On the existence of a unique class of yield and failure criteria comprising Tresca, von Mises, Drucker–Prager, Mohr–Coulomb, Galileo–Rankine, Matsuoka–Nakai and Lade–Duncan

In this paper, it is mathematically demonstrated that classical yield and failure criteria such as Tresca, von Mises, Drucker–Prager, Mohr–Coulomb, Matsuoka–Nakai and Lade–Duncan are all defined by the same equation. This can be seen as one of the three solutions of a cubic equation of the principal stresses and suggests that all such criteria belong to a more general class of non-convex formulations which also comprises a recent generalization...