Nowadays, several engineering components are made of high performance laminated composites and adhesively bonded interfaces. One of the most serious damage modes of laminated structures is related to the non-linear and irreversible delamination process, including the formation and propagation of inter-laminar cracks, up to the complete detachment of the adhering parts. This work focuses on the development of a new numerical formulation to determine the debonding onset and propagation along weak interfaces under different mixed-mode conditions. The interfacial problem is addressed by means of the cohesive crack modeling, concentrating all non-linearities at the interface. This means that interfaces are considered as an assemblage of two sublaminates, partly bonded together by an elastic interface, here modelled as a continuous distribution of elastic springs acting along the normal and/or tangential direction, depending on the interfacial mixed-mode condition. This generalizes the idea suggested recently in  for a single mode-I debonding, which is here extended to include mixed loading, geometrical and mechanical conditions. The numerical predictions in terms of crack advancement, length of the process zone, maximum load and load-deflection response, are compared to the main results based on a frictional contact formulation. This is here generalized to handle cohesive forces along the normal and tangential directions, as employed in [2-4]. The very good agreement between the proposed numerical approach and a combined contact- debonding algorithm, confirms the feasibility and accuracy of the proposed formulation when studying delamination phenomena occurring within composite materials or laminated joints, usually subjected to mixed-mode conditions.
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