Application of the upper bound theorem for metal forming processes considering an arbitrary isotropic pressure-independent yield criterion with no strength differential effect

The present paper concerns the application of the upper bound theorem based on the work function to analyze metal forming processes. An advantage of this theorem formulation is that it provides a unified method for finding solutions for any yield criterion. In particular, any available kinematically admissible velocity field used in conjunction with the von Mises yield criterion can be utilized with no modification. On the other hand, an explicit function representing the work function associated with a given yield criterion cannot readily be expressed except for some particular cases. The approach proposed in the present paper is to assume a work function instead of a yield criterion. The paper is restricted to the work functions represented by first-order homogeneous functions. Moreover, the material is supposed to be isotropic and incompressible. The strength differential effect is neglected. Illustrative examples reveal the effect of the yield criterion on the limit load for axisymmetric extrusion and ring compression processes. These solutions utilize kinematically admissible velocity fields available in the literature.