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We study a model for the rate-independent evolution of cohesive zone delamination in a visco-elastic solid, also exposed to dynamics effects. The main feature of this model, inspired by [

Due to the presence of multivalued and unbounded operators featuring non-penetration and the 'memory'-constraint in the strong formulation of the problem, we prove existence of a weaker notion of solution, known as *semistable energetic solution*, pioneered in [

We are interested in a good approximation of the discrete energy of this system for a large number of atoms, i.e., in the continuum limit.

We show that the canonical expansion by $\Gamma$-convergence does not provide an accurate approximation of the discrete energy if the boundary conditions for the deformation are close to the threshold between

*elastic*and fracture regimes. This suggests that a uniformly $\Gamma$-equivalent approximation of the energy should be made, as introduced by Braides and Truskinovsky, to overcome the drawback of the lack of accuracy of the standard $\Gamma$-expansion.

In this spirit we provide a uniformly $\Gamma$-equivalent approximation of the discrete energy at first order, which arises as the $\Gamma$-limit of a suitably scaled functional.

*energetic solutions*to such system is proved via approximation.

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