NURBS representational strategies for tracking moving boundaries and topological changes during phase evolution

Nucleation, growth, coalescence and separation are topological and shape changing events common to many physical problems including those aimed at modeling microstructural phase evolution. The common computational approaches to these problems rely on implicitly representing the geometric boundary of microstructural phases through level-sets and phase fields since explicit geometrical representations necessitate rediscretization in mesh or grid based solution approaches. In this paper, we develop an isogeometric explicit boundary tracking procedure that utilizes Non-Uniform Rational B-Splines (NURBS) to model both topology and shape changing events such as phase nucleation, growth, separation, and dissolution. The computational algorithms developed in the paper rely on a Constructive Solid Geometry (CSG)-inspired representation of phases that permits parametric immersion of void/inclusion phase boundaries in the underlying matrix phase. The representation also enables dynamically capturing topological and shape-changing events without modifying the underlying discretizations. The developed procedure is demonstrated through multiphysics examples that capture phase coalescence and separation caused by interactions of electrical field and surface energy under a constraint on mass conservation.