A new generalized potential with exchangeable functions of octahedral cross sections for modelling yielding or failure of frictional materials

Geomaterials, concrete, cast iron, selected high-strength steels and aluminium alloys, though apparently different, share common features: pressure dependence and strength difference in tension and compression, which allows us to describe their inelastic behaviour in terms of similar functions (yield/damage criteria, plastic potentials). From the standpoint of numerical calculations, it is favourable to unify various functions to a form, which a priori is convex and differentiable. In this work, a new generalized isotropic potential to be used in constitutive models is constructed. The function is dependent on three invariants of stress tensor and derives from two smoothly connected non-revolving hyperboloids. The meridional shape of the limit state surface is predetermined, and the function is generalized towards the shape of deviatoric cross sections. There are six material parameters plus two functions describing shape in the octahedral plane, which can be defined, to a great extent, arbitrarily. Convexity requirements are analysed and consequent restraints are put on the values of parameters. The function is differentiable in the whole stress domain. The presented formulae are adjustable, encompassing a wide range of existing functions including Drucker–Prager’s, Coulomb–Mohr’s and Lubliner’s criteria, but also allow for the generation of new criteria. A comparison with experimental data for concrete, geomaterials and others is shown.