# Compute Elasticity Tensor CP

Compute an elasticity tensor for crystal plasticity.

## Description

The material ComputeElasticityTensorCP is used to create an elasticity tensor for crystal plasticity simulations. This material builds an orthotropic elasticity tensor using the fill_method symmetric9 from ComputeElasticityTensor. ComputeElasticityTensorCP rotates the elasticity tensor both during the initial setup step, if Euler angles are provided, and at the start of each timestep.

warning:Crystal Plasticity Simulations use Active Rotation

The rotation matrix used in this class,ComputeElasticityTensorCP, is the transpose of the rotation matrix created from the Bunge Euler angles in the base class, ComputeElasticityTensor. This difference in the rotation matrix is because of the active rotation convention used in crystal plasticity simulations.

The fill method symmetric9 is appropriate for materials with three orthotropic planes of symmetry (Malvern, 1969), and is used for simulations of anistropic materials such as cubic crystals. The engineering elasticity tensor notation for an orthotropic material is given in Eq. (1): (1)

## Rotation Tensor Conventions

The Euler angle convention used in ComputeElasticityTensorCP is the -- (3-1-3) convention. The Euler angles arguments are expected in degrees, not radians, and are denoted as , , and , corresponding to the axis rotations. The rotation tensor, , is calculated from the current Euler angles at each timestep as shown in Eq. (2). (2) The elasticity tensor is then rotated with Eq. (3) (3) at the beginning of each material timestep calculation.

The crystal plasticity materials, including ComputeElasticityTensorCP employ an active rotation: the crystal system is rotated into the sample (loading) coordinate system. Generally the Bunge Euler angles are used to describe a passive rotation: rotating the sample coordinate system into the crystal coordinate system. As a result, the rotation tensor applied is the transpose of the rotation tensor given in Eq. (2) as noted in Eq. (3).

## Example Input File Syntax

[./elasticity_tensor]
type = ComputeElasticityTensorCP
C_ijkl = '1.684e5 1.214e5 1.214e5 1.684e5 1.214e5 1.684e5 0.754e5 0.754e5 0.754e5'
fill_method = symmetric9
[../]

(modules/tensor_mechanics/test/tests/cp_user_object/test.i)

## Input Parameters

• C_ijklStiffness tensor for material

C++ Type:std::vector

Options:

Description:Stiffness tensor for material

### 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

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.

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

C++ Type:FunctionName

Options:

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

• fill_methodsymmetric9The fill method

Default:symmetric9

C++ Type:MooseEnum

Options:antisymmetric symmetric9 symmetric21 general_isotropic symmetric_isotropic symmetric_isotropic_E_nu antisymmetric_isotropic axisymmetric_rz general principal

Description:The fill method

• 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

• euler_angle_30Euler angle in direction 3

Default:0

C++ Type:double

Options:

Description:Euler angle in direction 3

• euler_angle_20Euler angle in direction 2

Default:0

C++ Type:double

Options:

Description:Euler angle in direction 2

• euler_angle_10Euler angle in direction 1

Default:0

C++ Type:double

Options:

Description:Euler angle in direction 1

C++ Type:UserObjectName

Options:

• 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

### 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

• enableTrueSet the enabled status of the MooseObject.

Default:True

C++ Type:bool

Options:

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

Options:

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

Options:

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

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

## References

1. Lawrence E Malvern. Introduction to the Mechanics of a Continuous Medium. Prentice-Hall, 1969.[BibTeX]