A configurational force driven cracking particle method for modelling crack propagation in 2D

Abstract

This paper presents a novel combination of two numerical techniques to produce a method for solving fracture mechanics problems. A weak form meshless method, the cracking particles method, forms the basis of the mechanical model while crack propagation direction is calculated using configurational forces. The combined method is presented here for 2D quasi-brittle crack propagation. The configurational force approach has the advantage that it provides a prediction of the crack propagation direction which does not require decomposition of the stress and displacement fields for mixed-mode crack problems. The use of a meshless method removes the need for remeshing and it is therefore eminently suitable for multiple crack problems. The paper includes a discussion on the configurational force calculations via contour integration and domain integration and results are presented that show both approaches to be path independent when the integrations over the two crack surfaces cancel out, with domain integration generally providing better accuracy than contour integration. The contribution from the crack surfaces to the configurational force is discussed, and shown to have little influence on the final result while being easily affected by the oscillations around the crack tip. In addition, the relationship between the configurational force and the J-integral is explained. The proposed method is demonstrated on several examples, including multiple crack propagation, where good agreements with results from the literature are obtained.