> It's been surprising to me how poorly understood this field is. Even something as popular a the von Mises criterion seems to have got its popularity because T

> It's been surprising to me how poorly understood this field is. Even something as popular a the von Mises criterion seems to have got its popularity because Tresca was a more "pure" result of the supposed failure mechanisms but it needed rounded corners to fit dirty real world materials and von Mises has rounded corners, so it'll be good enough. I don't think this is an educated take. Tresca and von Mises are yield criteria that match experimental observations on controlled environments. Fatigue is not the same thing as yield failure. Fatigue can culminate in failure, but it is due to propagation of damage throughout time caused by repeated loads. Damage can assume multiple forms. This means that the structural system actually changes throughout time, and stresses propagate differently and concentrate on both places where damage forms and propagates and places where load is redistributed. Fatigue is highly dependent on load history and manufacturing techniques/quality control. There are a few classes of fatigue such as low-cycle fatigue and high-cycle fatigue. You cannot model this with an equation. The best you can do is spread sensors around to monitor load history and make educated guesses on when specific parts of a structural system is reaching the end of its service life. To add to the complexity, fatigue is also dependent on the microstructure of a structural material. The concept of very high cycle fatigue is relatively new. We had decades of engineering products being developed targeting high-cycle fatigue limits hoping it to be very robust or even eternal. Except we started to see structural systems in the real world, such as airframes, failing due to fatigue when they had a service life of very low loads. Some airframes designed to be practically eternal, such as the C-130, started to show weird fatigue patterns when subjected to neglectible load cycles. It turned out that the metal crystals were causing stress concentrations that caused microcracks even at very low loads. This was not known to even be a possibility, until things started to crack with no apparent reason, and engineers started troubleshooting. But engineers still manage to do wizardry with the limits of what we know. If you want to look at a domain where close to nothing is known, do not look at fatigue or yield criteria. Look at damping. The whole concept of damping is created by engineers hand-waving over the fact that energy leaves the system. The techniques in place have more to do with the convenience of mathematical models than with the actual phenomena. The main class of theological models is basically a linear model that's fitted to observations. There are still PhD thesis being done on how to monitor damping in specific problem settings.