fiber-Kiousis-uncoupled¶

Module: solid

Category: material

Type string: "fiber-Kiousis-uncoupled"

Parameters¶

Name	Description	Default	Units
`density`	density	1	[M/L^3]
`k`	bulk modulus	0	[P]
`pressure_model`	pressure_model	0	[]
`d1`	d1	0	[]
`d2`	d2	1	[]
`n`	n	2	[]
`fiber`			[]

Description¶

This material type is fiber-Kiousis-uncoupled. It is based on the material model proposed by Kiousis et al. ¹ ² for modeling the balloon in a balloon-stent system.

The fiber strain energy density is given by

\[ \tilde{\Psi}_{n}\left(I_{n}\right)=\begin{cases} \frac{d_{1}}{n}\left(\tilde{I}_{n}-d_{2}\right)^{n} & \tilde{I}_{n}\ge d_{2}\\ 0 & \tilde{I}_{n}<d_{2} \end{cases}\,, \]

where \(\tilde{I}_{n}=\tilde{\lambda}_{n}^{2}=\mathbf{n}_{r}\cdot\mathbf{\tilde{C}}\cdot\mathbf{n}_{r}\) is the square of the fiber stretch and \(\mathbf{n}_{r}\) is the unit vector along the fiber direction in its reference configuration.

Example:

(Fiber model as specified in a continuous fiber distribution)

<fibers type="fiber-Kiousis-uncoupled">
  <d1>500</d1>
  <d2>2.25</d2>
  <n>3</n>
</fibers>

Kiousis, DE, Gasser, TC, and Holzapfel, GA, "Smooth contact strategies with emphasis on the modeling of balloon angioplasty with stenting", International journal for numerical methods in engineering 75, 7 (2008), pp. 826--855. ↩
Kiousis, Dimitrios E, Wulff, Alexander R, and Holzapfel, Gerhard A, "Experimental studies and numerical analysis of the inflation and interaction of vascular balloon catheter-stent systems", Annals of Biomedical Engineering 37, 2 (2009), pp. 315--330. ↩