A new work function for pressure-independent materials exhibiting the strength-differential effect

The work function introduced in the 1950s significantly broadens the applicability of the upper-bound theorem, a vital tool for solving boundary-value problems in plasticity. However, few publications attempt to apply this technique. Notably, no work function has been proposed for pressure-independent materials exhibiting the strength-differential effect. This paper presents such a function involving the quadratic and cubic invariants of the deviatoric strain rate tensor. The function is a first-order homogeneous function. The yield criterion associated with this work function is calculated numerically. Results show that the yield locus in a generic plane orthogonal to the hydrostatic axis closely matches that reported in the literature. At a specific value of a parameter within the work function, the yield criterion reduces to the von Mises yield criterion. The upper-bound theorem based on this new yield function is used to determine the force required to extrude or draw the material through a conical die. The influence of the strength-differential effect on this force is also analyzed.