A rheological model for arbitrary symmetric distortion of the yield surface

A phenomenological model of metal viscoplasticity, which takes combined isotropic, kinematic, and distortional hardening into account, is motivated by a new rheological model. The distinctive advantage of the material model is that any smooth convex saturated form of the yield surface which is symmetric with respect to the recent loading direction can be captured. In particular, an arbitrary sharpening of the saturated yield locus in the loading direction combined with a flattening on the opposite side can be covered. Moreover, the yield locus evolves smoothly and its convexity is guaranteed at each hardening stage. The underlying two-dimensional rheological analogy can be used to provide insight into the main constitutive assumptions. This rheological model is utilized as a guideline for the construction of phenomenological constitutive relations. The distortion of the yield surface is described with the help of a so-called distortional backstress. Thus, 2nd rank tensors are utilized only. The resulting material model is thermodynamically consistent. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)