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 ${\mathbf{C}}^v$, subject to the physically-based constraint $det{\mathbf{C}}^v=1$, 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 $det{\mathbf{C}}^v=1$ 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.

在本文中，我们介绍了 Abaqus UMAT 子例程，用于一系列本构模型，用于任何可压缩性的各向同性弹性体（包括完全不可压缩的弹性体）在经历有限变形时的粘弹性响应。可以选择模型来解释各种非高斯弹性以及各种非线性粘度。从数学的角度来看，模型的结构是粘性耗散由内部变量来表征${\mathbf{C}}^v$，受到基于物理的约束$德特{\mathbf{C}}^v=1$，即非线性一阶 ODE 的时间解。该 ODE 通过能够保留约束的显式高阶龙格-库塔方案来求解$德特{\mathbf{C}}^v=1$相同。通过与几个 Abaqus 内置混合有限元（包括单纯单元 C3D4H 和 C3D10H 以及六面体单元 C3D8H 和 C3D20H）的精确解进行比较，以数值方式证明了代码的准确性和收敛性。本文的最后一部分致力于通过部署代码来计算双连续橡胶共混物的均质响应来展示代码的功能。