Endowing explicit cohesive laws to the phase-field fracture theory

One of the fundamental but unsolved problems in the phase-field theory is how to obtain the energy density expression based on an arbitrary cohesive law. In this paper, we propose a phase-field model with the energy density determined by the cohesive law with an arbitrary form, which builds a rigorous link between the phase-field theory and the cohesive zone theory. Using the proposed method, the energy density in the phase-field model for any cohesive law can be determined from a unified formula. As examples, we derive the explicit energy density expressions for the linear, exponential, polynomial, and Cornelissen cohesive laws. Five numerical examples are presented to show the effectiveness of the proposed method, including a uniaxial tension test for mode-I failure, a uniaxial compression test for mode-II failure, a mixed-mode fracture test, the mode-I failure in a wedge splitting test, and the mixed-mode failure of an L-shaped panel. In the first three numerical examples, the predicted mode-I, mode-II and mixed-mode cohesive laws are extracted and compared with the target analytical cohesive laws. Excellent agreements are observed. In the last two numerical examples, the predicted global responses and the crack paths are in good agreement with the experimental results.

Automated summary

This paper proposes a phase-field model with energy density determined by an arbitrary cohesive law, establishing a rigorous connection between phase-field theory and cohesive zone theory. The method allows for determination of energy density for any cohesive law from a unified formula. Numerical examples demonstrate the effectiveness of the proposed method in predicting cohesive laws and crack paths.