Improved back propagation neural network based on the enrichment for the crack propagation

Abstract

Numerical methods have been extensively applied to fracture mechanics, while they cannot simulate the problems without the mechanical models or constitutive equations. Artificial neural networks (ANNs) can be utilized to predict complex fracture problems, but these approaches require large amounts of data for the training. Therefore, in this paper, to combine the advantages of the numerical methods and the ANNs, an improved back propagation neural network (BPNN) is proposed by introducing the enrichment used in the numerical methods into the activation function utilized in the neural networks. The enrichment is able to represent the crack tip field which can accelerate the convergence. At the field near the crack tip, the improved BP solution can converge to the analytical solutions which validate the high accuracy of the proposed method. Without sufficient data, especially the data are missing in the near field of the crack tip, the improved BP method can also achieve high accuracy and convergence, while the conventional BP method may not converge to the predetermined error bound. Numerical simulations of the quasi‐static and fatigue crack problems demonstrate that the improved BP method can accurately predict the crack propagation and its growth rate with relatively little data.