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Add object documentation and make website more navigable for basic do…
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…cumentation review.

Refs idaholab#25 , idaholab#24
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cticenhour committed Apr 18, 2021
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20 changes: 20 additions & 0 deletions modules/electromagnetics/doc/content/bib/elk.bib
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@article{cincotti2007sps,
author = {Cincotti, A. and Locci, A. M. and Orrù, R. and Cao, G.},
title = {Modeling of {SPS} apparatus: Temperature, current and strain distribution with no powders},
journal = {AIChE Journal},
volume = {53},
number = {3},
pages = {703-719},
doi = {10.1002/aic.11102},
year = {2007}
}

@article{babu2001contactresistance,
author = {Babu, S. S. and Santella, M. L. and Feng, Z. and Riemer, B. W. and Cohron, J. W.},
title = {Empirical model of effects of pressure and temperature on electrical contact resistance of metals},
journal = {Sci Technol Weld Joining},
volume = {6},
number = {3},
pages = {126-132},
year = {2001}
}
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# ElectrostaticContactCondition

!syntax description /InterfaceKernels/ElectrostaticContactCondition

## Description

This interface kernel models the conductivity of electric field across a specified
boundary between two dissimilar materials, as described by [!citep](cincotti2007sps).
It accounts for the influence of electrostatic potential differences across the
interface, with appropriate electrical contact conductance / resistance coefficient
being provided either by the user as a constant scalar number or via a combination
of material properties and constants for calculation. The condition being applied is:

\begin{equation}
\sigma_{el,1} \frac{\partial \phi}{\partial \mathbf{r}} \bigg\rvert_1 \cdot \mathbf{\hat{n}} = \sigma_{el,2} \frac{\partial \phi}{\partial \mathbf{r}} \bigg\rvert_2 \cdot \mathbf{\hat{n}}
\end{equation}

and

\begin{equation}
\sigma_{el,1} \frac{\partial \phi}{\partial \mathbf{r}} \bigg\rvert_1 \cdot \mathbf{\hat{n}} = -C_E (\phi_1 - \phi_2)
\end{equation}

where

- $\sigma_{el, i}$ is the electrical conductivity of each material along the interface,
- $C_E$ is the electrical contact conductance, and
- $\phi_i$ is the electrostatic potential of the material at the interface.

The temperature- and mechanical-pressure-dependent electrical contact conductance, given by [!citep](babu2001contactresistance), is calculated using:

\begin{equation}
C_E(T, P) = \alpha_E \sigma_{el,Harm} \bigg( \frac{P}{H_{Harm}} \bigg)^{\beta_E}
\end{equation}

where

- $\alpha_E$ is an experimentally-derived proportional fit parameter (set to be 64, from [!citep](cincotti2007sps)),
- $\sigma_{el,Harm}$ is the harmonic mean of the temperature-dependent electrical conductivities on either side of the boundary,
- $P$ ($=F/S$) is the uniform mechanical pressure applied at the contact surface area (S) between the two materials,
- $H_{Harm}$ is the harmonic mean of the hardness values of each material, and
- $\beta_E$ is an experimentally-derived power fit parameter (set to be 0.35, from [!citep](cincotti2007sps)).

For reference, the harmonic mean calculation for two values, $V_a$ and $V_b$, is given by

\begin{equation}
V_{Harm} = \frac{2 V_a V_b}{V_a + V_b}
\end{equation}

## Example Input File Syntax

!listing contact_resistance_calculated.i block=InterfaceKernels/contact_resistance


!syntax parameters /InterfaceKernels/ElectrostaticContactCondition

!syntax inputs /InterfaceKernels/ElectrostaticContactCondition

!syntax children /InterfaceKernels/ElectrostaticContactCondition

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