Strong discontinuity approaches: An algorithm for robust performance and comparative assessment of accuracy

The Strong Discontinuity Approach (SDA) is a popular method to incorporate cracks as displacement discontinuities into finite elements. In the first part of the paper, different SDA formulations (denoted as SOS, KOS and SKON) are assessed numerically based upon different error norms including a norm to evaluate the variational consistency of SDA elements. Results are compared with analytical solutions as well as with results from interface elements and the element erosion technique for cohesionless cracks. In the second part of the paper, a new method to improve the computational robustness of SDA analyses is proposed. In addition to using arc-length control to solve the nonlinear equation system, a sequential un- and reloading scheme is proposed with the crack state frozen during unloading to avoid, that more than one new crack segment is activated within an increment. The performance of the algorithm is demonstrated by numerical analyses of a tension test on a dog-bone shaped specimen by means of different variants of the SDA and, for comparison, also using interface elements.