For a viscoelastic material, the second Piola Kirchhoff stress can be written as follows [46]: $$\mathbf{S}\left(t\right)=\int\limits _{-\infty}^{t}G\left(t-s\right)\frac{d\mathbf{S}^{e}}{ds}\,ds\,,$$ where $\mathbf{S}^{e}$ is the elastic stress 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 4.1.3↑.

Example:

<material id="1" name="Material 1" type="viscoelastic">
  <g1>0.95</g1>
  <t1>0.01</t1>
  <elastic type="neo-Hookean">
    <E>1</E>
    <v>0.0</v>
  </elastic>
</material>