reactive viscoelastic¶

Module: solid

Category: material

Type string: "reactive viscoelastic"

Parameters¶

Name	Description	Default	Units
`density`	density	1	[M/L^3]
`wmin`	wmin	0	[]
`kinetics`	kinetics	1	[]
`trigger`	trigger	0	[]
`emin`	emin	0	[]
`elastic`			[]
`bond`			[]
`relaxation`			[]
`recruitment`			[]

Description¶

The material type for a compressive reactive viscoelastic solid is reactive viscoelastic.

The kinetics parameter should be set to 1 for Type I bond kinetics or 2 for Type II bond kinetics.

The trigger parameter should be set 0 when weak bonds break and reform in response to any form of the strain; it should be set to 1 when the trigger is distortional strain; and it should be set to 2 when the trigger is dilatational strain,

\[\text{trigger}=\begin{cases} 0\text{ for any strain} & \left\Vert \Delta\mathbf{E}\right\Vert \\ 1\text{ for distortional strain} & \left\Vert \text{dev}\Delta\boldsymbol{\eta}\right\Vert \\ 2\text{ for dilatational strain} & \left|\ln\left(\det\Delta\mathbf{F}\right)\right| \end{cases} \]

where \(\Delta\mathbf{E}=\frac{1}{2}\left(\Delta\mathbf{F}^{T}\cdot\Delta\mathbf{F}-\mathbf{I}\right)\) is the incremental Lagrange strain, \(\Delta\boldsymbol{\eta}=\ln\Delta\mathbf{V}\) is the incremental natural strain, \(where \Delta\mathbf{V}\) is the left stretch tensor of \(\Delta\mathbf{F}\), and \(\Delta\mathbf{F}=\mathbf{F}\left(t_{n+1}\right)\cdot\mathbf{F}^{-1}\left(t^{m}\right)\), where \(t_{n+1}\) is the current time and \(t^{m}\) is the birth time of the most recent weak bond generation.

The elastic and bond materials may be selected from the list of unconstrained elastic materials.

The recruitment material can be used to model nonlinear viscoelasticity where the weak bond response becomes more significant with increasing strain.

The parameters wmin and emin can be adjusted to improve computational efficiency by reducing the number of generations u in an analysis. In practice, the value of emin should be no greater than one-hundredth of the equilibrium strain in a loading configuration. The parameter wmin must be in the range \(0\le w_{\min}\le1.\) In practice, a good balance between accuracy and efficiency is achieved by using \(w_{\min}\le0.05\).

Example:

<material id="1" name="RV solid" type="reactive viscoelastic">
  <kinetics>1</kinetics>
  <trigger>0</trigger>
  <wmin>0.05</wmin>
  <emin>0.001</emin>
  <elastic type="Holmes-Mow">
    <density>1</density>
    <E>1</E>
    <v>0.3</v>
    <beta>0.5</beta>
  </elastic>
  <bond type="Holmes-Mow">
    <density>1</density>
    <E>1</E>
    <v>0.3</v>
    <beta>0.5</beta>
  </bond>
  <relaxation type="relaxation-exponential">
    <tau>4</tau>
  </relaxation>
  <recruitment type="recruitment power">
    <mu0>1</mu0>
    <mu1>30</mu1>
    <alpha>2</alpha>
    <scale>1</scale>
</material>