  We present an adaptive space-time phase field formulation for dynamic
fracture of brittle shells. Their deformation is characterized by the
Kirchhoff-Love thin shell theory using a curvilinear surface description. All
kinematical objects are defined on the shell's mid-plane. The evolution
equation for the phase field is determined by the minimization of an energy
functional based on Griffith's theory of brittle fracture. Membrane and bending
contributions to the fracture process are modeled separately and a thickness
integration is established for the latter. The coupled system consists of two
nonlinear fourth-order PDEs and all quantities are defined on an evolving
two-dimensional manifold. Since the weak form requires $C^1$-continuity,
isogeometric shape functions are used. The mesh is adaptively refined based on
the phase field using Locally Refinable (LR) NURBS. Time is discretized based
on a generalized-$\alpha$ method using adaptive time-stepping, and the
discretized coupled system is solved with a monolithic Newton-Raphson scheme.
The interaction between surface deformation and crack evolution is demonstrated
by several numerical examples showing dynamic crack propagation and branching.
