Strong discontinuity formulations: A comparative study

In this paper, the computational modelling of fracture in quasi-brittle materials is addressed. An embedded discontinuity methodology is presented, which is called the discrete strong discontinuity approach ( Alfaiate and Sluys 2005 ). This formulation is derived within the scope of the strong discontinuity concept ( Oliver et al. 2002 ); however, instead of considering fracture as a natural evolution from continuum damage, a discrete crack approach is adopted: the onset of fracture gives rise to the formation of a localized discontinuity, which can evolve from a zero width fictitious crack to a fully open stress-free crack. The use of a pure discrete methodology was implemented by means of interface elements more than twenty years ago ( Hillerborg et al. 1976 ), ( Bocca et al. 1986 ). In spite of the drawbacks of this approach whenever the crack path is not known in advance, it is still known to be most numerically reliable for prescribed cracking. This is why this formulation is still being used nowadays, for instance, to model the interface behaviour between two materials, such as with masonry, the internal concrete-steel adhesion or the external concrete-FRP reinforcement. Recently, a new technique has been used to model fracture, known as the extended finite element method ( Mões et al. 1999 ). In this paper a comparison of these different strong discontinuity descriptions is given. Several simple examples obtained at element level are first presented, with the purpose of clearly illustrating the differences between the discrete-interface, the discrete strong discontinuity and the extended finite element approaches. Next, towards a unified view of these different strong discontinuity descriptions, a better approximation of the kinematics of the element ahead of the crack tip is proposed, common to both the discrete strong discontinuity approach and the extended finite element method.