Design for the additive manufacturing of structural elements with cellular materials using Voronoi diagrams and Delaunay triangulations: Biological and structural applications

Abstract

Porous structures are useful elements in several applications, such as in tissue engineering and in the refinement of optimized elements, with the benefit of offering minimum weight, diminishing costs, and reducing material use. This paper presents a method to design porous structures in two dimensions based on grayscale images, in which the porosity and pore size can be changed as a function of a distribution of densities (gray intensity). Generative design tools, Voronoi diagrams and Delaunay triangulations, are developed in which the size of the cells is related to the gray intensity distribution within the image. The method was tested on grayscale images from X-ray and topological optimization algorithms to obtain CAD models suitable for additive manufacturing. These models were subsequently manufactured through an additive manufacturing process. The results show that the developed tool is able to successfully obtain cellular structures; moreover, the 3D-printed specimens were evaluated through both FEM and physical tests to compare which of the trabeculae shapes was better for loading transmission.