A general DBEM for mixed-mode cohesive crack problems

Abstract

This work proposes a general dual boundary element method (DBEM) for cohesive mixed-mode crack problems. Local cohesive stiffnesses are defined to yield the boundary element nonlinear equations for any mixed-mode cohesive model in a direct way. The main novelty resides on the fact that the formulation can take into account all possible cohesive surface conditions: (i) contact, (ii) softening, (iii) unloading/reloading and (iv) complete failure, which may occur independently of the chosen cohesive model. Besides, the well-established Park–Paulino–Roesler (PPR) model was incorporated into DBEM methods. The tangent matrix of the discrete model is explicitly derived and the solution is sought by a proper degree-of-freedom (DOF) control method. The proposed formulation is validated reproducing mode I and mode II patch-tests. Some other relevant problems, including a mixed-mode fracture test, are also presented to demonstrate that the above conditions are essential to reproduce complex mixed-mode cohesive fractures. The results also shown that the control of a monotonically increasing DOF yields reliable solutions in problems with snap-back instabilities. In order to facilitate the validation of the method, predefined crack paths were assumed in the examples. Further developments may include incorporating arbitrary crack growth and damage-based cohesive models for fatigue crack growth analysis.