A continuous‐discontinuous model for crack branching

• Published in: International journal for numerical methods in engineering 2019-10, Vol.120 (1), p.86-104
• Main Authors: Tamayo‐Mas, Elena, Feliu‐Fabà, Jordi, Casado‐Antolin, Montserrat, Rodríguez‐Ferran, Antonio
• Format: Article
• Language: English
• Subjects: 65 Numerical analysis; 65L Ordinary differential equations; 74 Mechanics of deformable solids; 74R Fracture and damage; Anàlisi numèrica; Bifurcations; Classificació AMS; crack branching; Crack propagation; Cracks; Damage assessment; Difference equations; Equacions diferencials; Finite element method; finite elements; Fluid pressure; fracture; Fracture mechanics; gradient damage; Hydraulic fracturing; Matemàtica aplicada a les ciències; Matemàtiques i estadística; Mathematical models; Mecànica de fractura; medial axis; Mètodes en elements finits; Numerical solutions; solucions numèriques; X-FEM; Àrees temàtiques de la UPC
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.6125

Summary 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.