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Modeling of Grain Growth Using Voronoi Discretization and Natural Neighbor Interpolants

Modeling of material interface evolution in grain growth of polycrystalline materials poses considerable challenges in both finite element and meshfree methods. This paper presents a Voronoi discretization in conjunction with the natural neighbor interpolants for the effective approximation of field variables with evolving interface jump conditions and topological changes of grain structures in stressed grain growth. A new algorithm for Delaunay triangulation applicable to arbitrary grain geometries is employed, and natural neighbor interpolants that provide derivative discontinuity across the material interfaces are constructed. The proposed method is applied to the modeling of grain growth processes of polycrystalline material that exhibits complex topological changes in the grain structures.