This thesis deals with the derivation of a numerical approach to assess potential delamination in a SOFC during operation. Therefore, the fracture mechanical behavior of the interfaces is investigated by the cohesive element approach in the FEM program Abaqus / CAE, which allows a quantification of crack initiation as well as crack propagation. The numerical analysis is based on the thermal stresses during the heating, cool- down and operating phase. The required time and space dependent stress field was obtained by a previous thesis, which is based on a transient temperature field and mechanical boundary conditions. The aim of this work is to determine a simulation workflow in order to assess the local delamination of a single cell. Since the material identification and model validation will be investigated in further work packages, the gained results should not be treated as absolute values. In fact, the output of the calculations should be used for the standardization of the simulation process for further SOFC projects. The chosen methodology identifies the most critical cells for delamination based on the global stress field through calculation of an equivalent damage parameter. For further investigations a submodel of the critical cells including the cohesive elements is built up. By means of this detail model, it is feasible to assess the crack initiation and propagation of the interfaces and perform optimization loops. The necessary identification of the cohesive element material parameters are summarized in this thesis. A parameter analysis is conducted to determine the most appropriate process zone approach and the most efficient discretization of the cell. The final outcome of this thesis proves that the local delamination of a single cell can be assessed by analyzing the global stress field, applying an equivalent damage parameter and a delamination submodel of the most severe cells including cohesive elements. The Barenblatt model is identified as the most promising process zone approach for this SOFC design. This statement is confirmed by comparing the approaches with a model with perfect fracture mechanical mapping of the process zone.