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

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Abstract

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.

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Authors and Affiliations

  1. Dipartimento di Matematica F. Enriques, Università di Milano, Via Saldini 50, Milan, Italy

    Elena Bonetti

  2. Dipartimento di Ingegneria Civile, dell’Ambiente, del Territorio e Architettura, Università di Parma, Parco Area delle Scienze, 181/A, Parma, Italy

    Francesco Freddi

  3. Dipartimento di Matematica F. Casorati, Università di Pavia, Via Ferrata 1, Pavia, Italy

    Antonio Segatti

Authors
  1. Elena Bonetti
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  2. Francesco Freddi
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  3. Antonio Segatti
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Correspondence to Elena Bonetti.

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Communicated by Andreas Öchsner.

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Bonetti, E., Freddi, F. & Segatti, A. An existence result for a model of complete damage in elastic materials with reversible evolution. Continuum Mech. Thermodyn. 29, 31–50 (2017). https://doi.org/10.1007/s00161-016-0520-3

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  • DOI: https://doi.org/10.1007/s00161-016-0520-3

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