Analysis of Staggered Evolutions for Nonlinear Energies in Phase Field Fracture

  • Stefano Almi
  • Matteo NegriEmail author


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 viscosity evolutions, parametrized by their arc-length with respect to the \(L^2\)-norm (for the phase field) and the \(H^1\)-norm (for the displacement field). By a careful study of the energy balance we deduce that time-continuous evolutions may still exhibit an alternate behavior in discontinuity times.



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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Fakultät für Mathematik - TUMGarching bei MünchenGermany
  2. 2.Department of MathematicsUniversity of PaviaPaviaItaly

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