in-situ stretch

Module: solid

Category: materialprop

Type string: "in-situ stretch"

Parameters

Name	Description	Default	Units
stretch	stretch	1	[]
isochoric	isochoric	true	[]

Description

The in-situ stretch generator option calculates a prestrain gradient based on a fiber stretch and the fiber vector defined by the elastic material of the prestrain elastic material. This implies that this elastic material must define a fiber property.

This option generates one of the following prestrain gradients, depending on the isochoric option.

\[ \hat{\mathbf{F}}_{p,iso}=\mathbf{Q}\left[\begin{array}{ccc} \lambda\\ & \lambda^{-1/2}\\ & & \lambda^{-1/2} \end{array}\right]\mathbf{Q^{\mathrm{\mathit{T}}}},\qquad\hat{\mathbf{F}}_{p,uni}=\mathbf{Q}\left[\begin{array}{ccc} \lambda\\ & 1\\ & & 1 \end{array}\right]\mathbf{Q^{\mathit{T}}} \]

If the isochoric option is set to 1, then \(\hat{\mathbf{F}}_{p,iso}\) is used. Otherwise, \(\hat{\mathbf{F}}_{p,uni}\) is used.

The rotation tensor is defined implicitly via the fiber vector \(\boldsymbol{a}\) and the prestrain gradient tensor is effectively determined via,

\[ \hat{\mathbf{F}}_{p,iso}=\lambda\mathbf{A}+\mu\left(\boldsymbol{1-}\mathbf{A}\right) \]

where \(\mathbf{A}=\boldsymbol{a}\otimes\boldsymbol{a}\), \(\lambda\) the prescribed fiber stretch, and \(\mu=\lambda^{-1/2}\) or \(\mu=1\) depending on the isochoric option.

Example:

<material id="1" type="prestrain elastic">
   <elastic type="coupled trans-iso Mooney-Rivlin">
        <k>0.1</k>
        <density>1e-09</density>
        <c1>0.01</c1>
        <c2>0</c2>
        <c3>0.0139</c3>
        <c4>116.22</c4>
        <c5>535.09</c5>
        <lam_max>1.046</lam_max>
        <fiber type="vector">-0.0804,-0.508,-0.858</fiber>
  </elastic>
  <prestrain type="in-situ stretch">
    <stretch lc="1">1.05</stretch>
    <isochoric>1</isochoric>
  </prestrain>
</material>