relaxation-Fung¶
Module: solid
Category: materialprop
Type string: "relaxation-Fung"
Parameters¶
| Name | Description | Default | Units |
|---|---|---|---|
tau1 |
min. relaxation time | 0 | [t] |
tau2 |
max. relaxation time | 0 | [t] |
Description¶
This relaxation function, which is derived from a continuous relaxation spectrum, was introduced by Fung 1. The material type for this relaxation function is relaxation-Fung.
These parameters must satisfy \(\tau_{2}>\tau_{1}\). The reduced relaxation function for this material type is given by
\[
g\left(t\right)=\frac{\tau_{2}e^{-t/\tau_{2}}-\tau_{1}e^{-t/\tau_{1}}+t\left[\text{Ei}\left(-\frac{t}{\tau_{2}}\right)-\text{Ei}\left(-\frac{t}{\tau_{1}}\right)\right]}{\tau_{2}-\tau_{1}}
\]
where \(\text{Ei}\left(\cdot\right)\) is the exponential integral function.
-
Fung, Y. C, Biomechanics: mechanical properties of living tissues (New York: Springer-Verlag, 1981). ↩