The classical hypotheses describe the extremal states of material behavior (Chap. 4). In order to establish the ductile-brittle transition, the classical hypotheses can be combined by one or two parameters Lüpfert, Beurteilung der statischen Festigkeit und Dauerfestigkeit metallischer Werkstoffe bei mehrachsiger Beanspruchung. Dt. Verl. für Grundstoffindustrie, Leipzig, [1], e.g., the Mohr-Coulomb and the Sdobyrev, Pisarenko-Lebedev criteria (Sect. 6.3). Several further expressions for combination of the classical hypotheses are possible, e.g., the Hoek-Brown criterion (Sect. 2.2.17) and the UST of Yu (Sect. 2.3.5). These formulations can be an advantage for particular materials.
