Continuum Mechanics and Thermodynamics

, Volume 29, Issue 1, pp 31–50 | Cite as

An existence result for a model of complete damage in elastic materials with reversible evolution

  • Elena BonettiEmail author
  • Francesco Freddi
  • Antonio Segatti
Original Article


In this paper, we consider a model describing evolution of damage in elastic materials, in which stiffness completely degenerates once the material is fully damaged. The model is written by using a phase transition approach, with respect to the damage parameter. In particular, a source of damage is represented by a quadratic form involving deformations, which vanishes in the case of complete damage. Hence, an internal constraint is ensured by a maximal monotone operator. The evolution of damage is considered “reversible”, in the sense that the material may repair itself. We can prove an existence result for a suitable weak formulation of the problem, rewritten in terms of a new variable (an internal stress). Some numerical simulations are presented in agreement with the mathematical analysis of the system.


Complete damage Phase transition Non-smooth PDE system Existence result for weak solutions 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Elena Bonetti
    • 1
    Email author
  • Francesco Freddi
    • 2
  • Antonio Segatti
    • 3
  1. 1.Dipartimento di Matematica F. EnriquesUniversità di MilanoMilanItaly
  2. 2.Dipartimento di Ingegneria Civile, dell’Ambiente, del Territorio e ArchitetturaUniversità di ParmaParmaItaly
  3. 3.Dipartimento di Matematica F. CasoratiUniversità di PaviaPaviaItaly

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