Stretching-dominated truss lattice materials: Elastic anisotropy evaluation, control, and design

In this paper, an analytical homogenization formula is derived based on the numerical representative volume element (RVE) method and asymptotic homogenization (AH) method for the effective elastic properties of truss lattice materials. Compared with the numerical homogenization method, the analytical homogenization formula can treat the geometric parameters of the truss structure, the elastic properties of the base material as well as the loading direction as independent variables without repeated modelling. Compared with the Gibson and Ashby's meso-mechanics model, the analytical homogenization formula can not only obtain the same calculation results, but also can conveniently evaluate and control the elastic properties of the stretching-dominated compound truss lattice structure with complex truss configuration and multi-material composition. According to the anisotropy and deformation characteristics of the elementary trusses, design methodologies for stretching-dominated compound truss lattice structures with controllable anisotropy and optimal isotropic elasticity are proposed. Based on the analytical homogenization formula, the elastic isotropy conditions of the stretching-dominated compound truss lattice materials can be obtained. In the end, the designed 3D elastically isotropic truss lattice structures and 2D bi-material elastically isotropic lattice structures are manufactured and tested to verify the correctness of the isotropy conditions and calculation results obtained by the analytical homogenization formula.