Isotropic Growth on Cartesian Voxel Grids with von Neumann Neighborhoods for Rapid Generation of Synthetic Microstructures

Abstract Randomized instantiations of synthetic microstructures are needed to assess the statistical significance of microstructure variability. Algorithms that use Voronoi tessellations of random points produce synthetic polycrystalline microstructures with a less realistic appearance than random packing of spheroidal particles followed by growth-until-impingement. Additionally, Voronoi tessellations offer limited control of morphological parameters and are challenging to implement when the desired volume fraction is less than unity. However, unless additional physics-based constraints are applied, growth on a Cartesian voxel grid utilizing a von Neumann neighborhood element results in anisotropic growth that is generally not observable along the primary axes. The present work describes both analytical and empirically optimized corrections for directional growth rates and a framework for their inclusion in a synthetic microstructure generation algorithm. The presented algorithm can produce synthetic microstructures similar to those produced by random seed Monte Carlo techniques in a fraction of the computational time.