A numerical model of grain growth

A numerical model for grain growth has been developed. The governing equations for the model are derived from a variational principle that enforces the balance between energy dissipation and changes of internal energy. This approach significantly simplifies previous modelling of grain growth by replacing a curved grain boundary with several straight lines and relaxing constraints on triple point angles. Such simplifications provide a basis for a finite element method by reducing the analysis of a complex network of interconnected curved lines to the motion of interacting points. In the finite element formulation two approaches are used, namely an element based formulation and a node based formulation. In the latter case, the properties of the elements are lumped together at their common nodes. Such an approach allows the nodal velocity to be determined independently of the forces on other nodes in a lumped mobility methodology, leading to a further reduction of computer time. Several planar grain networks of Voronoi polygons have been studied. The evolution of the grain structures determined from these two approaches is found to exhibit the same trends as those obtained using other models published in the literature. Owing to its simplicity, the node based formulation is recommended.