relaxation-Prony¶
Module: solid
Category: materialprop
Type string: "relaxation-Prony"
Parameters¶
| Name | Description | Default | Range | Units |
|---|---|---|---|---|
t1 |
relaxation time t1 | 1 | \(\ge 0\) | t |
t2 |
relaxation time t2 | 1 | \(\ge 0\) | t |
t3 |
relaxation time t3 | 1 | \(\ge 0\) | t |
t4 |
relaxation time t4 | 1 | \(\ge 0\) | t |
t5 |
relaxation time t5 | 1 | \(\ge 0\) | t |
t6 |
relaxation time t6 | 1 | \(\ge 0\) | t |
g1 |
coefficient g1 | 0 | \([0, 1]\) | |
g2 |
coefficient g2 | 0 | \([0, 1]\) | |
g3 |
coefficient g3 | 0 | \([0, 1]\) | |
g4 |
coefficient g4 | 0 | \([0, 1]\) | |
g5 |
coefficient g5 | 0 | \([0, 1]\) | |
g6 |
coefficient g6 | 0 | \([0, 1]\) |
Description¶
The material type for this relaxation function is relaxation-Prony.
The reduced relaxation function for this material type is given by
\[
g\left(t\right)=\frac{\sum_{i=1}^{6}\gamma_{i}e^{-t/\tau_{i}}}{\sum_{i=1}^{6}\gamma_{i}}
\]
The coefficients \(\gamma_{i}\) are normalized by \(\sum_{i}\gamma_{i}\) to enforce \(g\left(0\right)=1\).