Quality improvement of non‐manifold hexahedral meshes for critical feature determination of microstructure materials

This paper describes a novel approach to improve the quality of non‐manifold hexahedral meshes with feature preservation for microstructure materials. In earlier works, we developed an octree‐based isocontouring method to construct unstructured hexahedral meshes for domains with multiple materials by introducing the notion of material change edge to identify the interface between two or more materials. However, quality improvement of non‐manifold hexahedral meshes is still a challenge. In the present algorithm, all the vertices are categorized into seven groups, and then a comprehensive method based on pillowing, geometric flow and optimization techniques is developed for mesh quality improvement. The shrink set in the modified pillowing technique is defined automatically as the boundary of each material region with the exception of local non‐manifolds. In the relaxation‐based smoothing process, non‐manifold points are identified and fixed. Planar boundary curves and interior spatial curves are distinguished, and then regularized using B‐spline interpolation and resampling. Grain boundary surface patches and interior vertices are improved as well. Finally, the optimization method eliminates negative Jacobians of all the vertices. We have applied our algorithms to two beta titanium data sets, and the constructed meshes are validated via a statistics study. Finite element analysis of the 92‐grain titanium is carried out based on the improved mesh, and compared with the direct voxel‐to‐element technique. Copyright © 2009 John Wiley & Sons, Ltd.