A quick doubt. From reading the Abaqus Documentation, I get the understanding that the deformation gradient (dfgrd1) is passed to the UMAT in the basis e_i x E_j. e_i is the basis in the current configuration at time t+dt and E_j is basis in the configuration at time, t.
I inferred this from the fact that del F is defined as d(x(t+dt))/d(x(t)), which gives the basis as mentioned above (e_i x E_j). Then using the formula dfgrd1 = del F . dfgrd0, taking dfgrd0 to be in the basis E_i x E_j, dfgrd1 has to in the basis e_i x E_j.
Am I wrong?