# Compute Axisymmetric 1D Finite Strain

Compute a strain increment and rotation increment for finite strains in an axisymmetric 1D problem

## Description

The material ComputeAxisymmetric1DFiniteStrain calculates the finite strain for 1D Axisymmetric systems and is intended for use with Generalized Plane Strain simulations. This material assumes symmetry about the -axis. This 'strain calculator' material computes the strain within the cylindrical coordinate system and relies on the specialized Axisymmetric RZ kernel to handle the stress divergence calcuation.

The axis of symmetry must lie along the -axis in a 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.

## 1D Axisymmetric Strain Formulation

The axisymmetric model uses the cylindrical coordinates, , , and , where the linear section formed by the axis is rotated about the axis in the direction. The incremental deformation gradient for the 1D axisymmetric system is defined as (1) where is the Rank-2 identity tensor, and the deformation gradient, , and the old deformation gradient, , are given as (2) Note that uses the values of the strain expressions from the previous time step. The components of the tensors in Eq. (2) are given as (3) where is a prescribed out-of-plane strain value: this strain value can be given either as a scalar variable or a nonlinear variable. The Generalized Plane Strain problems use scalar variables. The value of the strain depends on the displacement and position in the radial direction.

note:Notation Order Change

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 incremental deformation gradient (Eq. (1)) is calculated for the 1D 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 documentation.

## Example Input File

note:Use RZ Coordinate Type

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

The common use of the ComputeAxisymmetric1DFiniteStrain class is with the Generalized Plane Strain system; this type of simulation uses the scalar strain variables

[./strain]
type = ComputeAxisymmetric1DFiniteStrain
eigenstrain_names = eigenstrain
scalar_out_of_plane_strain = scalar_strain_yy
[../]

(modules/tensor_mechanics/test/tests/1D_axisymmetric/axisymm_gps_finite.i)

which uses a scalar variable for the coupled out-of-plane strain; the arguement for the scalar_out_of_plane_strain parameter is the name of the scalar strain variable:

[./scalar_strain_yy]
order = FIRST
family = SCALAR
[../]

(modules/tensor_mechanics/test/tests/1D_axisymmetric/axisymm_gps_finite.i)

## Input Parameters

• displacementsThe displacements appropriate for the simulation geometry and coordinate system

C++ Type:std::vector

Options:

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

### Required Parameters

• scalar_out_of_plane_strainScalar variable for axisymmetric 1D problem

C++ Type:std::vector

Options:

Description:Scalar variable for axisymmetric 1D problem

• decomposition_methodTaylorExpansionMethods to calculate the strain and rotation increments

Default:TaylorExpansion

C++ Type:MooseEnum

Options:TaylorExpansion EigenSolution

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

Options:

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

Options:

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

• global_strainOptional material property holding a global strain tensor applied to the mesh as a whole

C++ Type:MaterialPropertyName

Options:

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

• eigenstrain_namesList of eigenstrains to be applied in this strain calculation

C++ Type:std::vector

Options:

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

• volumetric_locking_correctionFalseFlag to correct volumetric locking

Default:False

C++ Type:bool

Options:

Description:Flag to correct volumetric locking

• out_of_plane_strainNonlinear variable for axisymmetric 1D problem

C++ Type:std::vector

Options:

Description:Nonlinear variable for axisymmetric 1D problem

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

C++ Type:std::vector

Options:

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

Options:

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

• subblock_index_providerSubblockIndexProvider user object name

C++ Type:UserObjectName

Options:

Description:SubblockIndexProvider user object name

### Optional Parameters

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

C++ Type:std::vector

Options:

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

Options:

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

### Outputs Parameters

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

C++ Type:std::vector

Options:

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

• enableTrueSet the enabled status of the MooseObject.

Default:True

C++ Type:bool

Options:

Description:Set the enabled status of the MooseObject.

• seed0The seed for the master random number generator

Default:0

C++ Type:unsigned int

Options:

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

Options:

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

Options:NONE ELEMENT SUBDOMAIN

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