A material energy–momentum flux-driven phase field fracture mechanics model

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This work introduces a novel phase-field solution for simulating and predicting fractures in elastic solids. In this phase-field fracture model, the crack growth is driven by the material energy–momentum flux, or the configurational force, inspired by a null divergence conservation law and its variational theory, as opposed to employing the commonly-used strain energy degradation-based crack-driving force. By doing so, the crack growth or material configuration change is solely determined by the physics-based Eshelby energy–momentum tensor density or the Rice J-integral flux, which aligns with the energy release criterion of the celebrated Griffith–Eshelby–Rice (GER) theory. The proposed method not only preserves the integrity of the balance of linear momentum principle at the crack tip region but also provides a correct stress asymptotic field in front of the crack tip, while accurately capturing the crack growth.The key idea of this approach is to use the monotonically increasing and irreversible phase field as the marker of the configurational change and form a phase field variational principle that couples the strain energy density with the configurational strain energy density. By doing so, we only damage the displacement field as a form of diffused crack, as opposed to damaging the stress field in the existing phase-field method. Moreover, from numerical simulations, we discovered two different forms of energy release rates: one drives crack growth by enforcing the crack-tip traction loading condition, and one drives crack growth by enforcing the crack-tip deformation condition, demonstrating the ability of the proposed method to naturally capture two distinct modes of fractures due to two different near-crack tip loading conditions. These advancements and contributions reveal previously unknown insights into fracture mechanics.