Discontinuous representation of brittle failure

摘要

The numerical analysis of structures made of brittle materials such as concrete requires robust models for the opening and propagation of cracks which adequately represent the discontinuous character of the fracture process. In the last decade, as an alternative to classical continuum-based models, various attempts have been made to represent the failure zone as a surface of discontinuous displacements within the respective finite elements. This idea provides the possibility to approximate failure zones, several dimensions smaller than the structure itself, by using only a relatively small number of finite elements. Therefore, this concept seems to be suitable for large scale computations. Two classes of models following this general concept are addressed in this paper: the Strong Discontinuity Approach (SDA) first proposed by Simo, Oliver & Armero (1993) and re-formulated within a rotating crack concept (Mosler and Meschke 2003) and the Extended Finite Element Method (X-FEM) more recently proposed by Moees, Dolbow & Belytschko (1999). In addition to a short review of the basic concepts of both methods, some important differences are pointed out and evaluated. Since the analysis of crack propagation using discrete crack models crucially depends on the crack growth criterion, special attention is paid to the determination of the crack propagation direction in the context of the Extended Finite Element Method. Three different crack propagation criteria proposed in literature are investigated including a criterion based on the maximum global strain energy release rate as proposed recently by (Peters, Hoppe, and Hackl 2004; Dumstorff and Meschke 2004). A numerical benchmark example, characterized by Mode-Ⅰ fracture, is used to study the performance and the robustness of the different crack propagation criteria.