# ELECTRICAL_RESISTIVITY_MODEL

Specifies an electrical resistivity model for the charge conservation equation. The electrical resistivity represents the ability of a material to resist the flow of current. Electrical resistivity model applies to solid materials only.

## Type

AcuSolve Command

## Syntax

ELECTRICAL_RESISTVITY_MODEL("name"){parameters...}

## Qualifier

User-given name.

## Parameters

- type (enumerated) [=none]
- Type of the electrical resistivity model.
- constant or const
- Constant electrical resistivity. Requires electrical_resistivity.
- linear_temperature
- Linear temperature dependent resistivity.
- piecewise_linear or linear
- Piecewise linear curve fit. Requires curve_fit_values and curve_fit_variable.
- cubic_spline or spline
- Cubic spline curve fit. Requires curve_fit_values and curve_fit_variable.
- user_function or user
- User-defined function. Requires user_function, user_values and user_strings.

- electric_resistivity (real) [=1.72e-8]
- Constant value of electrical resistivity. When type is constant.
- linear_temperature_reference_temperature (real) [=293.15]
- Reference temperature for linear_temperature resistivity type.
- linear_temperature_reference_temperature_resistivity (real) [=1.72e-8]
- Resistivity of the material at the reference temperature for linear_temperature resistivity type.
- linear_temperature_temperature_coefficient (real) [=0.00393]
- Relative change of resistivity for a given change in temperature for linear_temperature resistivity type.
- curve_fit_values or curve_values (array) [={0,0}]
- A two-column array of independent-variable/isotropic electrical resistivity data values. Used with piecewise_linear and cubic_spline types.
- curve_fit_variable or curve_var (enumerated) [=temperature]
- Independent variable of the curve fit for isotropic electrical resistivity. Used with piecewise_linear and cubic_spline types.
- user_function or user (string) [no default]
- Name of the user-defined function. Used with user_function type.
- user_values (array) [={}]
- Array of values to be passed to the user-defined function. Used with user_function type.
- user_strings (list) [={}]
- Array of strings to be passed to the user-defined function. Used with user_function type.

## Description

The resistivity model is used for both the charge conservation equation and for the coupling of charge conservation to the energy equation. A brief description of both models in the context of electrical resistivity is given below.

^{2}). Typically, it is assumed that the current density is proportional to the electric field, where the proportionality constant is the electrical conductivity ( $\sigma $ ) of the material. The current density can then be expressed as:

where $\text{\Phi}$ (units: V) is the electric potential field. The inverse of conductivity $\sigma $ is the electrical resistivity ${\rho}_{E}$ of the material.

```
ELECTRICAL_RESISTIVITY_MODEL( "my resistivity model" ) {
type = constant
electrical_resistivity = 2.9e-8
}
MATERIAL_MODEL( "my material model" ) {
electrical_resistivity_model = "my resistivity model"
}
```

The simplest case is type = constant. This applies a constant resistivity in both the conservation of charge equation and the source term in the energy equation. An example of a constant electrical resistivity value is shown above.

Where ${\rho}_{E}{}_{0}$ is the reference temperature resistivity, $\alpha $ the temperature coefficient, $T$ the local temperature and ${T}_{REF}$ the reference temperature. The temperature coefficient describes the relative change of resistivity for a given change in temperature.

```
ELECTRICAL_RESISTIVITY_MODEL( "my resistivity model" ) {
type = linear_temperature
linear_temperature_reference_temperature = 293.15
linear_temperature_reference_temperature_resistivity = 1.754e-8
linear_temperature_temperature_coefficient = 0.0039
}
```

Electrical resistivity models of types piecewise_linear and cubic_spline may be used to define electrical resistivity as a function of a single independent variable. These types of electrical resistivity models are consistent with other material models. Currently the only curve_fit_variable supported is temperature.

An electrical resistivity model of type user_function may be used to model more complex behaviors; see the AcuSolve User-Defined Functions Manual for a detailed description of user-defined functions.