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

An adaptive space-time phase field formulation for dynamic fracture of brittle shells based on LR NURBS