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

Gianni Dal Maso; Flaviana Iurlano

doi:10.3934/cpaa.2013.12.1657

Article Contents

2013, Volume 12, Issue 4: 1657-1686. Doi: 10.3934/cpaa.2013.12.1657

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

Gianni Dal Maso^1, and
Flaviana Iurlano^2,

1.
SISSA, via Bonomea 265, 34136 Trieste
2.
SISSA, Via Bonomea 265, 34136 Trieste

Received: May 31, 2011

Revised: May 31, 2012

Published: June 2013

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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.

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Mathematics Subject Classification: Primary: 74A45, 49J45; Secondary: 35A35.

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