Elasticity of Anisotropic Low-Density Lattice Materials

Abstract

Computational first-order homogenization theory is used for the elastic analysis of generally anisotropic lattice materials within classical continuum mechanics. The computational model is tailored for structural one-dimensional (1D) elements, which considerably reduces the computational cost comparing to previously developed models based on solid elements. The effective elastic behavior of lattice materials is derived consistently with several homogenization approaches including strain- and stress-based methods together with volume and surface averaging. Comparing the homogenization based on the Hill–Mandel Lemma and constitutive approach, a shear correction factor is also introduced. In contrast to prior studies that are usually limited to a specific class of lattice materials such as lattices with cubic symmetry or similarly situated joints, this computational tool is applicable for the analysis of any planar or spatial stretching- and bending-dominated lattices with arbitrary topology and anisotropy. Having derived the elasticity of the lattice, the homogenization is then complemented by the symmetry identification based on the monoclinic distance function. This step is essential for lattices with non-apparent symmetry. Using the computational model, nine different spatial anisotropic lattices are studied among which four are fully characterized for the first time, i.e., non-regular tetrahedron (with trigonal symmetry), rhombicuboctahedron type a (with cubic symmetry), rhombicuboctahedron type b (with transverse isotropy), and double-pyramid dodecahedron (with tetragonal symmetry).