AbstractA new cohesive contact model coupling the interfacial damage and the Coulomb friction is presented from the mathematical and engineering points of view. The formulation of the Cohesive Interface Model (CIM) predicts the interface damage assuming the frictional contact between debonded surfaces. The contribution discusses the role, influence and the intensity of the friction in the process of the interface debonding in two subsequent fracture effects: the crack initiation and the crack propagation. A concept of an energy-based formulation is applied to model the process of interface debonding. The numerical solution is approximated by a time stepping procedure and it has been implemented in the Symmetric Galerkin Boundary Element Met...