Solidification and cooling shrinkage

The heat transfer and solid mechanics model describing fiber motion during and after solidification was based on the PHYSICA package developed at the University of Greenwich [3], and employed a methodology similar to that described by Bailey and Wheeler [5]. To generate the mesh, the triangulated solder-air surface generated by Surface Evolver and meshes generated for the fiber surface and a portion of the substrate were filled with points on a regular lattice. The quickhull algorithm [4] was then used to find the Delaunay tetrahedra which make up the convex hull of those points. Tetrahedra outside of the original surface were eliminated and interior points moved to promote a more uniform tetrahedron volume distribution. These tetrahedra were then used as the volume mesh required by PHYSICA.

In a model problem, the fiber was given as a 25 $\mu$m diameter rod, the substrate as a 400$\times$400 $\mu$m square of 50 $\mu$m thickness with a 125$\times$125 $\mu$m square wetting patch at the center.