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

Abstract

SUMMARYThis 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.

Direct numerical simulations in solid mechanics for understanding the macroscale effects of microscale material variability

“…The explicit meshing of polycrystalline grains of general morphology, using a mesh that conforms to the grain boundaries, is tedious and far from robust [4][5][6][7][8]. Such meshes typically require regularization of the grain geometry and are mainly obtained using tetrahedral finite elements.…”

“…Each finite element is assigned the properties of the grain containing the centroid of the hexahedral element. This approach to microstructural embedding is simple and robust, unlike an explicit microstructural meshing approach in which degenerate elements are invariably created making it difficult to simulate many realizations of the microstructure [4][5][6][7][8]. In this work, we are less interested in detailed stresses near the grain boundaries, but rather with the stress fluctuations above the grain scale.…”

Unstructured and Semi-Structured Hexahedral Mesh Generation Methods

“…Reference [120] presents a method to correctly capture the boundary of assembly models using grid-based methods. Finally, it is important to point out that special efforts have been focused on the development of new templates to adapt the inner mesh to the geometry boundaries [121,122] …”

A NURBS-based generalized finite element scheme for 3D simulation of heterogeneous materials

“…Some of these approaches rely on the direct voxel-to-element translation to create a structured grid of hexahedral elements [2][3][4]. While this approach is particularly attractive due to its simplicity and robustness, it tends to create staircase representations of material interfaces [5], which might affect the solution unless an extremely refined (and computationally expensive) finite element model is adopted [4]. Another approach, based on discrete representation of the material interfaces combined with the generation of unstructured finite element meshes that conform to these interfaces [6,5,7], has shown to represent more accurately the geometrical details of the interface.…”