A novel butterfly-shaped auxetic structure with negative Poisson’s ratio and enhanced stiffness

Based on the butterfly pattern structure and the star-shaped honeycomb structure, a novel auxetic butterfly-shaped honeycomb structure (BSH) was constructed, which realized the coupling improvement of negative Poisson’s ratio and in-plane stiffness. Under uniaxial tension, the equivalent elastic modulus and Poisson's ratio of the BSH structure were derived by the energy method. The relationship between Poisson's ratio and structural parameters of the BSH structure was discussed to optimize the structural parameters by numerical analysis. Poisson’s ratio and relative elastic modulus were taken as the objective function groups. The Pareto solution set was obtained by the Gamultiobj multi-objective genetic algorithm method. The Pareto solution set was sorted based on the entropy-weight TOPSIS method, and the optimal solution was selected as the solution of the novel structure optimization design. The correctness of the theoretical results was verified by the finite element analysis and experiment results. Furthermore, compared with the traditional re-entrant hexagonal honeycomb structure and the star-shaped honeycomb structure, the relative elastic modulus and auxetic effect of the BSH structure were greatly improved, and the stiffness of the novel structure was improved while maintaining a high auxetic effect.