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

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


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