On the description of fracture propagation in brittle materials

In this paper, the problem of damage propagation in brittle materials is investigated. Two conceptually different frameworks are discussed, viz. Extended FEM as well as the standard FEM approach, the latter incorporating a constitutive law formulated through volume averaging in the neighborhood of the embedded discontinuity. The onset and the propagation of cracks are described using the level set method for both these approaches. Some numerical examples are provided that involve a three-point bending test, as well as a shear test in which a notched specimen is subjected to both shear and tension. It is demonstrated that the volume averaging technique, enhanced by the level set method for tracking the crack evolution, gives nearly the same results as those based on Extended FEM.