sliding-biphasic

Module: biphasic

Category: surfaceinteraction

Type string: "sliding-biphasic"

Parameters

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

Description

The sliding-biphasic implementation for sliding interfaces can deal with biphasic contact surfaces (including biphasic-on-biphasic, biphasic-on-elastic, biphasic-on-rigid) ^{1 2}. It allows for the possibility to track fluid flow across the contact interface. In other words, fluid can flow from one side of the contact interface to the other when both contact surfaces are biphasic.

Most of the parameters are identical to the sliding-elastic contact interface.

In order to model fluid flow across the interface, the user must define an additional parameter pressure_penalty:

<pressure_penalty>1.0</pressure_penalty>

In the same way that the penalty parameter controls the contact tractions, this parameter controls the penalty value that is used to calculate the Lagrange multipliers for the pressure constraint.

If the laugon flag is set, the augmented Lagrangian method is used to enforce the pressure constraint. And if the auto_penalty flag is defined (which is the recommended approach), an initial guess for the pressure penalty is calculated automatically using the following formula:

\[ \varepsilon_{p}=\frac{kA}{V}, \]

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

When either contact surface is biphasic, the surface outside the contact area(s) is automatically set to free-draining conditions (equivalent to setting the fluid pressure to zero).

As detailed in ² and the FEBio Theory Manual, the sliding-biphasic contact algorithm can include frictional contact. The effective friction coefficient \(\mu_{\text{eff}}\) in this frictional contact algorithm depends on the temporally evolving local fluid load support (the ratio of fluid pressure \(p\) to the normal component of the mixture contact traction \(t_{n}\)), according to

\[ \mu_{\text{eff}}=\mu_{\text{eq}}\left(1+\left(1-\varphi\right)\frac{p}{t_{n}}\right)\,. \]

Recall that \(t_{n}\) is negative whereas p is positive in compression. Here, \(\mu_{\text{eq}}\) (fric_coeff) is the friction coefficient in the limit when the fluid load support has reduced to zero, and \(\varphi\) (contact_frac) is the fraction of the apparent contact area over which the solid matrix of the primary surface contacts that of the secondary surface. Thus, \(1-\varphi\) is the fraction of the apparent contact area where fluid contacts fluid or solid. For perfectly smooth contact surfaces one may assume that \(\varphi=\varphi_{1}^{s}\varphi_{2}^{s}\), where \(\varphi_{1}^{s}\) and \(\varphi_{2}^{s}\) are the solid area (or volume) fractions of the primary and secondary contact surfaces, respectively. For example, when both contact surfaces are non-porous (\(\varphi_{1}^{s}=\varphi_{2}^{s}=1\)), the effective friction coefficient reduces to \(\mu_{\text{eff}}=\mu_{\text{eq}}\).

When performing biphasic-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, GA, Maas, SA, and Weiss, J.A., "Finite element algorithm for frictionless contact of porous permeable media under finite deformation and sliding", J. Biomech. Engn. 132, 6 (2010), pp. 1006-1019. ↩

2. Zimmerman, Brandon K, Maas, Steve A, Weiss, Jeffrey A, and Ateshian, Gerard A, "A Finite Element Algorithm for Large Deformation Biphasic Frictional Contact Between Porous-Permeable Hydrated Soft Tissues", J Biomech Eng 144, 2 (2022). ↩↩