Energy-based modeling of cohesive and cohesionless cracks via X-FEM

Numerical analyses of structures made of brittle materials such as glass or quasi-brittle materials such as concrete or ceramics require robust models for the opening and propagation of cracks which adequately represent the discontinuous character of the fracture process and consider adequately cohesive forces acting within the fracture process zone. The extended finite element method (X-FEM) is capable to model cracks as propagating discontinuities within the structure independent of the finite element discretization. Nevertheless, the analysis of crack propagation using discrete crack models crucially depends on the crack growth criterion. In this paper, a global energy-based method is proposed for the determination of the crack propagation length as well as for the crack propagation direction. The method is formulated within an X-FEM-based analysis model leading to a variational formulation in terms of displacements, crack lengths and crack angles. Both cohesive and cohesionless cracks are considered. The constitutive model for cohesive cracks considers the transfer of residual stresses parallel as well as orthogonal to the crack faces. For the representation of the displacement field in the vicinity of the tip of cohesive cracks, enriched approximations which do not lead to a singularity of the stresses at the crack tip are proposed in the paper. After linearization, the proposed energy-based finite element crack propagation model results in a coupled system of equations analogous to a multifield problem. The model is verified by means of comparisons with crack growth analyses based on linear elastic fracture mechanics using the maximum circumferential stress criterion for the determination of the crack propagation direction. Furthermore, two examples, characterized by Mode I and Mixed-Mode fracture, respectively, are used to study the performance of the developed energy-based crack propagation model.