Phase-field method with additional dissipation force for mixed-mode cohesive fracture

This paper develops a thermodynamic framework of phase-field fracture modeling for cases where the toughness depends on the fracture mode. Using a delicately constructed energy density and a novel dissipation force in the thermodynamic framework, we propose a phase field model that can implement arbitrary mixed-mode cohesive laws for cases where the mode-II fracture energy (G(IIc)) is larger than the mode-I fracture energy (G(Ic)). Four numerical examples are presented to validate the effectiveness of the proposed method, including a uniaxial tension test, a uniaxial compression test, a mixed-mode test on dogbone specimens, and a series of tests on double-edge notched concrete under mixed-mode loading. In the first three examples, the numerically predicted cohesive laws are extracted and compared with the analytical target cohesive laws. Excellent agreements are observed. In the last example, we show that very wrong crack paths may be obtained without distinguishing G(Ic) and G(IIc) in phase-field modeling.

Automated summary

This study presents a new phase-field fracture modeling method that can be applied to cases where toughness depends on different fracture modes, and validates the effectiveness of the method through numerical examples.