  This paper presents a computational framework for quasi-static brittle
fracture in three dimensional solids. The paper set outs the theoretical basis
for determining the initiation and direction of propagating cracks based on the
concept of configurational mechanics, consistent with Griffith's theory.
Resolution of the propagating crack by the finite element mesh is achieved by
restricting cracks to element faces and adapting the mesh to align it with the
predicted crack direction. A local mesh improvement procedure is developed to
maximise mesh quality in order to improve both accuracy and solution robustness
and to remove the influence of the initial mesh on the direction of propagating
cracks. 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 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.
