  In this paper, we introduce an Abaqus UMAT subroutine for a family of
constitutive models for the viscoelastic response of isotropic elastomers of
any compressibility -- including fully incompressible elastomers -- undergoing
finite deformations. The models can be chosen to account for a wide range of
non-Gaussian elasticities, as well as for a wide range of nonlinear
viscosities. From a mathematical point of view, the structure of the models is
such that the viscous dissipation is characterized by an internal variable
$\textbf{C}^v$, subject to the physically-based constraint
$\det\textbf{C}^v=1$, that is solution of a nonlinear first-order ODE in time.
This ODE is solved by means of an explicit Runge-Kutta scheme of high order
capable of preserving the constraint $\det\textbf{C}^v=1$ identically. The
accuracy and convergence of the code is demonstrated numerically by comparison
with an exact solution for several of the Abaqus built-in hybrid finite
elements, including the simplicial elements C3D4H and C3D10H and the hexahedral
elements C3D8H and C3D20H. The last part of this paper is devoted to showcasing
the capabilities of the code by deploying it to compute the homogenized
response of a bicontinuous rubber blend.
