Hi

From a strict numerical point of view, as you probably know, NLGEOM means Abaqus will try a non-linear projection of the solution to better converge the analysis in some cases, which means reach a "lower" error convergence faster. Therefore the stresses calculated within your element, whatever the defined constitutive law you are using depend on both the convergence fit and the element type you use (as it is an interpolated data). Hence stress state may vary within your element as a function of these AND the constitutive law. Then you to decide which is good enough for you. FE modeling is always an approximation of a solution.

Regards

NLGEOM means that your reference volume of your elements are updated. In simple terms. If you have a truss with an uniaxial load and you want to determine the Young's modulus; NLGEOM means that the cross section of your truss is updated.

As result you will get a nonlinear stress-strain characteristic, because your stress is

sigma = F/A

To get the Young's modulus

sigma = E * epsilon

F/A = E *epsilon

E=F/(A*epsilon)

If A is constant as it is in a linear analysis, E is realy your material property. If you chose NLGEO you will get for your nonlinear truss RVE an Young's modulus which is a function of the deformation. It is not a pure material property, but includes the change of the cross section as well. If you use the resulting parameters in a global model with large displacements, I think you will make an error.