A generalization of Gittus’ viscoplastic “mechanical equation of state” to multiaxial stress states

In this paper, a multiaxial generalization of the viscoplastic “mechanical equation of state” (MEOS) by Gittus is proposed that preserves the physical soundness of the theory. The concept of forward and backward mobility of dislocations is generalized to a concept of directional mobility by splitting the mobile dislocation density in an isotropic and a tensorial part, similar to the approach used in the Bodner unified viscoplastic model. It is shown that the formulation is equivalent to the original MEOS in the case of uniaxial loadings. The approach is easily applied to any uniaxial viscoplastic material model.