Calculus of Variations and Geometric Measure Theory

G. Dal Maso - F. Iurlano

Fracture models as Gamma-limits of damage models

created by dalmaso on 04 Jun 2011
modified by iurlano on 25 Nov 2013


Published Paper

Inserted: 4 jun 2011
Last Updated: 25 nov 2013

Journal: Commun. Pure Appl. Anal.
Volume: 12
Number: 4
Pages: 1657--1686
Year: 2013
Doi: 10.3934/cpaa.2013.12.1657
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