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

• Published in: Engineering fracture mechanics 2007-11, Vol.74 (16), p.2547-2573
• Main Authors: Yang, Z.J., Deeks, A.J.
• Format: Article
• Language: English
• Subjects: Applied sciences; Building structure; Buildings. Public works; Cohesive crack model; Concrete beams; Concrete structure; Construction (buildings and works); Exact sciences and technology; Finite element method; Fracture mechanics (crack, fatigue, damage...); Fundamental areas of phenomenology (including applications); Local arc-length method; Mixed-mode crack propagation; Physics; Scaled boundary finite element method; Solid mechanics; Static elasticity (thermoelasticity...); Structural and continuum mechanics
• ISSN: 0013-7944; 1873-7315
• DOI: 10.1016/j.engfracmech.2006.12.001

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 K I vanishes in the direction determined by LEFM criteria. Other salient algorithms associated with the SBFEM, such as mapping state variables after remeshing and calculating K I 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 K I ⩾ 0 criterion is objective with respect to the crack incremental length.