An Adaptive Generalized/eXtended FEM For Linear Elastic Fracture Me- chanics

Resumo

The Generalized/eXtended Finite Element Method (G/XFEM) has been recognized as a method able to accurately and efficiently solve problems that face difficulties when treated by standard methodologies, such as those from three-dimensional (3-D) Linear Elastic Fracture Mechanics (LEFM). The main advantages of G/XFEM for this class of problems are the fact that the finite element mesh does not need to fit the crack surface andthat optimal convergence rates in the energy norm are attained. This last advantage has been demonstrated for two dimensional (2-D) problems even when uniform meshes are adopted. For 3-D, however, in addition to using
enrichment functions, it has been shown that mesh refinement must be performed to obtain optimal convergence rates. In this case, since the level of refinement to be adopted is problem-dependent and difficult to be defined a priori, this work proposes an h-adaptive strategy, based on a posteriori error estimation, able to find optimal non uniform meshes that recover optimal convergence rates for 3-D LEFM problems. This is shown herein for a LEFM problem that exhibits 3-D effects.