Scholars have shown significant interest in the design and investigation of mechanical metamaterials with a negative Poisson’s ratio as a result of the rapid progress in additive manufacturing technology, giving rise to the concept of metamaterials. The mechanical properties of structures with a negative Poisson’s ratio, including Poisson’s ratio, elastic modulus, and impact performance, have received growing scrutiny. This paper introduces the design of a novel concave beetle-shaped structure with a negative Poisson’s ratio. The structure is developed using the variable density topology optimization method, with the design parameters adjusted to achieve optimal results from six datasets. The mechanical properties of the concave beetle-shaped structure are comprehensively assessed with the integration of mathematical models derived from mechanics theory, quasi-static compression tests, and finite element analyses. This study’s findings indicate that the intrinsic parameters of the structure significantly influence its properties. The structure’s Poisson’s ratio ranges from −0.267 to −0.751, the elastic modulus varies between 1.078 and 5.481 MPa, and the specific energy absorption ranges from 1.873 to 2.634 kJ/kg, demonstrating an improvement of up to 40%.

Due to their superior structural and mechanical properties, materials with negative Poisson’s ratio are of increasing interest to research scholars, especially in fuel-efficient vehicles. In this work, a new concave I-shaped honeycomb structure is established by integrating the re-entrant hexagon and the I-shaped beam structure, and its negative Poisson’s ratio characteristics and energy absorption properties are investigated. The effect of structural parameters on the energy absorption characteristics is analyzed using the finite element model. The results show that both the specific energy absorption and peak impact force decrease with the increase in cellular length and vertical short cellular height, and increase with the increase in horizontal short cellular length and cellular thickness. To obtain a smaller peak impact force and larger specific energy absorption with smaller mass, the four cell sizes were optimized by using Latin hypercube sampling, Gaussian radial basis function, and non-dominated sorting genetic algorithm II (NSGA-II). Compared with the original design, the SEA increased by 44.175%, and the PCF increased by 25.857%. Meanwhile, the mass decreased by 31.140%. Hence, the optimal structure has better crashworthiness.