Improving the accuracy of XFEM crack tip fields using higher order quadrature and statically admissible stress recovery

This study is concerned with improving the accuracy of crack tip fields obtained using the extended/ generalized finite element method (XFEM). First, the numerical integration of the element stiffness matrices, which guarantees convergence (with quadrature) of not only the regular nodal displacements but also additional degrees of freedom corresponding to the enrichment functions, is studied. As the accuracy of the stresses obtained by direct differentiation of the converged (with quadrature) regular nodal displacements and of the coefficients corresponding to enrichment functions is still not satisfactory, a statically admissible stress recovery (SAR) scheme is introduced. SAR uses basis functions, which meet the equilibrium equations within the domain and the local traction conditions on the boundary, and moving least squares (MLS) to fit the stresses at sampling points (e.g. quadrature points) obtained by the XFEM. Important parameters controlling the accuracy of crack tip fields using the XFEM and SAR, namely the order of quadrature, the number of retained terms in the crack tip asymptotic field, the number of enriched layers and use of arbitrary branch functions, a proper choice of the sampling points in the enriched element and the size of the domain of influence (DOI) of MLS, are investigated.