A well-conditioned and optimally convergent XFEM for 3D linear elastic fracture

A variation of the extended finite element method for 3D fracture mechanics is proposed. It utilizes global enrichment and point-wise as well as integral matching of displacements of the standard and enriched elements in order to achieve higher accuracy, optimal convergence rates and improved conditioning for two and three dimensional crack problems. A bespoke benchmark problem is introduced to determine the method's accuracy in the general 3D case where it is demonstrated that the proposed approach improves the accuracy and reduces the number of iterations required for the iterative solution of the resulting system of equations by 40% for moderately refined meshes and topological enrichment. Moreover, when a fixed enrichment volume is used, the number of iterations required grows at a rate which is reduced by a factor of 2 compared to standard XFEM, diminishing the number of iterations by almost one order of magnitude