$\newcommand{\Dev}{\operatorname{Dev}}$ $\newcommand{\dev}{\operatorname{dev}}$ $\newcommand{\grad}{\operatorname{grad}}$ $\newcommand{\divg}{\operatorname{div}}$ $\newcommand{\Ei}{\operatorname{Ei}}$ $\newcommand{\tr}{\operatorname{tr}}$

The sliding-biphasic implementation for sliding interfaces can deal with biphasic contact surfaces (including biphasic-on-biphasic, biphasic-on-elastic, biphasic-on-rigid) [10]. 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. To use this feature, the user must define an additional contact parameter, namely:

<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.