This is the peer reviewed version of the following article: Tamayo, E. [et al.]. A continuous-discontinuous model for crack branching. "International journal for numerical methods in engineering", 5 Octubre 2019, vol. 120, núm. 1, p. 86-104, which has been published in final form at https://doi.org/10.1002/nme.6125. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.

A new continuous-discontinuous model for fracture that accounts for crack branching in a natural manner is presented. It combines a gradient-enhanced damage model based on nonlocal displacements to describe diffuse cracks and the extended finite element method (X-FEM) for sharp cracks. Its most distinct feature is a global crack tracking strategy based on the geometrical notion of medial axis: the sharp crack propagates following the direction dictated by the medial axis of a damage isoline. This means that, if the damage field branches, the medial axis automatically detects this bifurcation, and a branching sharp crack is thus easily obtained. In contrast to other existing models, no special crack-tip criteria are required to trigger branching. Complex crack patterns may also be described with this approach, since the X-FEM enrichment of the displacement field can be recursively applied by adding one extra term at each branching event. The proposed approach is also equipped with a crack-fluid pressure, a relevant feature in applications such as hydraulic fracturing or leakage-related events. The capabilities of the model to handle propagation and branching of cracks are illustrated by means of different two-dimensional numerical examples.

Peer Reviewed