Extended Finite Element Method Based on Cosserat (Micropolar) Elasticity Theory for the Computation of Stress Intensity Factors

An extended finite element method (XFEM) considering the Cosserat (micropolar) elasticity theory is developed using the ABAQUS finite element analysis platform. The method is about the two-dimensional (2D) simulation which accurately describes the discontinuity and strong nonlinearity of crack displacement in materials with size effects. The interaction integral (I-integral) is used to solve the stress intensity factors (SIFs) at the crack tip. The effects of the integration domain near the crack tip and the number of integration points of the crack tip element on the accuracy of the SIFs are discussed based on the simulation and analysis of strip specimens with edge and central cracks. The results demonstrate that, for the same integration domain, the solution accuracy of the micropolar elastic XFEM (XFEM/Cosserat) is higher than that of the finite element method and classical elastic XFEM. Additionally, for the same number of integration points of the crack tip element, the solution accuracy of XFEM/Cosserat is higher than that of the classical elastic XFEM. This verifies the feasibility and accuracy of XFEM/Cosserat in simulating mode-I, mode-II, and I-II mixed mode cracks.