A new cohesive zone model to describe fracture of interfaces with a microstructurs made of fibrils with statistically distributed in-plane and out-of-plane orientations is proposed. The elementary forcedisplacement relation of each fibril is considered to obey the peeling theory of a tape, although other refined constitutive relations could be invoked for the adhesive constitutive response without any lack of generality. The proposed consistent 2D and 3D interface finite element formulations

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... large displacements account for both the mechanical and the geometrical tangent stiffness matrices, required for implicit solution schemes. After a preliminary discussion on model parameters identification, it is shown that by tailoring the spatial density of fibrils at different orientations can be a way to realize innovative interfaces enhancing adhesion or decohesion, depending on the need. For instance, it can be possible to realize microstructured adhesives to facilitate debonding of the glass cover in photovoltaic modules to simplify recycling purposes. Moreover, the use of probability distribution functions describing the density of fibrils at different orientations is a very effective approach for modeling the anisotropy in the mechanical bonding between paper tissues and for simulating the complex process of crazing in amorphous polymers.