Communications on Pure and Applied Analysis (CPAA)

Fracture models as $\Gamma$-limits of damage models

Pages: 1657 - 1686, Volume 12, Issue 4, July 2013      doi:10.3934/cpaa.2013.12.1657

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Gianni Dal Maso - SISSA, via Bonomea 265, 34136 Trieste, Italy (email)
Flaviana Iurlano - SISSA, Via Bonomea 265, 34136 Trieste, Italy (email)

Abstract: We analyze the asymptotic behavior of a variational model for damaged elastic materials. This model depends on two small parameters, which govern the width of the damaged regions and the minimum elasticity constant attained in the damaged regions. When these parameters tend to zero, we find that the corresponding functionals $\Gamma$-converge to a functional related to fracture mechanics. The corresponding problem is brittle or cohesive, depending on the asymptotic ratio of the two parameters.

Keywords:  Damage problems, fracture mechanics, $\Gamma$-convergence, free discontinuity problems.
Mathematics Subject Classification:  Primary: 74A45, 49J45; Secondary: 35A35.

Received: June 2011;      Revised: June 2012;      Available Online: November 2012.