WIAS Preprint No. 1414, (2009)

Complete-damage evolution based on energies and stresses


  • Mielke, Alexander
    ORCID: 0000-0002-4583-3888

2010 Mathematics Subject Classification

  • 35K65 35K85 49S05 74C05 74R05


  • Energetic solution, rate-independent system, complete damage, parametrized Gamma convergence




The rate-independent damage model recently developed in Bouchitté, Mielke, Roubíček ``A complete-damage problem at small strains" allows for complete damage, such that the deformation is no longer well-defined. The evolution can be described in terms of energy densities and stresses. Using concepts of parametrized Gamma convergence, we generalize the theory to convex, but non-quadratic elastic energies by providing Gamma convergence of energetic solutions from partial to complete damage under rather general conditions.

Appeared in

  • Discrete Contin. Dyn. Syst. Ser. S, 4 (2011) pp. 423--439.

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