Cálculo dos parâmetros de fratura linear elástico baseado numa estratégia auto-adaptativa

Abstract

Several finite element adaptive strategies are available for linear-elastic problems. However, few works deal with adaptive analysis of fracture problems1,2,3,4. This is due mainly to the singularity at crack tips. An efficient adaptive technique must be able to localize singularity regions, in addition to correctly define element sizes in these regions. The way the singularity is treated differs from author to author. Some2,4 incorporate the intensity of the singularity in the computation of the characteristic size of elements adjacent to the singularity region, while others3 clain that this is not necessary. In addition, in fracture problems, elements at the crack tip need to be sufficiently small to capture the existing singularity. Therefore, some requirements are imposed to the mesh generation algorithms such as to provide good mesh transition between regions of different element sizes and to avoid bad shaped elements at the crack tip. Previous work of the authors proposed mesh generation techniques for two-dimensional models with cracks5. This work describes the adopted adaptive strategy for linear-elastic fracture problems. This strategy is based on a type “h” refinement, with an ‘a posteriori’ error estimator, which is based on an energy norm4. To evaluate the proposed strategy, examples of numerical computation of fracture parameters are presented.