Modelling Of Cohesive Crack Growth And Size Effect Of Concrete

The scaled boundary finite element method (SBFEM) is a novel semi-analytical technique, combining the advantages of the finite element method and the boundary element method with unique properties of its own. Like the boundary element method, it discretises domain boundaries only so reduces the modelled dimentions by one; but it does not need fundamental solutions and thus has wider applicabilities. One of the most important advangtages of the SBFEM is that its displacement and stress solutions are analytical in the radial direction. This allows accurate stress intensity factors (SIFs) to be determined directly from the definition, and hence no special crack-tip treatments, such as refining the crack-tip mesh or using singular elements(needed in the traditional finite element method and boundary element method), is necessary.This study applies the SBFEM to fully-automatically model cohesive crack growth in quasi-brittle materials such as concrete. A domain is first divided into a few subdomains. Because the dimensions and shapes of subdomains can be flexibly varied and only the domain boundaries or common edges between subdomains are discretised, a remeshing procedure as simple as in the boundary element method was developed with minimum mesh changes whereas the generality and flexibility of the finite element method is well maintained. The simple linear elastic fracture mechanics (LEFM)-based remeshing procedure developed previously is augmented by inserting nonlinear interface finite elements automatically. Cohesive/fictitious crack model is used to simulate the fracture process zone. 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 K₁≥0 in the direction determined by LEFM criteria. The evolution of the FPZ is predicted by the present method.Comparison of the numerical results with those obtained from experiments and analytical studies shows that the SBFEM is able to accurately model the cohesive crack propagation and size effect in concrete beams using a small number of degreesof freedom. In particular, it can model similar concrete beams with a wide range of dimensions using the same initial mesh. This means tremendous reduction in pre-process and data preparation, which makes the SBFEM very suitable for modeling size effect in concrete beams.