Fully-automatic modelling of cohesive crack growth using a finite element-scaled boundary finite element coupled method

James Yang, AJ Deeks

Research output: Contribution to journalArticlepeer-review

120 Citations (Scopus)


This study develops a method coupling the finite element method (FEM) and the scaled boundary finite element method (SBFEM) for fully-automatic modelling of cohesive crack growth in quasi-brittle materials. The simple linear elastic fracture mechanics (LEFM)-based remeshing procedure developed previously is augmented by inserting nonlinear interface finite elements automatically. The constitutive law of these elements is modelled by the cohesive/fictitious crack model to simulate the fracture process zone, while the elastic bulk material is modelled by the SBFEM. The resultant nonlinear equation system is solved by a local arc-length controlled solver. The crack is assumed to grow when the mode-I stress intensity factor KI vanishes in the direction determined by LEFM criteria. Other salient algorithms associated with the SBFEM, such as mapping state variables after remeshing and calculating KI using a “shadow subdomain”, are also described. Two concrete beams subjected to mode-I and mixed-mode fracture respectively are modelled to validate the new method. The results show that this SBFEM–FEM coupled method is capable of fully-automatically predicting both satisfactory crack trajectories and accurate load–displacement relations with a small number of degrees of freedom, even for problems with strong snap-back. Parametric studies were carried out on the crack incremental length, the concrete tensile strength, and the mode-I and mode-II fracture energies. It is found that the KI ⩾ 0 criterion is objective with respect to the crack incremental length.
Original languageEnglish
Pages (from-to)2547-2573
Number of pages27
JournalEngineering Fracture Mechanics
Issue number16
Early online date5 Feb 2007
Publication statusPublished - Nov 2007
Externally publishedYes


  • Finite element method
  • Scaled boundary finite element method
  • Cohesive crack model
  • Mixed-mode crack propagation
  • Concrete beams
  • Local arc-length method


Dive into the research topics of 'Fully-automatic modelling of cohesive crack growth using a finite element-scaled boundary finite element coupled method'. Together they form a unique fingerprint.

Cite this