Hierarchical Infills for Additive Manufacturing Through a Multiscale Approach

A numerical method is presented to generate hierarchical infills for additive manufacturing, using homogenization and optimization. Given the shape and the allowed stages of grading, the macroscopic properties of each level of the hierarchical infill are computed through numerical homogenization. Then, a multi-material optimization problem is formulated to find the distribution of the prescribed discrete set of candidates that maximizes the structural stiffness of the object to be printed for a limited volume fraction. The formulation is endowed with an additional overturning constraint to achieve objects that resist gravity in a stable configuration. Numerical simulations, addressing the design of a self-supporting orthotropic rhombic infill and a stiff isotropic triangular one, are shown.