fiber-natural-NH

Module: solid

Category: material

Type string: "fiber-natural-NH"

Parameters

Name	Description	Default	Units
density	density	1	[M/L^3]
ksi	ksi	0	[]
lam0	lam0	1	[]
fiber			[]

Description

This material type is fiber-natural-NH.

The fiber strain energy density is given by

\[ \Psi_{n}\left(\lambda_{n}\right)=\frac{\xi}{2}H\left(\ln\frac{\lambda_{n}}{\lambda_{0}}\right)\left(\ln\frac{\lambda_{n}}{\lambda_{0}}\right)^{2}\,, \]

where \(\xi>0\) and \(\lambda_{0}\ge1\). The tensile response engages at the tensile stretch ratio \(\lambda_{0}\) (\(\lambda_{0}=1\) by default). The natural (logarithmic or Hencky) strain along the fiber is \(\ln\lambda_{n}\), whereas \(\ln\frac{\lambda_{n}}{\lambda_{0}}=\ln\lambda_{n}-\ln\lambda_{0}\) is the natural strain relative to the tensile stretch threshold. This model produces a stress response which varies linearly with the natural strain.

Example:

<material id="1" name="Material1" type="solid mixture">
  <density>1</density>
  <solid type="neo-Hookean">
    <E>0.13</E>
    <v>0.3</v>
  </solid>
  <solid type="fiber-natural-NH">
    <ksi>1</ksi>
    <lam0>1.25</lam0>
    <fiber type="vector">0,0,1</fiber>
  </solid>
</material>