Electrical Contact Properties

Abaqus/Standard can model the following types of electrical interactions (for degree of freedom conventions, see Degrees of Freedom):

• Electrical contact conductance based on the difference in the electrical potential of solids (DOF 9) across an interface.

• Electrical contact conductance based on the difference in the electrical potential of electrolyes (DOF 32) across an interface.

• Diffusion of electrical ions into and across a contact interface with consideration of ion concentrations in electrolytes (DOF 33).

• Diffusion of a species into and across a contact interface with consideration of species concentrations in the solid phase (DOF 34). For more information on the term “species,” see Terminology.

These electrical interaction models are intended for the transfer of electrical charge across touching or nearby surfaces. Modeling electrical interactions over large distances with these models is often inaccurate and can significantly degrade performance.

You can include electrical conductance properties in a contact property definition for surface-based contact. The electrical conductivity can be defined between solids or electrolytes.

SURFACE INTERACTION, NAME=name
GAP ELECTRICAL CONDUCTANCE, TYPE=SOLID

SURFACE INTERACTION, NAME=name
GAP ELECTRICAL CONDUCTANCE, TYPE=LIQUID

Interaction module: contact property editor: ElectricalElectrical Conductance

Abaqus/Standard models the electrical current flowing between two surfaces as

Common physical behavior is such that electrical conductance across an interface is much larger while surfaces are touching (“closed” contact status) than while separated (“open” contact status). By default, Abaqus assigns a large value of ${\sigma }_g$ to regions in contact (independent of the contact pressure, p) and assigns ${\sigma }_g=0$ to regions not actively in contact (independent of the contact clearance distance d), as shown in Figure 1.

Figure 1. Default electrical conductance behavior.

For heat transfer or coupled thermal-electrical analyses, the contact pressure is always zero. Therefore, electrical conductance at zero contact pressure is adopted for a closed initial contact status. When the contact status is open, an electrical conductance value that is a function of clearance (if provided) or a zero value is chosen.

You can define the electrical conductance directly or in user subroutine GAPELECTR.

Abaqus/Standard can include the effect of heat generated by electrical conduction between surfaces in a coupled thermal-electrical and a fully coupled thermal-electrical-structural analysis. By default, all dissipated electrical energy is converted to heat and distributed equally between the two surfaces. You can modify the fraction of electrical energy that is released as heat and the distribution between the two surfaces; see Modeling Heat Generated by Nonthermal Surface Interactions for details.

The following discussion describes the flow of ion concentration across a contact interface; however, this discussion is equally applicable to species concentration.

Abaqus/Standard assumes that ion concentration flows in the normal direction at a contact interface and does not flow tangentially along the interface. Two contributions to the ion concentration flow into each surface at a contact interface are generally present, as shown in Figure 5. The ion concentration flow into the main and secondary surfaces at corresponding points on the interface are $J_M$ and $J_S$ , respectively.

• One contribution ( $J_{across}$ ) is associated with flow across the interface. A positive value of $J_{across}$ corresponds to flow out from the main surface and into the secondary surface.

• The other contribution ( $J_{gapS}$ for the secondary surface and $J_{gapM}$ for the main surface) is associated with removing or adding ion concentration from the region between the surfaces while the gap distance is changing. The sign convention is such that $J_{gapS}$ and $J_{gapM}$ are positive when these contributions flow into the respective surfaces (while the gap width decreases). The sum of $J_{gapS}$ and $J_{gapM}$ (which is the same as the sum of $J_S$ and $J_M$ ) is equal to negative one times the rate of change of the gap width up to the threshold distance discussed in Controlling the Distance within Which Ionic/Species Flux Contact Properties Are Active.

In steady-state analyses the rate of separation of the surfaces is zero, so the ion concentration flow contributions $J_{gapS}$ and $J_{gapM}$ are zero; all fluid flowing out of one surface flows into the other in steady-state analyses.

Figure 5. Flow patterns in the interface contact element.

Ion concentration flow at a contact interface typically occurs even if contact diffusivity characteristics are not specified explicitly in the contact property definition. Alternatively, you can specify contact diffusivity characteristics directly for enhanced control over the ion concentration flow across a contact interface.

SURFACE INTERACTION, NAME=interaction_name
GAP DIFFUSIVITY

The following discussion describes the method of controlling the distance over which ion concentration flux contact properties are active; however, the discussion is equally applicable to species concentration flux.

The models governing ionic flux across a contact interface are most appropriate for two surfaces in contact or separated by a relatively small gap distance. By default, Abaqus assumes that no ionic flux occurs once the surfaces have separated by a distance larger than the characteristic element length of the underlying surfaces. Alternatively, you can specify a cutoff gap distance directly beyond which no ionic flux occurs. Separate controls are provided for the contribution of ionic flux across the interface ( $J_{across}$ ) and the contribution of ionic flux into the interface ( $J_{gap}$ ).

GAP DIFFUSIVITY, CUTOFF FLOW ACROSS=$d_{across}$

GAP DIFFUSIVITY, CUTOFF GAP FILL=$d_{gap}$

The following discussion describes controlling gap diffusivity associated with ionic flux across a contact interface; however, the discussion is equally applicable to species flux.

If you do not specify gap diffusivity characteristics, the implied physical model is as follows:

Alternatively, you can specify a gap diffusivity, $D_g$ , such that ionic flux across a contact interface ( $J_{across}$ , discussed above in Including Ion or Species Concentration Properties in a Contact Property Definition) is proportional to the difference in ion concentration magnitudes across the interface:

When defining $D_g$ directly, define it as

$p_{contact}$

is the contact pressure transmitted across the interface between A and B,

${\overline{C}}_e=\frac{1}{2}\left(C_{eA}+C_{eB}\right)$

is the average of the ion concentrations at A and B,

$\overline{\theta }=\frac{1}{2}\left({\theta }_A+{\theta }_B\right)$

is the average of the surface temperatures at A and B, and

${\overline{f}}_{\gamma }=\frac{1}{2}\left(f_{\gamma }^A+f_{\gamma }^B\right)$

is the average of any predefined field variables at A and B.

Figure 6 shows an example of $D_g$ depending on the contact pressure. Use tabular data to specify the value of $D_g$ at one or more contact pressures as p increases. The value of $D_g$ remains constant for contact pressures outside of the interval defined by the data points. Once the surfaces have separated, $D_g$ remains at a constant value until the separation between the surfaces exceeds the specified flow cutoff distance (see Controlling the Distance within Which Ionic/Species Flux Contact Properties Are Active), at which point $D_g$ drops to zero.

Figure 6. Contact pressure–dependent contact diffusivity.

GAP DIFFUSIVITY
$D_g$, $p_{contact}$, ${\overline{C}}_e$, $\overline{\theta }$

In addition to the dependencies mentioned previously, the gap diffusivity can depend on any number of predefined field variables, ${\overline{f}}_{\gamma }$ . To define gap diffusivity dependent on field variables, you must specify at least two data points for each field variable value.

GAP DIFFUSIVITY, DEPENDENCIES=n 
$D_g$, $p_{contact}$, ${\overline{C}}_e$, $\overline{\theta }$, ${\overline{f}}_{\gamma }$

Abaqus/Standard provides the following output variables related to the electrical interaction of surfaces:

ECD

Electric current per unit area leaving secondary surface.

ECDA

ECD multiplied by the area associated with the secondary node.

ECDT

Time integrated ECD.

ECDTA

Time integrated ECDA.

ECDE

Electrical current in electrolyte per unit area.

ECDEA

ECDE multiplied by the nodal area.

ECDET

Time integrated ECDE.

ECDETA

Time integrated ECDEA.

Additional surface variables are available as described in Ion Diffusivity of Electrolytes and Species Diffusivity in Solids.

The values of these variables are always given at the nodes of the secondary surface. They can be requested as surface output to the data, results, or output database files (see Surface Output from Abaqus/Standard and Writing Surface Output to the Output Database for details).

Contour plots of these variables can also be displayed in the Visualization module of Abaqus/CAE (Abaqus/Viewer).