Using enclosing ellipsoids in multiaxial fatigue strength criteria

We propose in this paper a scalar measure for the amplitude of shear stress variations based on the definition of an enclosing hyper-ellipsoid of minimum Frobenius norm. This equivalent shear amplitude is combined with the maximal mean stress, in both linear and quadratic functions, leading to two alternative fatigue criteria. The predictions of these criteria are compared with experimental data in order to validate the proposed shear amplitude measure. The crucial issue concerning the feasibility of the computation of the minimum norm ellipsoid is discussed and a practical algorithm is proposed and demonstrated.