Hierarchical NURBS and a higher-order phase-field approach to fracture for finite-deformation contact problems

•We present a hierarchical refinement scheme for isogeometric analysis.•A frictional Mortar contact algorithm for hierarchical refined NURBS is introduced.•A higher-order phase-field approach to brittle fracture is applied to the concept of HNURBS and combined with frictional contact problems.

In this paper we investigate variationally consistent Mortar contact algorithms applied to a phase-field approach to brittle fracture. Phase-field approaches allow for an efficient simulation of complex fracture problems, as they arise in contact and impact situations. To improve accuracy and convergence, a fourth-order phase-field model is considered, requiring C1C1 continuity throughout the domain. An isogeometrical framework is used for the spatial discretisation subject to hierarchical refinements to resolve local features. This reduces the computational effort tremendously, as will be shown in a series of representative examples.