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Accurate Configuration Force Evaluation via hp-adaptive Discontinuous Galerkin Finite Element Analysis

Engineers require accurate determination of the configurational force at the crack tip, and corresponding stress intensity factors, for fracture fatigue analysis and accurate crack propagation. However, obtaining highly crack tip configuration force values is challenging with the most accurate methods requiring knowledge of the stress field around the crack tip a priori. This paper proposes a method which aims to remove the necessity of knowing the stress field a priori whilst producing very accurate values of the configurational force at a static crack tip. The proposed method is demonstrated to be path independent and is combined with a robust a posteriori residual error estimator which is indicative of the accuracy of the configurational force calculation. This makes it possible to generate accurate values for the configurational force acting both perpendicular and parallel to the crack edges. Accuracies are achieved which are at least 10000 times more accurate than other numerical methods which make no assumption about the local tip stress field; with the error estimator providing the accuracy for each component. Therefore accurate benchmarks, with error bounds, are determined in this paper for inclined, split and tree crack problems. In addition the new method is shown to obtain very similar values for the configurational compared to results obtained using other methods which require knowledge of the stress field at the crack tip. The techniques presented in this paper open the door to configurational force-based methods being used for fatigue analysis.

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