It is customary to represent the yield condition as a surface in stress space, convex [1] and initially containing the origin. The current yield conditions for a metal are those of v. Mises [2] and of Tresca [3]. The flow rule generally accepted [4, 1] is also due to v. Mises [5]. It states that the strain increment vector lies in the exterior normal of the yield surface at the stress point. As to the hardening rule, there are mainly two versions in use. The rule of isotropic work-hardening given by Hill and Hodge [6, 7] assumes that the yield surface expands during plastic flow, retaining its shape and situation with respect to the origin. Another rule, developed by Prager [8], assumes that the yield surface is rigid but undergoes a translation in the direction of the strain increment.

The rule of isotropic work-hardening does not account for the Bauschinger effect observed in the materials in question. Prager's hardening rule accounts for this effect. However, as Perrone and Hodge Jr.[9] have shown in special cases and Shield and the author [10] in a general investigation, Prager's hardening rule is not invariant with respect to reductions in dimensions possible in almost any applications. In other words: if the yield surface in 9-space uik moves in the direction of the exterior normal at the stress point, the two-dimensional yield locus, eg, in plane stress vx,< ry does not do so. In certain cases, eg, if only< rx and txv are different from zero, the Tresca yield locus in the plane< jx, txv even deforms.