On local tracking algorithms for the simulation of three-dimensional discontinuities

The present manuscript focuses on the algorithmic treatment of three-dimensional discontinuities within a purely displacement based finite element setting. In contrast to two-dimensional cracks, the local element based geometric representation of three-dimensional crack surfaces is non-unique and thus not straightforward. Accordingly, we compare different crack tracking strategies, one being algorithmically extremely efficient but yet somehow restrictive, the other one being more complex but rather general in nature. While the first method is able to represent entirely smooth discontinuity surfaces, the second approach introduces inter-element discontinuities in the overall crack surface representation. Both methods are compared systematically and additional comments about the algorithmic realization are provided. From the numerical results we conclude that neither of the two algorithms is able to solve all defined quality criteria satisfactorily, although both are mesh independent, computationally cheap and rather efficient. The ultimate solution might be an overall global crack surface representation that a priori circumvents a number of algorithmic deficiencies and at the same time provides a unique and smooth three-dimensional crack surface representation.