Analysis of Staggered Evolutions for Nonlinear Energies in Phase Field Fracture

@article{Almi2019AnalysisOS,
  title={Analysis of Staggered Evolutions for Nonlinear Energies in Phase Field Fracture},
  author={Stefano Almi and Matteo Negri},
  journal={Archive for Rational Mechanics and Analysis},
  year={2019},
  volume={236},
  pages={189-252}
}
We consider a class of separately convex phase field energies employed in fracture mechanics, featuring non-interpenetration and a general softening behavior. We analyze the time-discrete evolutions generated by a staggered minimization scheme, where fracture irreversibility is modeled by a monotonicity constraint on the phase field variable. After recasting the staggered scheme by means of gradient flows, we characterize the time-continuous limits of the discrete solutions in terms of balanced… 
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