Well-conditioned and optimally convergent second-order Generalized/eXtended FEM formulations for linear elastic fracture mechanics

The Generalized/eXtended Finite Element Method (G/XFEM) has been established as an approach to provide optimally convergent solutions for classes of problems that are challenging the standard version (FEM). For with non-smooth solutions, those within Linear Elastic Fracture Mechanics (LEFM) context, FEM convergence rates often not optimal and bounded by strength singularity in analytical solution. This can be overcome G/XFEM many researches have focused on delivering first-order LEFM problems. difficulty obtaining higher-order accurate approximations, however, relies mainly also controlling growth rate stiffness matrix condition number. In this paper, well-conditioned second-order G/XFEMs proposed simulations augmenting Lagrangian approximation spaces. More specifically, two strategies order accurately represent discontinuous functions along a crack. Also, third strategy essentially improves use linear Heaviside sense these enrichments no longer cause dependencies among set shape is proposed. numerical experiments show robustness formulations presented herein crack topologies.