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 Γ-converge to a functional related to frac- ture mechanics. The corresponding problem is brittle or cohesive, depending on the asymptotic ratio of the two parameters.
Fracture models as Gamma-limits of damage models / Dal Maso, Gianni; Iurlano, F.. - In: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS. - ISSN 1534-0392. - 12:4(2013), pp. 1657-1686. [10.3934/cpaa.2013.12.1657]
Fracture models as Gamma-limits of damage models
Dal Maso, Gianni;
2013-01-01
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 Γ-converge to a functional related to frac- ture mechanics. The corresponding problem is brittle or cohesive, depending on the asymptotic ratio of the two parameters.| File | Dimensione | Formato | |
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