Efficient methods for implicit geometrical representation of complex material microstructures

We present two methods for initializing distance functions on adaptively-refined finite element meshes to represent complex material microstructures from segmented x-ray tomographic data. Implicit microstructure representation combined with the extended FEM allows modelers to represent complex material microstructures with consistent mesh quality and accuracy. In the first method, a level set evolution equation is formulated and solved by the Galerkin method on an adaptively-refined mesh. We show that the convergence and stability of this method is optimal for the order of elements used. In the second approach, we initialize the distance field by the fast marching method on a uniform grid, and then project the solution onto the finite element mesh by least-squares. We show that this latter approach is superior in speed and accuracy. As an example problem, both methods are demonstrated in the initialization of distance fields for two inclusion phases within a Al-7075 alloy.