An Enriched Equilibrium Finite Element Method for Crack Problems With Direct Access to Stress Intensity Factors and Strict Error Estimation

This paper proposes an enriched equilibrium finite element method (EFEM) for addressing crack problems within the framework of linear elastic fracture mechanics and complementary energy principle. The key ingredient of enriched EFEM is to construct the equilibrated stress field using equilibrated tractions along with asymptotic enrichment. Specifically, an auxiliary field is employed to capture the asymptotic singular behavior of the near‐tip stress field, while the traction‐based equilibrium finite element accounts for the residual terms. The remarkable property of the proposed enriched EFEM is that the stress intensity factors (SIFs) and the stress fields are directly obtained with high accuracy, even on a very coarse mesh. Moreover, in combination with the compatible solution acquired by the enriched finite element method (FEM), strict estimation of the discretization error is obtained for crack problems by dual analysis. Numerical examples are finally conducted to verify the performance of the proposed method on strict error estimation and accurate computation of the SIFs.