Isogeometric Finite Element Modeling of Phase Fields on Deforming Surfaces

A wide range of biological, chemical, electro- and thermo-mechanical applications are governed by local effects that influence the physical behavior. Phase transition effects can be temporary and spontaneously arise and grow, reduce and vanish, or move. Phase field approaches can model the evolution of such local effects. The phase separation of a binary mixture that is governed by the Cahn-Hilliard equation is studied on deforming shells. The material behavior of the shell is depending on the local phase state. The phase separation process therefore directly affects the mechanical behavior. A monolithic coupling formulation of the phase field and the mechanical field is proposed. An adaptive time-stepping algorithm for the coupled formulation is proposed. The algorithm incorporates both, the error of the phase field and the mechanical field.