Abstract

Modelling fracture in brittle materials remains a challenging problem in computational mechanics. In order to make fracture/fatigue predictions, engineers require accurate determination the stress intensity factors at the tips/fronts of evolving fracture networks. Most methods that are able to obtain accuracies suitable for fatigue predictions do so by incorporating knowledge of the stress field around the crack tip within the numerical method. However, these stress field solutions are only valid for specific materials and in the immediate vicinity of the crack tips, there are also computational issues when analysing problems involving several propagating fractures. This presentation will detail a Configurational Force-based method that removes the necessity of knowing the stress field a priori whilst producing very accurate stress intensity values at crack tips [1]. The proposed method is demonstrated to be path independent and is combined with a robust a posteriori residual error estimator [2] which can be used to quantify the errors associated with the fracture predictions. Accuracies are achieved which are at least 100 times more accurate than other numerical methods which make no assumption about the local tip stress field. This opens the door for Configurational Force-based methods to be used for fatigue predictions.

[1] Bird, R.E., Coombs, W.M. & Giani, S. (2019). Accurate Configuration Force Evaluation via hp-adaptive Discontinuous Galerkin Finite Element Analysis. Engineering Fracture Mechanics 216: 106370. [2] Bird, R. E., Coombs, W. M. & Giani, S. (2019). A posteriori discontinuous Galerkin error estimator for linear elasticity. Applied Mathematics and Computation 344-345: 78-96.