damage fiber power

Module: solid

Category: material

Type string: "damage fiber power"

Parameters

Name	Description	Default	Range	Units
density	density	1	\(\ge 0\)	M/L^3
t0	t0	1e+09	\(\ge 0\)
Dmax	Dmax	1	\([0, 1]\)
beta_s	beta_s	0	\(\gt 0\)
gamma_max	gamma_max	0	\(\ge 0\)
D2_a	D2_a	0	\(\in \mathbb{R}\)
D2_b	D2_b	0	\(\in \mathbb{R}\)
D2_c	D2_c	0	\(\in \mathbb{R}\)
D2_d	D2_d	0	\(\in \mathbb{R}\)
D3_inf	D3_inf	0	\(\in \mathbb{R}\)
D3_g0	D3_g0	0	\(\in \mathbb{R}\)
D3_rg	D3_rg	1	\(\in \mathbb{R}\)
a1	a1	0	\(\ge 0\)
a2	a2	0	\(\gt 1\)
kappa	kappa	0	\([0, 0.666667]\)
fiber	fiber		N/A

Description

The material type for Damage Fiber Power is damage fiber power.

By setting,

\[ \Psi^{0}=\kappa\mathit{I_{1}}+\left(1-\frac{3}{2}\kappa\right)\mathit{K_{3}} \]

and \(\mathit{m(P)=\alpha_{1}(P)^{\alpha_{2}},}\) the strain-energy form above can be made suitable for modeling damage,

\[ \varPsi(C,D)=\alpha_{1}\left(\left(1-D\right)\left[\kappa I_{1}+\left(1-\frac{3}{2}\kappa\right)K_{3}\right]-c\right)^{\alpha_{2}} \]

The Cauchy stress takes on the following form,

\[ \sigma=\frac{2}{J}(1-D)\frac{dm}{dP}\left[\kappa b+\left(1-\frac{3}{2}\kappa\right)\left[bI_{4}+I_{1}I_{4}m-I_{4}a\bigodot ba\right]\right] \]

Example:

<solid type="damage fiber power">
  <a1>1400</a1>
  <a2>2.2</a2>
  <kappa>1e-08</kappa>
  <t0>0.98</t0>
  <Dmax>0.96</Dmax>
  <beta_s>0.06</beta_s>
  <gamma_max>17.98</gamma_max>
  <fiber type="angles">
    <theta>-39.87</theta>
    <phi>90</phi>
  </fiber>
</solid>