An extended modified Cam-Clay yield surface for arbitrary meridional and deviatoric shapes retaining full convexity and double homothety

This paper presents a new yield function, defined in terms of stress invariants and suitable for isotropic geomaterials. It is a generalisation of that of the modified Cam-Clay (MCC) model and as such it retains all the mathematical advantages of the original formulation, which are particularly convenient for the numerical integration of the constitutive law. In addition the proposed function is capable of providing a wide range of shapes and it is therefore suitable for defining both the yield and the plastic potential surfaces. As compared to the original MCC ellipse, one additional parameter is introduced for defining the shape of the meridional section, which conveniently controls also the relative position of the normal compression and critical state lines. In the deviatoric plane the function not only provides the exact shape of classical failure criteria, such as von Mises, Drucker–Prager, Matsuoka–Nakai, Lade–Duncan, Tresca and Mohr–Coulomb, but it is also capable of rounding the hexagons of the last two criteria with a continuity of class at least C2 required for achieving a quadratic convergence of the integration scheme. The new function has an unrestricted domain of definition, expands/shrinks homothetically with respect both to the origin of the stress space and to its centre and is characterised by convexity for any level set. The last two important features were obtained by applying a convexification technique proposed by the authors elsewhere.