5. Conclusion
Auxetic materials present a series of particular characteristics in comparison to conventional materials, such as enhancement of shear modulus, indentation resistance, and fracture toughness. However, the in-plane stiffness of them is relatively low. In this paper, a novel honeycomb, comprised of re-entrant hexagonal con- figuration and rhombic configuration, is developed. The new structure can be regarded as an optimization to the NRHH by embedding four reinforcing walls into every cell of it. The inplane effective modulus, i.e., the Young’s modulus and Poisson’s ratio, of the new honeycomb are analytically derived, which later verified by finite element simulations. Both the results obtained from the analytical and numerical analysis reveal that the new honeycomb can achieve negative Poisson’s ratio and the in-plane effective Young’s modulus of it is significantly improved compared to the NRHH. The dependence of the in-plane elastic constants on the reentrant angle h0, the cell wall length ratio h0=l0, normalized axial rigidity of the reinforcing walls ðE1A1Þ=ðE0A0Þ and the relative density q=q0 are further studied by using the numerically validated analytical solutions. With respect to the NRHH, the new proposed structure allows more geometric parameters in the unit cell, which provide enhanced in-plane flexibility and tailoring of properties. Results show that, for maintaining a superior auxetic performance, the reinforcing walls should be designed with appropriate axial rigidity. A comparison of in-plane stiffness is carried out between the present design and other periodic topologies. The results reveal that the new honeycomb developed in this paper shows superior stiffness and auxetic behavior with respect to the others.
