Gradient-enhanced damage modeling of cracked bodies by reproducing kernel element method

In crack modeling by extended finite element method, the enrichment by the asymptotic analytical solution works excellent for linear elastic fracture mechanics. However for the more sophisticated condition of a gradient-enhanced damage model, firstly the analytical solution is not available and secondly higher order continuity of the shape functions is required. In this study, the extended finite element model of the cracked body is augmented with shape functions of higher order continuity and higher order consistency generated by reproducing kernel element method. They are used in a region near the crack tip to have an appropriate interpolation of the damaged zone while for the rest of the solution domain standard shape functions are used to reduce the computational cost. No new nodes are needed when defining the higher order shape functions by reproducing kernel element method and thus remeshing is avoided during the crack growth. After describing the formulations, several numerical examples are implemented to investigate the ability of the proposed method, for both the linear elastic fracture mechanics and the gradient-enhanced damage models.