- displacementsThe displacements appropriate for the simulation geometry and coordinate system
C++ Type:std::vector

Description:The displacements appropriate for the simulation geometry and coordinate system

# Compute Axisymmetric RZ Finite Strain

Compute a strain increment for finite strains under axisymmetric assumptions.

## Description

The material `ComputeAxisymmetricRZFiniteStrain`

calculates the finite strain for 2D Axisymmetric systems.

Axisymmetric (cylindrical) materials are included in Tensor Mechanics for revolved geometries and assume symmetrical loading. These 'strain calculator' materials compute the strain within the appropriate coordinate system and rely on specialized AxisymmetricRZ kernels to handle the stress divergence.

The axis of symmetry must lie along the -axis in a or cylindrical coordinate system. This symmetry orientation is required for the calculation of the residual and of the jacobian. See StressDivergenceRZTensors for the residual equation and the germane discussion.

The `AxisymmetricRZ`

` material is appropriate for a 2D simulation and assumes symmetry revolved about the z-axis. A 2D formulation of an appropriate simulation problem can reduce the simulation run time while preserving key physics. Axisymmetric simulations are appropriate to problems in which a solid is generated by revolving a planar area about an axis in the same plane.`

The coordinate type in the Problem block of the input file must be set to ** COORD_TYPE = RZ**.

## Axisymmetric Strain Formulation

The axisymmetric model employs the cylindrical coordinates, , , and , where the planar cross section formed by the and axes is rotated about the axial axis, along the length of the cylinder, in the direction. The cylindrical coordinate system strain tensor for axisymmetric problems has the form

(1) where the value of the strain depends on the displacement and position in the radial direction (2)

Although axisymmetric problems solve for 3D stress and strain fields, the problem is mathematically 2D. Using an appropriate set of geometry and boundary conditions, these types of problems have strain and stress fields which are not functions of the out of plane coordinate variable. In the cylindrical coordinate axisymmetric system, the values of stress and strain in the direction do not depend on the coordinate.

The axisymmetric system changes the order of the displacement vector from , usually seen in textbooks, to . Take care to follow this convention in your input files and when adding eigenstrains or extra stresses.

Once the deformation gradient is calculated for the specific 2D geometry, the deformation gradient is passed to the strain and rotation methods used by default 3D Cartesian simulations, as described in the Finite Strain Class page.

## Example Input File

```
[./strain1]
type = ComputeAxisymmetricRZFiniteStrain
block = 1
[../]
```

(modules/combined/test/tests/cavity_pressure/cavity_pressure_rz.i)## Input Parameters

- global_strainOptional material property holding a global strain tensor applied to the mesh as a whole
C++ Type:MaterialPropertyName

Description:Optional material property holding a global strain tensor applied to the mesh as a whole

- decomposition_methodTaylorExpansionMethods to calculate the strain and rotation increments
Default:TaylorExpansion

C++ Type:MooseEnum

Description:Methods to calculate the strain and rotation increments

- 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.

- 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

- eigenstrain_namesList of eigenstrains to be applied in this strain calculation
C++ Type:std::vector

Description:List of eigenstrains to be applied in this strain calculation

- out_of_plane_directionzThe direction of the out-of-plane strain.
Default:z

C++ Type:MooseEnum

Description:The direction of the out-of-plane strain.

- volumetric_locking_correctionFalseFlag to correct volumetric locking
Default:False

C++ Type:bool

Description:Flag to correct volumetric locking

- 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

- 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.

- enableTrueSet the enabled status of the MooseObject.
Default:True

C++ Type:bool

Description:Set the enabled status of the MooseObject.

- 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

### Advanced Parameters

- 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