In our paper (León Baldelli & Maurini, 2021) we discuss the numerical stability and bifurcation analysis of gradient damage models and we provide a algorithm to filter-out unstable evolution.

  1. León Baldelli, A. A., & Maurini, C. (2021). Numerical bifurcation and stability analysis of variational gradient-damage models for phase-field fracture. Journal of the Mechanics and Physics of Solids, 152, 104424. [Publisher] [Pdf]