Study of equivalent mechanical properties on pyramidal lattice materials

The equivalent mechanical properties of pyramidal lattice materials were established by theoretical analysis and numerical simulation. According to the deformation of pyramidal unit cells and multi-layered pyramidal materials under the action of vertical, horizontal, and shear forces, the equivalent elastic modulus, equivalent shear modulus, and equivalent Poisson's ratios of pyramidal lattice materials in three main directions were derived. The influence of the unit cell parameters on the equivalent elastic modulus, shear modulus, and Poisson's ratios were analyzed at constant relative density of the material. With the increase of the inclination angle of the strut, the equivalent elastic modulus in the z-direction(E-z) increases, and the equivalent elastic modulus in the x-direction(E-x) and y-direction(E-y) first increases and then decreases; the equivalent shear modulus in the x-y plane (G(xy)) decreases, while the equivalent shear modulus in the x-z plane (G(xz)) and y-z plane (G(yz)) first increases and then decreases; the equivalent Poisson's ratios nu(zx), nu(zy) increases, while nu(xy), nu(yx), nu(xz), nu(yz) decreases. The size of the unit cell did not affect the equivalent elastic properties of the material, and the axial and flexural deformations of the struts are considered in displacement calculation. The solutions of analytical and numerical of the equivalent mechanical parameters were very close, and the results of the equivalent model agree well with the exact numerical model results, which proves the rationality of the homogenized equivalent method and can realize the cross-scale characterization and analysis of the pyramidal lattice materials.