How does the initial cell configuration influence the final topology in a metamaterial generation process?

Abstract

This research aims to evaluate the impact of the initial cell configuration on generating mechanical metamaterial cells. Cell creation was achieved by integrating a robust topological optimization with a numerical homogenization process. The procedure was developed in Fortran and used a three-stage methodology to facilitate fast exploration of possible metamaterial cell space design. The initial cell consisted of a square or cube of material with a central circular or spherical void of 10 mm, 20 mm, and 30 mm in diameter. In addition, the generation process employed three limit volume fractions (30 %, 40 %, and 50 %) and eleven objective functions for 2D and 3D scenarios. These functions were intended to generate cells that maximize stiffness in one or multiple directions and cells with maximum compressibility or shear modulus. It merits attention that the tailored mechanical properties produced novel geometrical configurations. The volume fraction was one of the most significant factors in the generation process. Well-defined metamaterial cells were generated using a volume fraction of 50 % and those with low to medium void diameters. The code used in this work is available in the open-source GitHub repository.