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Traditional formulations of
elastoplasticity in the presence of finite strain and large rotation are
Eulerian type and widely used; they are based upon, among other things,
the additive decomposition of the stretching or the Eulerian strain-rate
into elastic and plastic parts. In such formulations, yield functions
and objective rate constitutive equations are expressed in terms of
objective Eulerian tensor quantities, including the stretching, the
Kirchhoff stress, internal state variables, etc. Each of these
quantities transforms in a corotational manner under a change of the
observing frame. According to the principle of material
frame-indifference or objectivity, each constitutive function should be
invariant, whenever the observing frame is changed to another one by any
given time-dependent rotation. In this work the general form of
constitutive equations is discussed. Several frequently used objective
rates are analyzed with respect to their serviceability to develop a
self-consistent formulation, i.e. to be integrable to deliver an elastic
in particular hyperelastic relation for vanishing plastic deformation.
This would be of great importance, e.g., for so-called spring back
calculations in metal forming.
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