Perturbation technique based on forward difference approximation

Hi,

 I am trying to implement (in Abaqus) the elasticity tensor using a numerical approach.  I have come across a paper by C.Miehe (Numerical computation of algorithmic (consistent) tangent moduli in large-strain computational inelasticity, 1996).

There are a few things I don't quite understand.  

In some equations he uses Tensors in indices form and Tensors without indices (same equation). For example:  F^e_(CD)=F+deltaF^e_(CD) which is the perturbated deformation gradient (CD are indices and e is just a letter showing it is different from F).  Would that mean that to every element of F deltaF is added?  If so, why not using indices for F as well?  The actual calculation of the elasticity tensor is also not quite clear:

   C^(ABCD)= (1/eps)*(Spert^(AB)(F^e_(CD))-S^(AB))  (Eq. 2.10) 

   where eps is the perturbation constant, S is the 2PK, and Spert^AB is perturbated 2PK as a function of  F^e_(CD) 

    _{ABCD are indices}

So say I wanted to calculate C⁽¹²³⁴⁾ than I would have  have to calculate Sspert¹² as a function of F^{e₍₃₄₎} subtract S¹² which is known.  Would that make sense?  But how do I calculate a component of Sspert¹² as a function of component of F^e ? One idea I had is to calculate the perturbated deformation tensor  F^e by adding the deltaF to each component of the original F (from Abaqus) and basically use this new deformation tensor F^e as input into my constitutive equation and calculate a "perturbated stress" for each increment.  But then how to I get C from that using 2.10?  

I'm quite confused here.

Has anyone ever used this approach?

Any thoughts are highly appreciated!

Thanks,

Andreas