  In this paper we investigate a rate--independent model for hybrid laminates
described by a damage phase--field approach on two layers coupled with a
cohesive law governing the behaviour of their interface in a one-dimensional
setup. For the analysis we adopt the notion of energetic evolution, based on
global minimisation of the involved energy. Due to the presence of the cohesive
zone, as already emerged in literature, compactness issues lead to the
introduction of a fictitious variable replacing the physical one which
represents the maximal opening of the interface displacement discontinuity
reached during the evolution. A new strategy which allows to recover the
equivalence between the fictitious and the real variable under general
loading--unloading regimes is illustrated. The argument is based on temporal
regularity of energetic evolutions. This regularity is achieved by means of a
careful balance between the convexity of the elastic energy of the layers and
the natural concavity of the cohesive energy of the interface.
