Asymptotic numerical methods (ANM) are useful for monitoring highly non-linear re-sponse curves, such as those given by plasticity, damage and crack propagation. ANM are based on the computation of a Taylor series expansion per step [1]. Unfortunately they cannot be directly used for nonsmooth behaviours such as plasticity or damage because the Taylor series exists only if the governing equations are defined by regular functions. Nevertheless, non-smooth constitutive equations can be regularised as proposed in [2, 3]. In this work, a relevant ANM computational procedure is presented to predict onset and crack growth in the Continuum Damage Mechanics (CDM) framework using cohe-sive zone model and irreversible thermodynamics concepts. The existence of irreversible processes induced by plasticity and damage evolution legitimates the introduction of in-trinsic dissipation. For the sake of simplicity, we limit our analysis to 1-D damageable interfaces. The interface models, considered hereafter, relate normal load to normal dis-placement discontinuity. This modelling approach is often used to describe the initiation of composite delamination [4] or crack propagation. We will progressively consider: the elastic-damageable interface law Fig.1(a), the sequential perfect-plastic-damageable inter-face laws Fig.1(b) and the coupled plastic-damageable law Fig.1(c). In the generalized standard materials (GSM) framework, free energies are formulated respectively for the elastic-damageable model, denoted Ψ 1 (x, x d), and for the plastic-damageable models, de-noted Ψ 2 (x, x d , x p): Ψ 1 (x, x d) =