Fracture models for elasto-plastic materials as limits of gradient damage models coupled with plasticity: the antiplane case

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 ε, which forces damage concentration on regions of codimension one. We determine the Gamma-limit as ε tends to zero and show that it contains an energy term involving the crack opening.