Keywords: fracture, hp-refinement, configurational mechanics.

This chapter presents a computational framework for brittle fracture in three dimensional solids. The chapter briefly describes the theoretical basis for crack propagation based on the concept of configurational mechanics, consistent with Griffith’s theory. The chapter describes two approaches to resolving the propagating crack by the finite element mesh. In both cases cracks are restricted to element faces. In the first approach, the mesh is adapted to align element faces with the predicted crack direction and then the face is split to introduce the displacement discontinuity. In the second approach, the mesh topology does not change and we are able to capture continuous crack propagation in a smooth manner. A local mesh improvement procedure is developed to maximise mesh quality in order to improve both accuracy and solution robustness. An arc-length control technique is derived to enable the dissipative load path to be traced. A hierarchical hp-refinement strategy is implemented in order to improve both the approximation of displacements and crack geometry. The performance of this modelling approach is demonstrated on two numerical examples that qualitatively and quantitatively illustrate its ability to predict complex crack paths.

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