Efficient algorithms for calculation of shear stress amplitude and amplitude of the second invariant of the stress deviator in fatigue criteria applications

Criteria based on both critical plane and stress invariant approaches require routines for the calculation of the amplitude of critical stress quantities. The definition of the shear stress amplitude on a material plane as well as the evaluation of the amplitude of the second invariant of the stress deviator can be led back to an optimization problem which can be quickly solved with already existing routines. In this paper a new method is presented and results are compared with those obtained with other previously proposed algorithms.