Material design of elastic structures using Voronoi cells

Abstract

New tools for the design of metamaterials with periodic microarchitectures are presented. Initially, a two-scale material design approach is adopted. At the structure scale, the material effective properties and their spatial distribution are obtained through a Free Material Optimization technique. At the microstructure scale, the material microarchitecture is designed by appealing to a Topology Optimization Problem (TOP). The TOP is based on the topological derivative and the level set function. The new proposed tools are used to facilitate the search of the optimal microarchitecture configuration. They consist of the following: (i) a procedure to choose an adequate shape of the unit cell domain where the TOP is formulated and shapes of Voronoi cells associated with Bravais lattices are adopted and (ii) a procedure to choose an initial material distribution within the Voronoi cell being utilized as the initial configuration for the iterative TOP.