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Subsection 4.4.1: Uncoupled Viscoelastic Materials Up Section 4.4: Viscoelastic Solids Section 4.5: Reactive Viscoelastic Solid

### 4.4.2 Unconstrained Viscoelastic Materials

The material type for viscoelastic materials is “viscoelastic”. The following parameters need to be defined:
 parameter description default value units viscoelastic coefficient 1 [ ] - relaxation times 1 [t] - viscoelastic coefficients 0 [ ] elastic component (must be an unconstrained elastic solid)
For a viscoelastic material, the second Piola Kirchhoff stress can be written as follows [46]: where is the elastic stress and is the relaxation function. It is assumed that the relaxation function is given by the following discrete relaxation spectrum: Note that the user does not have to enter all the and coefficients. Instead, only the values that are used need to be entered. So, if is 2, only , , and 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>


Subsection 4.4.1: Uncoupled Viscoelastic Materials Up Section 4.4: Viscoelastic Solids Section 4.5: Reactive Viscoelastic Solid