sliding-multiphasic

Module: multiphasic

Category: surfaceinteraction

Type string: "sliding-multiphasic"

Parameters

Name	Description	Default	Units
laugon	Enforcement method	0	[]
tolerance	tolerance	0.1	[]
gaptol	gaptol	0	[L]
ptol	ptol	0	[]
ctol	ctol	0	[]
penalty	penalty	1	[]
auto_penalty	auto_penalty	false	[]
update_penalty	update_penalty	false	[]
two_pass	two_pass	false	[]
knmult	knmult	1	[]
search_tol	search_tol	0.01	[]
pressure_penalty	pressure_penalty	1	[]
concentration_penalty	concentration_penalty	1	[]
symmetric_stiffness	symmetric_stiffness	true	[]
search_radius	search_radius	1	[L]
seg_up	seg_up	0	[]
node_reloc	node_reloc	false	[]
fric_coeff	fric_coeff	0	[]
contact_frac	contact_frac	0	[]
smooth_aug	smooth_aug	false	[]
smooth_fls	smooth_fls	true	[]
minaug	minaug	0	[]
maxaug	maxaug	10	[]
ambient_pressure	ambient_pressure	0	[]
ambient_concentration			[]

Description

The sliding-multiphasic formulation is similar to the sliding-biphasic-solute. This contact implementation supports multiphasic contact (see below) ¹. When using multiphasic materials, the non-symmetric version must be used.

The sliding-multiphasic contact interface can deal with multiphasic contact surfaces. These contact interfaces allow for the possibility to track fluid and solute flow across the contact interface. In other words, fluid and solute can flow from one side of the contact interface to the other. To use this feature, the user must define additional contact parameters, namely:

<pressure_penalty>1.0</pressure_penalty>
<concentration_penalty>1.0</concentration_penalty>
<ambient_pressure>0</ambient_pressure>
<ambient_concentration sol="id">0</ambient_concentration>

In the same way that the penalty parameter controls the contact tractions, these penalty parameters control the penalty values that are used to calculate the Lagrange multipliers for the pressure and concentration constraints. If the laugon flag is set, the augmented Lagrangian method is used to enforce the pressure and concentration constraints. And if the auto_penalty flag is defined, an initial guess for the pressure and concentration penalty is calculated automatically using the following formulas:

\[ varepsilon_{p}=\frac{k\cdot A}{V}\,,\quad\varepsilon_{c}=\frac{d\cdot A}{V}\,, \]

where \(A\) is the element's area, \(V\) is the element's volume, \(k\) is a measure of the fluid permeability which is defined as one third of the trace of the material's initial permeability tensor, and \(d\) is a measure of the solute diffusivity which is defined as one third of the trace of the material's initial diffusivity tensor.

When either contact surface is multiphasic, the surface outside the contact area(s) is automatically set to ambient conditions (equivalent to setting the effective fluid pressure and effective solute concentration to the and values, respectively). Ambient conditions may also be associated with a load curve, for example:

<ambient_pressure lc="2">1.0</ambient_pressure>
<ambient_concentration lc="3">1.0</ambient_concentration>

When performing multiphasic-on-rigid contact, a two-pass analysis should not be used; the rigid surface should be the secondary surface.

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1. Ateshian, Gerard A, Maas, Steve, and Weiss, Jeffrey A, "Solute transport across a contact interface in deformable porous media", J Biomech 45, 6 (2012), pp. 1023-7. ↩