Sounds great, thank you all for extra confirmation, which helps me piece together the proper way to set up the constitutive model using *DEFORMATION PLASTICITY .
For the sake of others who may come to this discussion with the same question I had, and until the manual is updated to reflect these changes, here’s the short summary of Ramberg-Osgood material model calibration details:
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The Ramberg-Osgood curve parameter set (E, v, sigma_0, n, alpha) needs to be fit to uniaxial test data in the true stress and true strain form (note true=logarithmic=Hencky strain). The uniaxial R-O curve equation from the manual:

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Use
*DEFORMATION PLASTICITYcard to define the material parameters in the input deck. -
After the analysis is done, the CalculiX output stress-strain will come out as true stress and Lagrangian strain. To compare it to the original Ramberg-Osgood curve, one will need to convert the Lagrangian strain output to the true strain (or vice versa) using the definitions given here:
Deformation Plasticity. Eulerian strain - #12 by Calc_em
Here’s the analytical curve compared to CalculiX response for an example uniaxial tension model set-up with the parameters:
*DEFORMATION PLASTICITY
70000.0,0.3,360.,14.,7.
