On the analysis of crack‐closure behaviour using the phase‐field method together with the novel concept of Representative Crack Elements

For the analysis of crack closure behaviour and the determination of forces transferred across the crack, several stress‐based splits are used for the phase‐field method so far. Steinke and Kaliske [1] proposed a kinematic analysis of the crack‐closure behaviour for isotropic linear‐elastic material behaviour, which overcomes some important issues of the previous splits (volumetric‐deviatoric and spectral split). The paper presents a novel approach for the phase‐field method, which adopts the idea of a kinematic crack analysis. Therefore, an underlying representative model of a discrete crack is coupled to the phase‐field model in order to determine the degraded and the crack‐closure behaviour. Finally, a closed form solution of the approach is presented for linear elasticity and results for thermo‐elasticity are shown. The model is validated by showing self‐consistency and the results are compared to those from the previously mentioned splits.