The reason I start this thread is the following statement from Abaqus User Subroutines Manual regarding UMAT:
Which means that tensor variables for instance are updated according to the equationIn finite-strain problems any vector-valued or tensor-valued state variables must be rotated to account for rigid body motion of the material, in addition to any update in the values associated with constitutive behavior. The rotation increment matrix, DROT, is provided for this purpose.
and analogously for a vector variable.
The way I see it, the rule given above is valid only if an objective time derivative (it's incremental form to be specific) is used to calculate dA. For example: calculating stress increment using a hypoelastic relation. If the stresses are update in a different way there is no point to stick to the given formula.
In my case I developed a UMAT for finite-strain nonlinear viscoelasticity. I use QLV theory. Basicly I do everything as shown in Puso M. A. and Weiss J. A. "Finite Element Implementation of Anisotropic Quasi-linear Viscoelasticity Using a Discrete Spectrum Approximation", Journal of Biomechanical Engineering, 120, 1998.
This theory is very similar to those presented in Holzapfel's book. An algorithm of finite implementation is given also in "Computational Inelasticity" by Simo & Hughes (pages 372-373).
My UMAT uses a hyperelastic relation to update the Cauchy stress. A number of viscoelastic overstresses are updated at each increment using Taylor's recurrence-update formula (presented in Holzapfel's book for instance; page 292, Eq. (6.267)). The sufficient 4th order siffness tensor was pushed forward to the current configuration.
I have no convergence problems for both statics and dynamics with large number of elements. I had some problems once but the geometry was complicated and I think it was due to inadequate boundary conditions (negative eigenvalues). But that was only for this single case. In numerous other tests there was no convergence problems.
There is also a very good agreement between predictions of Abaqus and a Matlab code I wrote to verify the UMAT. Both for tension/compression and simple shear simulations. Slight differences between Abaqus and Matlab predictions appear for very large deformations only (the amount of shear angle over 60 degrees).
Is my reasoning correct?