relaxation-Prony¶

Module: solid

Category: materialprop

Type string: "relaxation-Prony"

Parameters¶

Name	Description	Default	Units
`t1`	relaxation time t1	1	[t]
`t2`	relaxation time t2	1	[t]
`t3`	relaxation time t3	1	[t]
`t4`	relaxation time t4	1	[t]
`t5`	relaxation time t5	1	[t]
`t6`	relaxation time t6	1	[t]
`g1`	coefficient g1	0	[]
`g2`	coefficient g2	0	[]
`g3`	coefficient g3	0	[]
`g4`	coefficient g4	0	[]
`g5`	coefficient g5	0	[]
`g6`	coefficient g6	0	[]

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 \(g\left(0\right)=1\).