A comparison of approaches to compute the crack opening/sliding within the phase-field method

The phase-field method has been used widely in the analysis of fracture due to its easy description of cracks, which obviates the introduction of geometric discontinuities in the domain. The discrete crack is regularised as a smeared surface, defined by a phase-field variable, and there is no need to explicitly define a crack path. Due to the smeared nature of the phase-field method, the crack opening and crack sliding do not directly result from a phase-field computation, but need to be computed a posteriori. Herein, we provide a complete overview of methods to compute the crack opening and crack sliding, resulting from the phase-field computation, namely the auxiliary field method, the integration method and the Taylor expansion method. The advantages and disadvantages of the methods are demonstrated by numerical examples, for crack opening/sliding. The auxiliary field and integration methods provide stable and relatively accurate results, but the Taylor expansion method is the faster approach to compute the crack opening/sliding, with a guaranteed accuracy.