Variational phase-field fracture with controlled nucleation

We briefly review the Γ-convergence of phase-field fracture to Griffith fracture, and describe how softening and nucleation occur when implementing phase-field models. An example is given of how this softening and nucleation can be completely stopped, while preserving crack growth and Γ-convergence. We then show how nucleation can locally be turned back on, based on any criterion, such as a stress threshold. Again, these modifications preserve Γ-convergence, and they can be applied to static, quasi-static, and dynamic models. Additionally, we describe why these modifications can be expected to improve the convergence of phase-field models. •We review Γ-convergence of phase-field fracture to Griffith fracture.•Modifications are introduced which preserve Γ-convergence and prevent nucleation.•The modifications preserve growth of existing cracks.•We show how nucleation can locally be turned back on.