Young measure flow as a model for damage

Marc Oliver Rieger, J Zimmer

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Models for hysteresis in continuum mechanics are studied that rely on a time-discretised quasi-static evolution of Young measures akin to a gradient flow. The main feature of this approach is that it allows for local, rather than global minimisation. In particular, the case of a non-coercive elastic energy density of Lennard-Jones type is investigated. The approach is used to describe the formation of damage in a material; existence results are proved, as well as several results highlighting the qualitative behaviour of solutions. Connections are made to recent variational models for fracture.
Original languageEnglish
Pages (from-to)1-32
Number of pages32
JournalZeitschrift für Angewandte Mathematik und Physik
Issue number1
Early online date5 Jul 2008
Publication statusPublished - Jan 2009


  • Fracture
  • Elasticity
  • Continuum mechanics


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