The core issue raised by Preumont and Pitoiset is the question of why one would be interested in von Mises stress—as ordinarily defined—since it appears to have features that make it difficult to apply to fatigue analysis.

The answer is that this work, as well as most other work that evaluates the von Mises stress, is focused on other forms of structural and material failure than fatigue. In problems of yield and ductile fracture, the features of von Mises stress that Preumont and Pitoiset find off-putting are believed to capture the physics reasonably well. In such problems, the statistics of von Mises stress are standard tools to assess reliability.

In their final comments Preumont and Pitoiset advocate the utility of the autospectral density function of the stress vector in studying fatigue problems. To us, those comments suggest the interesting notion of extending the probabilistic methods presented in our paper to frequency space.