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

摘要

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