In notches of metallic components under exterior loading, stresses are so large that local plasticity comes into play. As an effect the elastic stress, which is linearly related to the elastic strain via Hooke's law, overestimates the real stress.

Now in practice, it is usually too elaborate and expensive to perform a fully nonlinear FEM simulation with an appropriate elastoplastic hysteresis law (e. g. Melan-Prager, Armstrong, Frederick, Mróz, Caboche, Jiang, ...) transiently over a long time interval. If present, one uses the effect of elastic support and corrects an elastic equivalent stress magnitude via Neuber's method or the ESED method. So far, tensorial corrections (3D-multiaxial) have not been practicable, since they have not been proper enough.

In the MDF department, existing multiaxial elastoplastic correction methods have been improved and numeric algorithms for the resulting DAE-systems have been developed. The new enhanced methods allow a sufficiently exact approximation of all the three components of the real plane stress tensor at the notch root.

For the identification of the numerous parameters of the elastoplastic material law, we use the automatic differentiation (AD) technique, which allows an exact gradient evaluation. That way, more accurate matching with notch strain measurements or transient FEM computations can be achieved.