Study of Mechanical Properties of Three-Dimensional Framed Plate Protective Structures with Negative Poisson’s Ratio

In this paper, the negative Poisson’s ratio and rigidity of a protective structure are improved to allow the structure to exert a negative Poisson’s ratio effect in multiple directions and to enhance the structural load-carrying capacity. Therefore, a 3D framed plate honeycomb is designed on the basis of a traditional 2D negative Poisson’s ratio honeycomb. The Poisson’s ratio and modulus of elasticity are derived, and the equivalent mechanics model (EMM) of a 3D framed plate protective structure is established by combining bending deformation, shear deformation, and compression deformation. To verify the validity of the equivalent mechanics model (EMM), a compression test and numerical simulation study are carried out by combining 3D printing technology and numerical simulation methods. In addition, the effects of structural parameters on the modulus of elasticity, negative Poisson’s ratio, and other mechanical properties are discussed. The results show that, under vertical loading, the equivalent Poisson’s ratio and the modulus of elasticity of the cell elements decrease with the increase in the ratios of the lengths of the cell element walls in the upper and lower planes to the length of the diagonal cell element in the concave direction. In addition, it is shown that the elastic modulus increases with increasing concave angle and thickness. Moreover, under lateral loading, the equivalent Poisson’s ratio of the cell elements increases with the ratios of the lengths of the upper and lower planar cell element walls to the length of the diagonal cell element walls, with the angle of concavity and with the thickness of the plate frame, while the modulus of elasticity of the cell elements exhibits the opposite trend and decreases with the thickness of the framed plate structure.