Error estimation for the finite element evaluation of GI and GII in mixed-mode linear elastic fracture mechanics

A discretization error estimator for the finite element evaluation of the strain energy release rates (SERRs) GI, GII is presented for mixed-mode bidimensional problems of the linear elastic fracture mechanics (LEFM). The estimator is related to one of the most efficient energetic methods: the equivalent domain integral method (EDI). A continuum approach of the shape design sensitivity analysis (SDSA) is applied to the fracture mechanics problem in combination with the field decomposition technique to obtain separate estimates of the discretization error for each mode. The error estimator enables an a posteriori improvement of GI, GII for a given finite element mesh. The improvement is achieved by adding the estimated errors to the previously calculated values of GI, GII by means of the discrete analytical stiffness derivative method (DASD). This is verified through numerical examples based on the Westergaard's problem and a finite domain problem.