relaxation-exp-distortion¶
Module: solid
Category: materialprop
Type string: "relaxation-exp-distortion"
Parameters¶
| Name | Description | Default | Units |
|---|---|---|---|
tau0 |
constant coefficient | 0 | [t] |
tau1 |
power coefficient | 0 | [t] |
alpha |
power exponent | 1 | [] |
Description¶
The material type for this relaxation function is relaxation-exp-distortion.
The reduced relaxation function for this material type is given by
\[
g\left(\mathbf{F}\left(v\right);t-v\right)=e^{-\left(t-v\right)/\tau\left[K_{2}\left(v\right)\right]}
\]
where
\[
\tau\left(K_{2}\left(v\right)\right)=\tau_{0}+\tau_{1}\cdot\left(K_{2}\left(v\right)\right)^{\alpha}
\]
In general, \(K_{2}=\left|\dev\boldsymbol{\eta}\right|\) where \(\boldsymbol{\eta}=\ln\mathbf{V}\) is the spatial natural (left Hencky) strain tensor and \(\mathbf{V}\) is the left stretch tensor. \(K_{2}\) is evaluated at the time \(v\) when weak bonds from the \(u\)-generation start breaking.