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We study an approximation scheme for a variational theory of cohesivefracture in a one-dimensional setting. Here, the energy functional isapproximated by a family of functionals depending on a small parameter $0 <\varepsilon \ll 1$ and on two fields: the elastic part of the displacementfield and an eigendeformation field that describes the inelastic response ofthe material beyond the elastic regime. We measure the inelastic contributionsof the latter in terms of a non-local energy functional. Our main result showsthat, as $\varepsilon \to 0$, the approximate functionals $\Gamma$-converge toa cohesive zone model.

Eigendamage: an Eigendeformation model for the variational approximation of cohesive fracture -- a one-dimensional case study