An automated h-adaptive G/XFEM for the analysis and SIF extraction of 3-D fracture mechanics problems

Resumo

The Generalized/eXtended Finite Element Method (G/XFEM) is a numerical method whose approximation space is obtained by augmenting standard FEM spaces with functions designed to capture well the behavior of local features of the problem under investigation, such as cracks and material interfaces. In the context of linear elastic fracture mechanics (LEFM) problems, the G/XFEM significantly alleviates mesh requirements and facilitates mesh generation by allowing cracks to cut through finite elements, with the discontinuity inside an element being captured by enrichment functions. At the same time, it also enables using coarser meshes close to crack fronts if the appropriate singular enrichments are adopted. In the case of second-order G/XFEM formulations for 3-D LEFM problems, mesh refinement close to crack fronts is still needed to reach optimal convergence rates if singular enrichment functions that represent only the square root of r singularity are adopted. To address this, we present a computationally efficient and robust h-adaptive algorithm. The procedure is driven by a block-diagonal Zienkiewicz and Zhu (ZZ-BD) error estimator, specifically tailored to estimate well discretization errors of 3-D LEFM problems solved by second-order G/XFEM. It also enables automatic non-uniform mesh refinement around crack fronts, effectively resolving problems with strong three-dimensional effects. The proposed h-adaptive strategy recovers optimal convergence rates for second-order G/XFEM and holds practical significance, as it delivers final discretizations on the fly that satisfy a user-defined tolerance for the discretization error. The influence of this h-adaptive technique on quantities of interest, such as stress intensity factors, is also investigated in this contribution.