetic metamaterial is more convenient fabricated by 3D printing technique as less stress concertation occurs in the connecting tips of star subordinate cell when compared with other zero Poisson's ratio star cellular structure. However, the inclined angle of parent re-entrant RUC is restricted to 45◦ due to the symmetric simplification of star subordinate cell; as a result, in-plane effective mechanical behavior of the new hierarchical metamaterial can be limited by lacking another internal inclined angle of sub cell. In general, optimum results such as small values of parameters *L*0, *t* and θ for sub cell as well as small amount of *Nx* and moderate number of *Ny* for parent RUC can provide the new hierarchical metamaterial with whole auxetic behavior and strong specific stiffness in-plane simultaneously. It is believed that the innovative hierarchical metamaterials will greatly expand the potential applications in the construction, manufacturing and transportation industries due to the inherent low-weight associated with hierarchical systems, like doubly curved panels in aerospace or marine structures. It can also be used in conformable and stretchable electronics, biomedical devices such as porous smart bandage releasing different classes of medications to different extents, as well as the design of smart auxetic stents, etc.

**Author Contributions:** W.Z., J.W. and F.S. conceived, designed and directed the project. W.Z., S.Z. and R.S. performed the simulations. W.Z. and S.Z. wrote the paper. All authors analyzed the data, discussed the results, and commented on the manuscript.

**Funding:** This work was funded by Pre-research Foundation of Shenyang Aircraft Design and Research Institute, Aviation Industry Corporation of China (Grant No. JH20128255) as well as Pre-research Key Laboratory Foundation of General Armament Department of China (Grant No. JZ20180035).

**Acknowledgments:** Wenjiao Zhang would like to thank British Council and Chinese Scholarship Council (CSC) for the funding of her research work through University of Bristol.

**Conflicts of Interest:** The authors declare no conflicts of interest.
