# Zirconium Oxide Elasticity Tensor

Computes the Young's Modulus and Poisson's ratio for zirconium oxide.

## Description

The ZrO2ElasticityTensor material model, determines the Young's Modulus and Poisson's ratio of zirconium oxide using the MAPTRO (Allison et al., 1993) correlations.

The Poisson's ratio for ZrO is constant and assumed to be equal to 0.3. The Young's Modulus is a temperature dependent function that depends upon the solidus temperature of the oxide. The solidus temperature is a function of the atomic fraction of oxygen in the oxide. The atomic fraction of oxygen is calculated from the oxygen to metal ratio as follows: (1) where is the atomic fraction of oxygen and is the oxygen-to-metal ratio. Here it is assumed that the oxide that is formed is pure ZrO and therefore = 2 corresponding to an atomic fraction of oxygen of =0.667. Given this value the solidus temperature is given by: (2)

Thus, using the known atomic fraction of oxygen the solidus temperature used in the Young's Modulus equations below is = 2980.27 K. The correlation for Young's Modulus is: (3) where is the temperature in K.

## Example Input Syntax

[./elasticity_tensor]
type = ZrO2ElasticityTensor
temperature = temperature
[../]
(test/tests/tensor_mechanics/zro2_mechanics/elasticity.i)

## Input Parameters

• temperatureCoupled temperature

C++ Type:std::vector

Description:Coupled temperature

### Required Parameters

• 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

• 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.

• 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

• 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

• elasticity_tensor_prefactorOptional function to use as a scalar prefactor on the elasticity tensor.

C++ Type:FunctionName

Description:Optional function to use as a scalar prefactor on the elasticity tensor.

### 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

• 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. C. M. Allison, G. A. Berna, R. Chambers, E. W. Coryell, K. L. Davis, D. L. Hagrman, D. T. Hagrman, N. L. Hampton, J. K. Hohorst, R. E. Mason, M. L. McComas, K. A. McNeil, R. L. Miller, C. S. Olsen, G. A. Reymann, and L. J. Siefken. SCDAP/RELAP5/MOD3.1 code manual, volume IV: MATPROâ€“A library of materials properties for light-water-reactor accident analysis. Technical Report NUREG/CR-6150, EGG-2720, Idaho National Engineering Laboratory, 1993.[BibTeX]