We study the asymptotic behavior of a variational model for damaged elasto-plastic materials in the case of antiplane shear. The energy functionals we consider depend on a small parameter $\varepsilon$, which forces damage concentration on regions of codimension one. We determine the $\Gamma$-limit as $\varepsilon$ tends to zero and show that it contains an energy term involving the crack opening.

%B Calculus of Variations and Partial Differential Equations %V 55 %P 45 %8 Apr %G eng %U https://doi.org/10.1007/s00526-016-0981-z %R 10.1007/s00526-016-0981-z %0 Journal Article %J Communications on Pure and Applied Analysis 12 (2013) 1657-1686 %D 2013 %T Fracture models as Gamma-limits of damage models %A Gianni Dal Maso %A Flaviana Iurlano %XWe 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.

%B Communications on Pure and Applied Analysis 12 (2013) 1657-1686 %I American Institute of Mathematical Sciences %G en %U http://hdl.handle.net/1963/4225 %1 3952 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-23T11:09:07Z\\r\\nNo. of bitstreams: 1\\r\\nDalMaso_Iurlano_25_M.pdf: 360594 bytes, checksum: a0e0909b1c483748ede26b7e785a1d79 (MD5) %R 10.3934/cpaa.2013.12.1657