Inserted: 4 jun 2011
Last Updated: 25 nov 2013
Journal: Commun. Pure Appl. Anal.
Links: online publication
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: $\Gamma$-convergence, free discontinuity problems, fracture mechanics, Damage problems