A Modelling Framework for Three-Dimensional Brittle Fracture

This paper presents a finite element based numerical framework for the predictive modelling of three dimensional crack propagation in brittle solids. The presentation briefly sets out the theoretical basis for determining the initiation and direction of propagating cracks, based on the concept of configurational forces. Attention is focussed on resolution of cracks by the finite element mesh. Cracks are restricted to the element faces and the mesh is adapted in order to align element faces with the predicted crack path. A local mesh improvement procedure is developed to maximise mesh quality in order to improve accuracy and solution robustness and to reduce the influence of the initial mesh on the direction of propagating cracks. The performance of this modelling approach is demonstrated on three numerical examples that qualitatively illustrate its ability to predict complex crack paths. All problems are three-dimensional, including a torsion problem that results in the accurate prediction of a doubly-curved crack. In order to trace the dissipative load-displacement path, fully consistent with the assumption of quasi-static crack propagation, an arc-length scheme is adopted with a control function taken as an increment in change in crack surface area. Finally, the influence of hp-adaptivity is studied and the smoothing influence on the loaddisplacement response is demonstrated.