Effective Mechanical Properties of Periodic Cellular Solids with Generic Bravais Lattice Symmetry via Asymptotic Homogenization

Abstract

In this paper, the scope of discrete asymptotic homogenization employing voxel (cartesian) mesh discretization is expanded to estimate high fidelity effective properties of any periodic heterogeneous media with arbitrary Bravais’s lattice symmetry, including those with non-orthogonal periodic bases. A framework was developed in Python with a proposed fast–nearest neighbour algorithm to accurately estimate the periodic boundary conditions of the discretized representative volume element of the lattice unit cell. Convergence studies are performed, and numerical errors caused by both voxel meshing and periodic boundary condition approximation processes are discussed in detail. It is found that the numerical error in periodicity approximation is cyclically dependent on the number of divisions performed during the meshing process and, thus, is minimized with a refined voxel mesh. Validation studies are performed by comparing the elastic properties of 2D hexagon lattices with orthogonal and non-orthogonal bases. The developed methodology was also applied to derive the effective properties of several lattice topologies, and variation of their anisotropic macroscopic properties with relative densities is presented as material selection charts.