Analytical model of mechanical properties for a hierarchical lattice structure based on hierarchical body-centered cubic unit cell

Hierarchical structure features complex geometric topology and excellent mechanical properties. In this work, analytical models are developed to predict the mechanical properties as Young's modulus, Poisson's ratio, and yield stress of a lattice structure composed of hierarchical body-centered cubic. Analytical results were validated by finite element simulations. The compressed experiments of lattice samples fabricated by powder bed fusion were conducted to examine mechanical properties. The analytical model agrees well with the simulation results and experimental results. The largest discrepancy from the analytical model to the finite element simulations for Young's modulus of lattice structures is 7.5%. Regarding Poisson's ratio and yield stress, the largest discrepancy are 0.05% and 13.1%, respectively. Furthermore, the Young's modulus shows an increasing trend as the relative density of lattices increases and geometrical ratio λ decreases. Moreover, the influence of shear deformation on the mechanical properties of the lattice structures decreases with the gradual increase of geometrical ratio λ. The Young's modulus and yield stress for the lattices increase as geometrical ratio λ decreases with increasing relative density. The Poisson's ratio shows an opposite trend to the Young's modulus as well as the yield stress. Finally, the degree of anisotropy of Young's modulus for the lattice structure is investigated. The range of anisotropy values for the lattice structure is large, i.e., 2.98∼745. The anisotropy value of Young's modulus decreases with the relative density increasing. And, the anisotropy value of lattices decreases with increasing relative density, i.e., the monotonic trend. This work provides guidance for future designs of the hierarchical lattice structures from the aspects of theoretical prediction.