Abstract: Based on the cohesive crack model, a virtual node extended finite element method (XFEM) was developed to simulate the fracturing process of quasi-brittle materials, such as rock and concrete. Numerical principles and governing equations of this method were also proposed. Typical numerical examples were presented, including tension fracture of the three-point bending beam, I–II mixed mode fracture of a single edge notched specimen and fracture of multiple cracks in the Nooru-Mohammed experiment. Moreover, these results were compared with existing solutions or experimental results. It is found that this method is suitable to simulate fracturing process of quasi-brittle materials dominated by opening-mode cracks. Pre-assignment of crack-growth paths is not necessary for the proposed method, in comparison with the node-separation finite element method (FEM). Contrary to the plastic-damage FEM, this method also can reliably simulate the propagation of multiple cracks. Meanwhile, it is not necessary to introduce crack-tip elements and calculate stress intensity factors in comparison with the normal XFEM. Lastly, it is particularly applicable to the acquirement of convergent computational results by contrast with the XFEM with higher-order enriched elements. Moreover, the developed method can be easily embedded into conventional finite element software to solve complex problems by applying powerful nonlinear computational functions of the latter for its displacement description based on elements.

Key words: extended finite element method (XFEM), virtual node, cohesive crack model, quasi-brittle materials, crack propagation