Adaptive phantom node method: An efficient and robust approach towards complex engineering cracks

Abstract

An efficient and robust approach in the framework of the finite element method for numerical analysis of crack problems is presented. In this method, the discontinuity due to the presence of cracks is described by the technique of phantom nodes. The idea of introducing adaptive mesh refinement along with crack extension into the original phantom node method is presented. The hanging nodes which present in the locally refined mesh is treated by the simple technique of constrained approximation. No additional enrichment functions (and the corresponding extra degrees of freedom) or special elements are involved. As a result, the proposed adaptive phantom node method is almost as simple (and its implementation is as convenient) as the standard finite element method. Numerical results show that the proposed method is able to pass discontinuous patch test accurately and to model crack extension efficiently. In particular, according to its comparison with the original phantom node method in the computation of stress intensity factors, the proposed method consumes less than one percent of the CPU time of the original phantom node method, but it still shows much better accuracy. The capability of the proposed method in modeling multiple cracks, even in complex engineering structures, is also demonstrated.