# Mo Thermal Expansion Eigenstrain

Computes eigenstrain due to thermal expansion using a function that describes the mean thermal expansion as a function of temperature.

## Description

The equation below calculates the mean thermal expansion coefficient ( (m/m-K)): (1) where is the temperature in .

Figure 1: Coefficient of thermal expansion versus temperature.

The method of Niffenegger and Reichlin (2012) is employed to convert the mean thermal expansion values into instantaneous values. The details of the methodology described by Niffenegger and Reichlin (2012) can be found on the page for ComputeMeanThermalExpansionFunctionEigenstrain.

Eq. 1 used in Bison is compared to the equation provided by UCSD (2003) and to the tabulated experimental data in Cverna and others (2002). Figure 1 shows the comparison and hence the applicability of the Bison equation.

## Example Input Syntax


[./thermal_expansion]
type = MoThermalExpansionEigenstrain
temperature = temperature
stress_free_temperature = 300.0
eigenstrain_name = thermal_expansion
[../]
(test/tests/tensor_mechanics/mo_mechanics/combined_temperature_mechanics.i)

The eigenstrain_name parameter value must also be set for the strain calculator, and an example parameter setting in the Tensor Mechanics Master Action is shown below:


[Modules]
[./TensorMechanics]
[./Master]
[./all]
strain = FINITE
incremental = true
eigenstrain_names = 'thermal_expansion'
generate_output = 'stress_yy elastic_strain_xx elastic_strain_yy elastic_strain_zz'
[../]
[../]
[../]
[]
(test/tests/tensor_mechanics/mo_mechanics/combined_temperature_mechanics.i)

## Input Parameters

• stress_free_temperatureReference temperature at which there is no thermal expansion for thermal eigenstrain calculation

C++ Type:std::vector

Description:Reference temperature at which there is no thermal expansion for thermal eigenstrain calculation

• eigenstrain_nameMaterial property name for the eigenstrain tensor computed by this model. IMPORTANT: The name of this property must also be provided to the strain calculator.

C++ Type:std::string

Description:Material property name for the eigenstrain tensor computed by this model. IMPORTANT: The name of this property must also be provided to the strain calculator.

### Required Parameters

• computeTrueWhen false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the Material via MaterialPropertyInterface::getMaterial(). Non-computed Materials are not sorted for dependencies.

Default:True

C++ Type:bool

Description:When false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the Material via MaterialPropertyInterface::getMaterial(). Non-computed Materials are not sorted for dependencies.

• temperatureCoupled temperature

C++ Type:std::vector

Description:Coupled temperature

• base_nameOptional parameter that allows the user to define multiple mechanics material systems on the same block, i.e. for multiple phases

C++ Type:std::string

Description:Optional parameter that allows the user to define multiple mechanics material systems on the same block, i.e. for multiple phases

• boundaryThe list of boundary IDs from the mesh where this boundary condition applies

C++ Type:std::vector

Description:The list of boundary IDs from the mesh where this boundary condition applies

• blockThe list of block ids (SubdomainID) that this object will be applied

C++ Type:std::vector

Description:The list of block ids (SubdomainID) that this object will be applied

### Optional Parameters

• enableTrueSet the enabled status of the MooseObject.

Default:True

C++ Type:bool

Description:Set the enabled status of the MooseObject.

• use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Default:False

C++ Type:bool

Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

• control_tagsAdds user-defined labels for accessing object parameters via control logic.

C++ Type:std::vector

Description:Adds user-defined labels for accessing object parameters via control logic.

• seed0The seed for the master random number generator

Default:0

C++ Type:unsigned int

Description:The seed for the master random number generator

• implicitTrueDetermines whether this object is calculated using an implicit or explicit form

Default:True

C++ Type:bool

Description:Determines whether this object is calculated using an implicit or explicit form

• constant_onNONEWhen ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeSubdomainProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped

Default:NONE

C++ Type:MooseEnum

Description:When ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeSubdomainProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped

• cte_scale_factor1Scale factor to be applied to the thermal expansion coefficient. Used for calibration and sensitivity studies

Default:1

C++ Type:double

Description:Scale factor to be applied to the thermal expansion coefficient. Used for calibration and sensitivity studies

• output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type)

C++ Type:std::vector

Description:List of material properties, from this material, to output (outputs must also be defined to an output type)

• outputsnone Vector of output names were you would like to restrict the output of variables(s) associated with this object

Default:none

C++ Type:std::vector

Description:Vector of output names were you would like to restrict the output of variables(s) associated with this object

## References

1. Fran Cverna and others. ASM ready reference: thermal properties of metals. ASM International, 2002.[BibTeX]
2. M. Niffenegger and K. Reichlin. The proper use of thermal expansion coefficients in finite element calculations. Nuclear Engineering and Design, 243:356â€“359, 2012.[BibTeX]
3. UCSD. Molybdenum and its Alloys. http://www-ferp.ucsd.edu/LIB/PROPS/PANOS/moa.aspx, 2003.[BibTeX]