  There is a large variety of concepts used to generalize the classical
Prandtl-Reuss relations of infinitesimal elasto-plasticity to finite strains.
In this work, some basic approaches are compared in a qualitative way with
respect to a certain invariance property. These basic approaches include the
additive hypoelasto-plasticity with corotational stress rates, additive
plasticity in the logarithmic strain space, and multiplicative
hyperelasto-plasticity.
  The notion of weak invariance is introduced in this study. Roughly speaking,
a material model is weakly invariant under a certain transformation of the
local reference configuration if this reference change can be neutralized by a
suitable transformation of initial conditions, leaving the remaining
constitutive relations intact. We analyse the basic models in order to find out
if they are weakly invariant under arbitrary volume-preserving transformations
of the reference configuration.
  It is shown that the weak invariance property corresponds to a generalized
symmetry which provides insights into underlying constitutive assumptions. This
property can be used for a systematic study of different frameworks of finite
strain elasto-plasticity. In particular, it can be used as a classification
criterion.
