  A popular version of the finite strain Maxwell fluid is considered, which is
based on the multiplicative decomposition of the deformation gradient tensor.
The model combines Newtonian viscosity with hyperelasticity of Mooney-Rivlin
type; it is a special case of the viscoplasticty model proposed by Simo and
Miehe (1992). A simple, efficient and robust implicit time stepping procedure
is suggested. Lagrangian and Eulerian versions of the algorithm are available,
with equivalent properties. The numerical scheme is iteration free,
unconditionally stable and first order accurate. It exactly preserves the
inelastic incompressibility, symmetry, positive definiteness of the internal
variables, and w-invariance. The accuracy of the stress computations is tested
using a series of numerical simulations involving a non-proportional loading
and large strain increments. In terms of accuracy, the proposed algorithm is
equivalent to the modified Euler backward method with exact inelastic
incompressibility; the proposed method is also equivalent to the classical
integration method based on exponential mapping. Since the new method is
iteration free, it is more robust and computationally efficient. The algorithm
is implemented into MSC.MARC and a series of initial boundary value problems is
solved in order to demonstrate the usability of the numerical procedures.
