This paper presents a general theory and isogeometric finite element implementation of phase fields on deforming surfaces. The problem is governed by two coupled fourth order partial differential equations (PDEs) that live on an evolving manifold. For the phase field, the PDE is the Cahn-Hilliard equation for curved surfaces, which can be derived from surface mass balance. For the surface deformation, the PDE is the thin shell equation following from Kirchhoff-Love kinematics. Both PDEs can be efficiently discretized using $C^1$-continous interpolation free of derivative dofs (degrees-of-freedom) such as rotations. Structured NURBS and unstructured spline spaces with pointwise $C^1$-continuity are considered for this. The resulting finite element formulation is discretized in time by the generalized-$\alpha$ scheme with time-step size adaption, and it is fully linearized within a monolithic Newton-Raphson approach. A curvilinear surface parameterization is used throughout the formulati 查看全文>>