Journal
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Volume 472, Issue 2185, Pages -Publisher
ROYAL SOC
DOI: 10.1098/rspa.2015.0713
Keywords
failure criteria; yield surface; plastic potential; meridional section; deviatoric section; constitutive models
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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 of the Galileo-Rankine criterion. The derived equation is always convex and can also provide a smooth approximation of continuity of at least class C-2 of the original Tresca and Mohr-Coulomb criteria. It is therefore free from all the limitations which restrain the use of some of them in numerical analyses. The mathematical structure of the presented equation is based on a separate definition of the meridional and deviatoric sections of the graphical representation of the criteria. This enables the use of an efficient implicit integration algorithm which results in a very short machine runtime even when demanding boundary value problems are analysed.
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