Eigendamage: An Eigendeformation Model for the Variational Approximation of Cohesive Fracture

In this book, a novel approximation scheme for the variational theory of cohesive fracture is presented. The energy functionals that are considered in this scheme depend on a small parameter and two fields: the displacement field and an eigendeformation field, where the latter one describes the permanent deformations that may occur in the body. The asymptotic behavior of these energy functionals is investigated in the case of antiplane shear. Our analysis, in particular, shows that the minimal energies with respect to the eigendeformation field are related to a cohesive energy functional in the sense of Gamma-convergence.