On adaptive remeshing techniques for crack simulation problems

This paper has presented error estimate procedures for the energy norm of discrete crack propagation simulations. The estimated error is based on the residual error measure of Babuska and Rheinboldt. Since the contribution to the error bound for elements with quadratic polynomial shape functions is dominated by the interior residual part, the second error term covering stress discontinuities at the element boundaries could been neglected. Therewith the error can be calculated locally for every element domain without need for a global solution. Bi-linear interpolation functions for the stress distribution in every element lead to the stress gradients, the computation of which applies a least squares method to minimize the deviation between the interpolation function and the discrete Gauss-point values. Based on this error estimator, an adaptive remeshing procedure has been developed, accounting for the distribution and the magnitude of the error. The element error is used to decide on the mesh refinement and the relative error in the energy norm for each mesh is considered as a convergence criterion for the engineering analysis. The error estimator in conjunction with the adaptive remeshing procedure has been applied successfully for a couple of discrete crack propagation simulations, showing the bounding capability of the error in the energy norm. With such efficient refinement strategy desired relative errors in the energy norm can be obtained for a minimum number of degrees of freedom.