Beam-based lattices: A novel geometry generation algorithm and thermo-mechanical characterization via Asymptotic Homogenization

For their ease of production through additive manufacturing, beam-based lattices have been extensively used in engineering applications. However, a rigorous methodology for the generation of unit-cell geometry is not exhaustively treated in the literature and geometrical intuition, rather than proper algorithms, is usually employed for design. This fact also confuses the taxonomy, as authors suggest different names for the same cell type. In this talk, a novel geometrical algorithm for the generation of beam-based cubic unit cells with spherical inertia ellipsoid and thermal conductivity tensor is presented. The algorithm allows the production of complex but self-connecting - that impart structural integrity to the lattice - unit cells that otherwise are difficult to devise and suggests a novel taxonomy based on the parameters adopted. Under this categorization, classes of unit cells are defined by the variation of a single geometrical variable. Furthermore, a thermo-mechanical characterization of the static effective properties is presented for each cell class by means of a FEM implementation of the Asymptotic Homogenization method. The results are presented as gridded data, made available on GitHub repository, dependent on the unit cell’s volume fraction (solid-to-void ratio), on the Poisson’s ratio (spanning in the thermodynamically admissible range for conventional materials 0 < ν < 0.5), and on the class of geometrical parameter of the cell. The effective parameters are normalized with respect to the solid bulk properties, thus becoming purely geometrical properties of the unit cell family, and act as scaling functions on the bulk properties. These results can be readily implemented in any optimization scheme for the optimization of the static performance of lattices, providing a useful tool for real-world engineering applications.