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

Beam-based lattices have gained significant popularity in engineering applications due to their ease of production using additive manufacturing [1,2,3]. However, the design of the unit cell geometry is mostly based on intuition rather than on proper geometrical algorithms: this leads to confusion in the classification of the cell types, as authors propose different names for the same type of cell. In our work, a novel geometric algorithm is introduced for the generation of beam-based cubic unit cells of the Oh symmetry group. This algorithm enables the creation of complex unit cells that are self-connecting, providing structural integrity to the lattice, by the variation of two geometrical parameters. Typically, such unit cells are challenging to design, but our algorithm simplifies the process and proposes a new taxonomy based on the selected geometrical parameters. The variation of the geometrical variables determines the categorization, and four distinct classes of cells are suggested. Additionally, thermo-mechanical analysis of the static effective properties is performed for each class of unit cells using the Asymptotic Homogenization method [4,5], implemented in a Finite Element Method (FEM) framework. The results are presented as gridded data, available on a GitHub repository, and depend on the unit cell's volume fraction, Poisson's ratio (variable within the thermodynamically admissible range 0 < ν < 0.5), and the geometrical parameters of the unit cell class. The effective parameters are normalized with respect to the solid bulk properties, thus behaving as purely geometrical properties of the unit cell class. These parameters act as scaling functions on the bulk properties and can be readily utilized in optimization schemes for enhancing the static performance of lattices. Overall, these findings provide a valuable tool for real-world engineering applications.