UMAT in ABAQUS

Hi,

I've been learning how to implement material models using UMAT in ABAQUS and I have

some simple questions:

I've been trying to implement the viscoelastic models in the paper:

Formulation and implementation of three-dimensional viscoelasticity at small and finite strains

1) The variable "STRAN" in UMAT corresponds to the strain at time $t = t_n$ or $t = t_(n+1)$,

I mean, in Eq. (43) of this paper, the strain $\epsilon^(n+1)$ is described by

$STRAN$ or $STRAN + DSTRAN$ in UMAT?

 2) In order to implement a nonlinear model (finite viscoelasticity),

do I always have to calculate quantities in the reference configuration (e.g. the 2nd Piola-Kirchhof stress tensor)

and pull-back/push-foward these quantities to the material configuration (e.g. Cauchy stress, Jacobi matrix etc)?

many thanks

Augustus