Summary The realistic representation of material degradation at a fully evolved crack is still one of the main challenges of the phase‐field method for fracture. An approach with realistic degradation behavior is only available for isotropic elasticity in the small deformation framework. In this paper, a variational framework is presented for the standard phase‐field formulation, which allows to derive the kinematically consistent material degradation. For this purpose, the concept of representative crack elements (RCE) is introduced to analyze the fully degraded material state. The realistic material degradation is further tested using the self‐consistency condition, where the behavior of the phase‐field model is compared to a discrete crack model. The framework is applied to isotropic elasticity, anisotropic elasticity and thermo‐elasticity, but not restricted to these constitutive formulations.

No abstract

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.

No abstract