WIAS Preprint No. 1228, (2007)

A complete-damage problem at small strains


  • Bouchitté, Guy
  • Mielke, Alexander
    ORCID: 0000-0002-4583-3888
  • Roubíček, Tomáš

2010 Mathematics Subject Classification

  • 35K65 35K85 49S05 74C05 74R05


  • Inelastic damage, small strain, variational inequality, energetic formulation




The complete damage of a linearly-responding material that can thus completely disintegrate is addressed at small strains under time-varying Dirichlet boundary conditions as a rate-independent evolution problem in multidimensional situations. The stored energy involves the gradient of the damage variable. This variable as well as the stress and energies are shown to be well defined even under complete damage, in contrast to displacement and strain. Existence of an energetic solution is proved, in particular, by detailed investigating the $Gamma$-limit of the stored energy and its dependence on boundary conditions. Eventually, the theory is illustrated on a one-dimensional example.

Appeared in

  • Z. Angew. Math. Phys., 60 (2009) pp. 205--236.

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