Adaptive mesh refinement for the numerical modelling of complex microstructural evolution applications

The objective of this note is to demonstrate the necessity of using an appropriate automatic adaptive meshing technique so as to handle complex microstructural evolutions. Examples of such microstructural evolutions include the deformation and recrystallization of polycrystalline aggregates or the growth of dendrites occurring during the solidification of metallic alloys. In such applications, it is required to track and/or capture accurately the interface between two or several domains having different mechanical behaviour. Also, the interface is a region where strong physical and/or kinematic incompatibilities, stemming from the heterogeneity of the mechanical response, occur. Gradients of the various mechanical fields develop across the interface and are expected to be significant in the direction perpendicular to the boundary. For these reasons, anisotropic mesh refinement along the interface, with a smaller mesh size in the perpendicular direction to it, is needed. This strategy represents a good compromise between accuracy and computation time as the mesh refinement is performed only where it is necessary. The level set framework used in our approach to represent and follow the boundaries is fully compatible with this meshing technique and allows for the remeshing to be handled quite easily throughout the evolution of the microstruture as often as needed.