The material type for these materials is “uncoupled viscoelastic”. The following parameters need to be defined:

$$\mathbf{S}\left(t\right)=\int\limits _{-\infty}^{t}G\left(t-s\right)\frac{d\mathbf{S}^{e}}{ds}\,ds$$ For a uncoupled viscoelastic material, the second Piola Kirchhoff stress can be written as follows [46]: $$\mathbf{S}\left(t\right)=pJ\,\mathbf{C}^{-1}+J^{-2/3}\int\limits _{-\infty}^{t}G\left(t-s\right)\frac{d\left(\Dev\left[\mathbf{\tilde{S}}^{e}\right]\right)}{ds}\,ds\,,$$ where $\mathbf{\tilde{S}}^{e}$ is the elastic stress derived from $\tilde{W}\left(\mathbf{\tilde{C}}\right)$ (see Section 4.1.2↑) and $G$ is the relaxation function. It is assumed that the relaxation function is given by the following discrete relaxation spectrum: $$G\left(t\right)=\gamma_{0}+\sum\limits _{i=1}^{N}\gamma_{i}\exp\left(-t/\tau_{i}\right),$$ Note that the user does not have to enter all the $\tau_{i}$ and $\gamma_{i}$ coefficients. Instead, only the values that are used need to be entered. So, if $N$ is 2, only $\tau_{1}$ , $\tau_{2}$ , $\gamma_{1}$ and $\gamma_{2}$ have to be entered.

The elastic parameter describes the elastic material as given in Section 4.1.2↑.

Example:

<material id="1" name="Material 1" type="uncoupled viscoelastic">
  <g1>0.95</g1>
  <t1>0.01</t1>
  <k>100</k>
  <elastic type="Mooney-Rivlin">
    <c1>1</c1>
    <c2>0.0</c2>
  </elastic>
</material>