An integer programming approach for mesh generation in polycrystalline materials using the electron back-scatter diffraction map

摘要

This paper provides a novel approach for generating polycrystalline microstructure meshes for computational analysis from electron back-scatter diffraction measurements. This procedure allows re-usability of a finite element (FE) mesh by adaptively assigning measured voxel information to elements while preserving important features like the grain boundary surface area/length. This methodology is not restricted to convex grains and allows efficient meshing of both isotropic and anisotropic microstructures. The basis of this approach is a novel Potts energy formulation to allow integer optimization on the dual of the FE mesh. The Potts energy can be decomposed into two terms: the field energy/data cost and the interaction energy/smoothing cost. The field term is used to represent the likelihood of a grain label on an element based on the experimental voxel data. The interaction term encodes a prior on this labeling, in particular, it is used for smoothening the grain boundary. Energy minimization of this system leads to a multi-way cut problem which is solved using Graph-cuts.