Complete-damage evolution based on energies and stresses

Alexander Mielke

doi:10.3934/dcdss.2011.4.423

Article Contents

2011, Volume 4, Issue 2: 423-439. Doi: 10.3934/dcdss.2011.4.423

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Complete-damage evolution based on energies and stresses

Alexander Mielke^1,

1.
Weierstraß-Institut für Angewandte Analysis und Stochastik, Mohrenstraße 39, 10117 Berlin

Received: April 2009

Revised: August 2009

Published: April 2011

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Abstract

The rate-independent damage model recently developed in [1] 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.

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Mathematics Subject Classification: 35K65, 35K85, 49S05, 74C05, 74R05.

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