Purpose is the formulation, numerical implementation, identification and application of a material model for ductile damage and failure during cyclic and non-proportional loading. The authors combined a hyperelasticity-based elasto-plastic model for non-linear isotropic as well as kinematic hardening with a modified Gurson model. Evolution strategy helped identify the model parameters for the high-strength steel 10MnMoNi5-5. The simulation of ductile failure in fracture mechanics specimens verified the model with respect to cyclic loading at two temperatures. The simulation of additional fracture mechanics applications validated the model as to the development of residual stresses at the crack tip under cyclic loads.