| A number of procedures exist in fracture Mechanics to evaluate the stress intensity factor K (or, equivalently, the strain energy release rate G) from a finite element analysis. Due to the approximate nature of the FE solution, all the extraction methods, for K or G transfer the so-called discretization error to the evaluation of K or G.; The aim of this Thesis is to quantify the effect that the discretization error induces in K or G, i.e. to provide an estimation of the error in K or G due to the use of the FEM. To achieve this goal, a new a posteriori error estimator of high effectivity has been proposed.; A thorough review of the main techniques available to extract K or G has been performed, identifying those methods which are prone to an error estimation. These methods have an energetic character and are based on the concept of virtual crack extension. In this Thesis, methods based on the virtual crack extension concept are interpreted from a more general approach given by a shape design sensitivity analysis (SDSA), by assuming that the virtual crack growth is simply a shape change. Therefore, an approach which unifies the shape design sensitivity analysis and this kind of energetic methods has been presented.; The new error estimator is based on the continuum approach of the shape design sensitivity analysis and can be associated with the error committed when one of the most accurate and efficient methods is used: the EDI method (equivalent domain integral to the contour integral J). By means of 2D numerical examples with a known solution of reference, it has been verified that the error estimation given by the new estimator closely approaches to the true error. As a consequence, an improvement of the results obtained through the EDI method is given, which has been proven to be very useful from a practical point of view. Finally, the application of the new error estimator has been extended, under certain conditions, to 2D mixed mode problems. |
