EFD Donnan equilibrium¶

Module: solid

Category: material

Type string: "EFD Donnan equilibrium"

Parameters¶

Name	Description	Default	Units
`density`	density	1	[M/L^3]
`phiw0`	phiw0	-1	[]
`cF0`	cF0	0	[c]
`bosm`	bosm	-6.27744e+66	[c]
`Phi`	Phi	1	[]
`beta`	beta		[]
`ksi`	ksi		[P]
`mat_axis`			[]

Description¶

The material type for a swelling pressure combined with an ellipsoidal continuous fiber distribution is EFD Donnan equilibrium. The swelling pressure is described by the equations for ideal Donnan equilibrium, assuming that the material is porous, with a charged solid matrix, and the external bathing environment consists of a salt solution of monovalent counter-ions.

The Cauchy stress for this material is given by,

\[ \boldsymbol{\sigma}=\boldsymbol{\sigma}_{DE}+\boldsymbol{\sigma}_{f}\,. \]

\(\boldsymbol{\sigma}_{f}\) is the stress contribution from the fibers. \(\boldsymbol{\sigma}_{DE}\) is the stress from the Donnan equilibrium response, as described in Donnan-Equilibrium-Swelling.

Example (using units of mm, N, s, nmol, K):

<Globals>
  <Constants>
    <R>8.314e-6</R>
    <T>310</T>
  </Constants>
</Globals>

<material id="1" type="EFD Donnan equilibrium">
  <phiw0>0.8</phiw0>
  <cF0 lc="1">1</cF0>
  <bosm>300</bosm>
  <beta>3,3,3</beta>
  <ksi>0.01,0.01,0.01</ksi>
  <mat_axis type="local">0,0,0</mat_axis>
</material>

<LoadData>
  <loadcurve id="1">
    <loadpoint>0,0</loadpoint>
    <loadpoint>1,150</loadpoint>
  </loadcurve>
</LoadData>