Dynamic crack propagation with a variational phase-field model: limiting speed, crack branching and velocity-toughening mechanisms

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Phase-field modeling of anisotropic brittle fracture including several damage mechanisms (2018, unknown): “…in particular the branching of a single crack into multiple cracks [27–29], for which a simple energetic criterion has been proposed [30], the existence of a limiting speed below the Rayleigh wave speed [30], the occurrence of a microbranching instability inherent to 3D eﬀects [31, 32], etc.”
An open-source Abaqus implementation of the phase-field method to study the effect of plasticity on the instantaneous fracture toughness in dynamic crack propagation (2020, background): “This result is consistent with the fact that the instabilities were not present in the 2D simulation of Bleyer & Molinari [86] either.”