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This contribution presents a novel approach of the cohesive finite element method based on an initially rigid traction separation law which allows to insert the cohesive elements during the simulation depending on a crack growth criterion. In order to represent arbitrary crack patterns, this procedure is combined with an adaptive modification regarding the nodal coordinates and element boundaries of the initial discretization. In addition to the description of the formulation and algorithmic implementation of both the discrete crack model and the adaptive system modification, the influence of the traction-separation-dependencies on the global structural response in comparison with traction-free crack propagation models are investigated. The application of the proposed model to different analytical and experimental problems confirms its capabilities regarding the simulation of arbitrary discrete crack growth.