COMSOL 6.4 - Contact Impedance Comparison

The contact impedance boundary condition is meant to approximate a thin layer of material that impedes the flow of current normal to the boundary, but does not introduce any additional conduction path tangential to the boundary. This example compares the contact impedance boundary condition to a full-fidelity model and discusses the range of applicability of this boundary condition.

Figure 1: A square two-dimensional domain of conductive material, with a circular inclusion. The wall of the inclusion is made of a material with lower conductivity.

Model Definition

The situation being modeled is shown in Figure 1. A square two-dimensional domain of conductive material has a DC voltage difference applied to it. Within the square domain, there is a circular inclusion. The walls of this inclusion are modeled two ways: using a full fidelity model that includes the thickness of the walls, and using the contact impedance boundary condition. The interior of the inclusion has the same properties as the bulk.

The location of the contact impedance condition is at the centerline, midway between the inner and outer radii of the full fidelity model. Note that, when using the contact impedance boundary condition, the total volume of the surrounding material is slightly larger, since the thickness of the wall is not being explicitly modeled. The conductivity of the wall of the inclusion is varied between a value several orders of magnitude smaller to a value equal to the conductivity of the bulk.

Results and Discussion

The voltage distribution and the current density norm is plotted in Figure 2 for the case where the electric conductivity is a thousand times smaller in the wall of the inclusion. This case represents a thin walled object that resists current flow through the surface, that is, it presents a high impedance to the voltage source. The field lines can be observed to deform around the object. The solutions agree well for the cases where the conductivity of the contact impedance boundary condition is less than the surrounding medium.

Figure 2: A surface plot of the current density norm, together with isolines of the electric potential and streamlines indicating the current direction, for the case of a thin layer of material that has a high impedance. The full fidelity and contact impedance solutions are almost identical.

The case of equal conductivities is plotted in Figure 3, and shows the limit of the contact impedance boundary condition. As the conductivities becomes equal, there can be no current flow tangential to the boundary.

Figure 3: A surface plot of the current density norm, together with isolines of the electric potential and streamlines indicating the current direction. The contact impedance boundary condition (right) prevents any tangential current flow and the solutions do not agree for this case.

The Contact Impedance boundary condition can be used in cases where the thickness of the boundary being approximated is much smaller than the characteristic size of the model domain, and when the conductivity of the layer is smaller than the surrounding medium. When this boundary condition can be used, the resulting number of mesh element is much smaller, saving solution time and memory.

ACDC_Module/Introductory_Electric_Currents/contact_impedance_comparison

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select > > .

Click .

Click

In the tree, select > .

Click

Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
sigma_1	1[S/m]	1 S/m	Conductivity, material 1
sigma_2	1[S/m]	1 S/m	Conductivity, material 2

Geometry 1

Square 1 (sq1)

In the toolbar, click

In the window for , locate the section.

In the text field, type 0.05.

Square 2 (sq2)

In the toolbar, click

In the window for , locate the section.

In the text field, type -1.05.

Click

Click the

button in the toolbar.

Circle 1 (c1)

In the toolbar, click

In the window for , locate the section.

In the text field, type 0.245.

Locate the section. In the text field, type 0.55.

In the text field, type 0.5.

Circle 2 (c2)

In the toolbar, click

In the window for , locate the section.

In the text field, type 0.25.

Locate the section. In the text field, type -0.55.

In the text field, type 0.5.

Click to expand the section. In the table, enter the following settings:


Layer name	Thickness (m)
Layer 1	0.01

Form Union (fin)

In the toolbar, click

Click the

button in the toolbar.

In the window, click .

The geometry on the left side describes the full fidelity model. The geometry on the right side replaces the thin layer with a boundary in order to use the feature.

Create a set of selections for use before setting up the physics. First, create a selection for the wall of the inclusion.

Definitions

Full Fidelity

In the toolbar, click

Select Domains 2–5 only.

In the window for , type Full Fidelity in the text field.

Add a selection for the contact impedance boundaries.

Contact Impedance

In the toolbar, click

In the window for , locate the section.

From the list, choose .

Select Boundaries 21–24 only.

In the text field, type Contact Impedance.

Add a selection for the bulk area. These are the domains complementary to the wall of the inclusion.

Bulk

In the toolbar, click

In the window for , locate the section.

Under , click

In the dialog, select in the list.

Click .

In the window for , type Bulk in the text field.

Electric Currents (ec)

Ground 1

In the toolbar, click

and choose .

Select Boundary 10 only.

Ground 2

In the toolbar, click

and choose .

Select Boundary 2 only.

Boundary Terminal 1

In the toolbar, click

and choose .

Select Boundary 11 only.

In the window for , locate the section.

From the list, choose .

Boundary Terminal 2

In the toolbar, click

and choose .

Select Boundary 3 only.

In the window for , locate the section.

From the list, choose .

Contact Impedance 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the ds text field, type 1[cm].

Materials

Material 1 (mat1)

In the window, under right-click and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Electric conductivity	sigma_iso ; sigmaii = sigma_iso, sigmaij = 0	sigma_1	S/m	Basic
Relative permittivity	epsilonr_iso ; epsilonrii = epsilonr_iso, epsilonrij = 0	1	1	Basic

Material 2 (mat2)

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Electric conductivity	sigma_iso ; sigmaii = sigma_iso, sigmaij = 0	sigma_2	S/m	Basic
Relative permittivity	epsilonr_iso ; epsilonrii = epsilonr_iso, epsilonrij = 0	1	1	Basic

Material 3 (mat3)

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Electric conductivity	sigma_iso ; sigmaii = sigma_iso, sigmaij = 0	sigma_2	S/m	Basic
Relative permittivity	epsilonr_iso ; epsilonrii = epsilonr_iso, epsilonrij = 0	1	1	Basic

Mesh 1

In the window, under right-click and choose .

Study 1

Parametric Sweep

In the toolbar, click

In the window for , locate the section.

Click

In the table, enter the following settings:


Parameter name	Parameter value list	Parameter unit
sigma_2 (Conductivity, material 2)	1 0.01 0.0001	S/m

In the toolbar, click

Begin the result analysis by excluding the interior of the wall of the inclusion which is not of interest.

Results

Study 1/Solution 1 (sol1)

In the window, expand the > node, then click .

Selection

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Create a custom plot to show the direction and norm of the current density.

Current Density (ec)

In the toolbar, click

In the window for , type Current Density (ec) in the text field.

Surface 1

Right-click and choose .

In the window for , click in the upper-right corner of the section. From the menu, choose > > > .

Locate the section. From the list, choose .

Next, add a contour plot showing the electric potential.

Contour 1

In the window, right-click and choose .

In the window for , click to expand the section.

From the list, choose .

Click to expand the section. From the list, choose .

Clear the checkbox.

Color Expression 1

Right-click and choose .

In the window for , click in the upper-right corner of the section. From the menu, choose .

Locate the section. From the list, choose .

Clear the checkbox.

Then, add a streamline plot showing the current density.

Streamline 1

In the window, right-click and choose .

Select Boundaries 3 and 11 only.

Click the

button in the toolbar.

In the window for , click to expand the section.

From the list, choose .

Click to expand the section. From the list, choose .

Clear the checkbox.

Color Expression 1

In the window, under > > right-click and choose .

Color Expression 1

In the window, right-click and choose .

In the toolbar, click

Click the

button in the toolbar.

Compare the plot with Figure 2.

Current Density (ec)

In the window, under click .

In the window for , locate the section.

From the list, choose .

In the toolbar, click

This plot should look like Figure 3. Note that due to the selection defined in , the streamlines in the full fidelity model are not completely visualized.