Study of equivalent mechanical properties on pyramidal lattice materials

Abstract

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 ν_zx, ν_zy increases, while ν_xy, ν_yx, ν_xz, ν_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.

Highlights

• The equivalent mechanical expression of multi-layered pyramidal lattice material

• Relationship between equivalent mechanical parameter and struts inclination angle

• Solution of the equivalent stiffness matrix of multi-layered pyramidal materials

• Numerical calculation of the exact finite element and the equivalent models

Keywords:

• Pyramidal lattice materials
• effective mechanical properties
• theoretical analysis
• numerical simulation
• homogenization

Additional information

Funding

This work was supported by the Natural Science Foundation of Beijing Municipality [grant number 3202001].