Compute Elasticity Tensor

Compute an elasticity tensor.

Description

The material ComputeElasticityTensor builds the elasticity (stiffness) tensor with various user-selected material symmetry options. ComputeElasticityTensor also rotates the elasticity tensor during the initial time step only; this class does not rotate the elasticity tensor during the simulation. The initial rotation is performed if the user provides arguments to the three Euler angle parameters; the Bunge Euler angles provided in this class are used to perform passive (from the sample to the crystal) rotations using the extrinsic $var element = document.getElementById("moose-equation-845de853-7bea-4f4b-b3d9-fb6441a27ebc");katex.render("Z_1 X_2 Z_3", element, {displayMode:false,throwOnError:false});$ convention to build the rotation matrix $var element = document.getElementById("moose-equation-2ee1a8ac-d1c2-4182-8959-85e8ed15f4b0");katex.render("R", element, {displayMode:false,throwOnError:false});$ . Alternatively, the 3x3 rotation matrix can be defined directly in the input file. Rotations to the elasticity tensor are applied as $(1)var element = document.getElementById("moose-equation-a03864e4-9871-47e8-973a-2427a4271578");katex.render(" C_{ijkl} = R_{im} R_{jn} R_{ko} R_{lp} C_{mnop}", element, {displayMode:true,throwOnError:false});$ See below for examples of tensor rotations.

For a general stiffness tensor with 21 independent components, the elasticity tensor within the tensor mechanics module can be represented with the notation shown in Eq. (2). Nonetheless, the full Rank-4 tensor with all 81 components is created by ComputeElasticityTensor. $(2)var element = document.getElementById("moose-equation-0a59ab68-7c2f-4226-b22f-c78cc1d45a8c");katex.render(" \\begin{aligned} C_{ijkl} \\implies & \\underbrace{\\begin{bmatrix} C_{11} & C_{12} & C_{13} & C_{14} & C_{15} & C_{16} \\\\ C_{21} & C_{22} & C_{23} & C_{24} & C_{25} & C_{26} \\\\ C_{31} & C_{32} & C_{33} & C_{34} & C_{35} & C_{36} \\\\ C_{41} & C_{42} & C_{43} & C_{44} & C_{45} & C_{46} \\\\ C_{51} & C_{52} & C_{53} & C_{54} & C_{55} & C_{56} \\\\ C_{61} & C_{62} & C_{63} & C_{64} & C_{65} & C_{66} \\end{bmatrix}}_{\\text{textbook engineering notation}} \\\\[5.0em] \\implies & \\underbrace{\\begin{bmatrix} C_{1111} & C_{1122} & C_{1133} & C_{1123} & C_{1131} & C_{1112} \\\\ C_{2211} & C_{2222} & C_{2233} & C_{2223} & C_{2231} & C_{2212} \\\\ C_{3311} & C_{3322} & C_{3333} & C_{3323} & C_{3331} & C_{3312} \\\\ C_{2311} & C_{2322} & C_{2333} & C_{2323} & C_{2331} & C_{2312} \\\\ C_{3111} & C_{3122} & C_{3133} & C_{3123} & C_{3131} & C_{3112} \\\\ C_{1211} & C_{1222} & C_{1233} & C_{1223} & C_{1231} & C_{1212} \\end{bmatrix}}_{\\text{textbook Einstein index notation}} \\\\[5.0em] \\implies & \\underbrace{\\begin{bmatrix} C_{0000} & C_{0011} & C_{0022} & C_{0012} & C_{0020} & C_{0001} \\\\ C_{1100} & C_{1111} & C_{1122} & C_{1112} & C_{1120} & C_{1101} \\\\ C_{2200} & C_{2211} & C_{2222} & C_{2212} & C_{2220} & C_{2201} \\\\ C_{1200} & C_{1211} & C_{1222} & C_{1212} & C_{1220} & C_{1201} \\\\ C_{2000} & C_{2011} & C_{2022} & C_{2012} & C_{2020} & C_{2001} \\\\ C_{0100} & C_{0111} & C_{0122} & C_{0112} & C_{0120} & C_{0101} \\end{bmatrix}}_{\\text{Compute Elasticity Tensor indices}} \\end{aligned}", element, {displayMode:true,throwOnError:false});$

There are several different material symmetry options that a user can apply to build the elasticity tensor for a mechanics simulation that are discussed below.

General Symmetry

The fill method symmetric21 is used to create the elasticity tensor for a linear hyperelastic material with 21 independent components: the symmetries shown in Eq. (3) are used to determine the independent components (Slaughter, 2012). $(3)var element = document.getElementById("moose-equation-400ab018-1b28-4a59-b67b-f3a114ee3e12");katex.render(" \\begin{aligned} C_{ijkl} & = C_{jikl} \\impliedby \\quad \\text{satisfies angular momentum} \\\\ C_{ijkl} & = C_{ijlk} \\impliedby \\quad \\text{symmetric strain tensor assumption} \\\\ C_{ijkl} & = C_{klij} \\impliedby \\quad \\text{linear hyperelastic material assumption} \\end{aligned}", element, {displayMode:true,throwOnError:false});$

Example Input File Syntax

[./elasticity_tensor]
  type = ComputeElasticityTensor
  fill_method = symmetric21
  C_ijkl = '1111 1122 1133 1123 1113 1112 2222 2233 2223 2213 2212 3333 3323 3313 3312 2323 2313 2312 1313 1312 1212'
[../]

which shows the expected order of the elasticity tensor components in the input argument string.

Orthotropic Symmetry

The fill method symmetric9 is appropriate for materials with three orthotropic planes of symmetry (Malvern, 1969), and is often used for simulations of anistropic materials such as cubic crystals. The enginering elasticity tensor notation, Eq. (2), for an orthotropic material is given in Eq. (4) $(4)var element = document.getElementById("moose-equation-96a7457f-bff2-4388-9b50-a782c10a1731");katex.render(" C_{ijkl}^{orthotropic} = \\begin{bmatrix} C_{11} & C_{12} & C_{13} & 0 & 0 & 0 \\\\ C_{12} & C_{22} & C_{23} & 0 & 0 & 0 \\\\ C_{13} & C_{23} & C_{33} & 0 & 0 & 0 \\\\ 0 & 0 & 0 & C_{44} & 0 & 0 \\\\ 0 & 0 & 0 & 0 & C_{55} & 0 \\\\ 0 & 0 & 0 & 0 & 0 & C_{66} \\end{bmatrix}", element, {displayMode:true,throwOnError:false});$

The user can also select the fill method orthotropic, which generates an elasticity tensor based directly on material parameters. That is, the elasticity tensor is computed via moduli of elasticity, Poisson's ratios, and shear stiffnesses, see Eq. (5) $(5)var element = document.getElementById("moose-equation-81e07012-29ec-4afe-b77f-0b97598f4afd");katex.render(" C_{ijkl}^{orthotropic} = \\begin{bmatrix} E_{1} (1 - \\nu_{23} \\nu_{32})/k & E_{1} (\\nu_{23} \\nu_{31} + \\nu_{21})/k & E_{1} (\\nu_{21} \\nu_{32} + \\nu_{31})/k & 0 & 0 & 0 \\\\ E_{2} (\\nu_{13} \\nu_{32} + \\nu_{12})/k & E_{2} (1 - \\nu_{13} \\nu_{31})/k & E_{2} (\\nu_{12} \\nu_{31} + \\nu_{32})/k & 0 & 0 & 0 \\\\ E_{3} (\\nu_{12} \\nu_{23} + \\nu_{13})/k & E_{3} (\\nu_{13} \\nu_{21} + \\nu_{23})/k & E_{3} (1 - \\nu_{12} \\nu_{21})/k & 0 & 0 & 0 \\\\ 0 & 0 & 0 & G_{12} & 0 & 0 \\\\ 0 & 0 & 0 & 0 & G_{31} & 0 \\\\ 0 & 0 & 0 & 0 & 0 & G_{23} \\end{bmatrix}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-74f8617e-298d-498e-aa5f-983c31eb8531");katex.render("k = 1 - \\nu_{12} \\nu_{21} - \\nu_{23} \\nu_{32} - \\nu_{31} \\nu_{13} - \\nu_{12} \\nu_{23} \\nu_{31} - \\nu_{21} \\nu_{32} \\nu_{13}", element, {displayMode:false,throwOnError:false});$ .

Example Input File Syntax

[./elasticity_tensor]
  type = ComputeElasticityTensor
  C_ijkl = '1.684e5 0.176e5 0.176e5 1.684e5 0.176e5 1.684e5 0.754e5 0.754e5 0.754e5'
  fill_method = symmetric9
[../]

In the Einstein index notation shown in Eq. (2), the parameter C_ijkl expects the elasticity components in the order C_ijkl = '1111 1122 1133 2222 2233 3333 2323 3131 1212' for the symmetric9 fill method option. Note that, in this case, the method symmetric9 is used to enter an isotropic elasticity tensor.

[elasticity_tensor]
  type = ComputeElasticityTensor
  fill_method = orthotropic
  C_ijkl = '2.0e3 2.0e5 2.0e3 0.71428571e3 0.71428571e3 0.71428571e3 0.4 0.2 0.004 0.004 0.2 0.4'
[]

For the orthotropic fill method, the material parameters need to be referred to the global frame and introduced in the following order: $var element = document.getElementById("moose-equation-ebedcd47-9c48-4183-ab1a-dcc3ee63291e");katex.render("E_{11}\\;E_{22}\\;E_{33}\\;G_{12}\\;G_{23}\\;G_{31}\\;\\nu_{21}\\;\\nu_{31}\\;\\nu_{32}\\;\\nu_{12}\\;\\nu_{13}\\;\\nu_{23}", element, {displayMode:false,throwOnError:false});$ . For cases where axes of orthotropy do not coincide with global axes, Euler angles can be provided to perform a general rotation of the elasticity tensor at the beginning of the simulation.

Linear Isotropic Symmetry

The two constant isotropic symmetry fill methods symmetric_isotropic and symmetric_isotropic_E_nu are used in the dedicated isotropic elasticity tensor ComputeIsotropicElasticityTensor. These two fill methods use the symmetries shown in Eq. (6) to build the elasticity tensor. $(6)var element = document.getElementById("moose-equation-1e53641a-dfb7-4924-8a83-876a9c9ca8f0");katex.render(" C_{ijkl} = C_{klij} = C_{jikl} = C_{jilk}", element, {displayMode:true,throwOnError:false});$ Please see the documentation page for ComputeIsotropicElasticityTensor for details and examples of the input file syntax for linear elastic isotropic elasticity tensors.

Antisymmetric Isotropic Symmetry

The fill method antisymmetric_isotropic is used for an antisymmetric isotropic material in a shear case. The elasticity tensor is built using the symmetries shown in Eq. (7) $(7)var element = document.getElementById("moose-equation-4d6c0cc7-7866-4f7f-91d9-e7afa1651dc4");katex.render(" C_{ijkl}^{antisymmetric-isotropic} = \\kappa e_{ijm} e_{klm}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-cdcdd02e-4099-4ea9-bb77-4709b7b1c359");katex.render("e", element, {displayMode:false,throwOnError:false});$ is the permutation tensor and $var element = document.getElementById("moose-equation-a6f80f30-2ae1-4f08-a3ee-8d3ad57677e8");katex.render("m", element, {displayMode:false,throwOnError:false});$ is the summation index.

Transverse Isotropic (Axisymmetric)

The fill method axisymmetric_rz is used for materials which are isotropic with respect to an axis of symmetry, such as a material composed of fibers which are parallel to the axis of symmetry (Slaughter, 2012). The engineering notation matrix in this case is shown by Eq. (8). $(8)var element = document.getElementById("moose-equation-ddea775e-79a7-438a-a7c9-3d6e5e8b7375");katex.render(" C_{ijkl}^{axisymmetric} = \\begin{bmatrix} C_{11} & C_{12} & C_{13} & 0 & 0 & 0 \\\\ C_{12} & C_{11} & C_{13} & 0 & 0 & 0 \\\\ C_{13} & C_{13} & C_{33} & 0 & 0 & 0 \\\\ 0 & 0 & 0 & C_{44} & 0 & 0 \\\\ 0 & 0 & 0 & 0 & C_{44} & 0 \\\\ 0 & 0 & 0 & 0 & 0 & \\frac{1}{2} \\left( C_{11} - C_{12} \\right) \\end{bmatrix}", element, {displayMode:true,throwOnError:false});$

Example Input File Syntax

[./elasticity_tensor]
  #Material constants selected to match isotropic lambda and shear modulus case
  type = ComputeElasticityTensor
  C_ijkl = '1022726 113636 113636 1022726 454545'
  fill_method = axisymmetric_rz
[../]

In the Einstein index notation shown in Eq. (2), the parameter C_ijkl expects the elasticity components in the order C_ijkl = '1111, 1122, 1133, 3333, 2323' for the axisymmetric_rz fill method option.

Principal Directions for Stress and Strain

The fill method principal is appropriate for the case when the principal directions of strain and stress align. The engineering notation representation of the elasticity tensor is shown in Eq. (9). $(9)var element = document.getElementById("moose-equation-f7ced51b-31c0-430b-b948-d839b8543995");katex.render(" C_{ijkl}^{orthotropic} = \\begin{bmatrix} C_{11} & C_{12} & C_{13} & 0 & 0 & 0 \\\\ C_{21} & C_{22} & C_{23} & 0 & 0 & 0 \\\\ C_{31} & C_{32} & C_{33} & 0 & 0 & 0 \\\\ 0 & 0 & 0 & 0 & 0 & 0 \\\\ 0 & 0 & 0 & 0 & 0 & 0 \\\\ 0 & 0 & 0 & 0 & 0 & 0 \\end{bmatrix}", element, {displayMode:true,throwOnError:false});$

In the Einstein index notation shown in Eq. (2), the parameter C_ijkl expects the elasticity components in the order C_ijkl = '1111 1122 1133 2211 2222 2233 3311 3322 3333' for the principal fill method option.

Cosserat Elasticity Specific Fill Methods

The following fill methods are available within ComputeElasticityTensor, but the use cases for these methods fall within the Cosserat applications which do not preserve the equilibruim of angular momentum.

General Isotropic Symmetry

The fill method general_isotropic is used for the case of three independent components of an elasticity tensor, Eq. (10). $(10)var element = document.getElementById("moose-equation-32b99e87-5486-4716-84e0-b551eba40001");katex.render(" C_{ijkl}^{isotropic} = \\lambda \\delta_{ij} \\delta_{kl} + \\mu \\delta_{ik} \\delta_{ji} + \\kappa \\delta_{il} \\delta_{jk}", element, {displayMode:true,throwOnError:false});$

This fill method case is used in the child class ComputeCosseratElasticityTensor; please see the documentation for ComputeCosseratElasticityTensor for details and examples of the input file syntax.

General Antisymmetric

The fill method antisymmetric builds an antisymmetric elasticity tensor for a shear-only case. The symmetries shown in Eq. (11) are used to create the complete tensor $(11)var element = document.getElementById("moose-equation-0fbec10b-4969-4a36-b3b5-31eed744f0eb");katex.render(" C_{ijkl} = - C_{jikl} = - C_{ijlk} = C_{klij}", element, {displayMode:true,throwOnError:false});$ and the engineering notation representation of the anitsymmetric elasticity tensor is given in Eq. (12). $(12)var element = document.getElementById("moose-equation-e2be854e-4c94-4906-ac6c-2034534fa604");katex.render(" C_{ijkl}^{antisymmetric} = \\begin{bmatrix} 0 & 0 & 0 & 0 & 0 & 0 \\\\ 0 & 0 & 0 & 0 & 0 & 0 \\\\ 0 & 0 & 0 & 0 & 0 & 0 \\\\ 0 & 0 & 0 & C_{44} & -C_{54} & C_{64} \\\\ 0 & 0 & 0 & -C_{54} & -C_{55} & -C_{65} \\\\ 0 & 0 & 0 & C_{64} & -C_{65} & C_{66} \\end{bmatrix}", element, {displayMode:true,throwOnError:false});$

This fill method case is used in the child class ComputeCosseratElasticityTensor; please see the documentation for ComputeCosseratElasticityTensor for details and examples of the input file syntax.

No Symmetry

The general fill method for the Compute Elasticity Tensor class does not make any assumptions about symmetry for the elasticity tensor and requires all 81 components of the stiffness tensor as an input string. This fill method case is used in the child class ComputeCosseratElasticityTensor; please see the documentation for ComputeCosseratElasticityTensor for details and examples of the input file syntax.

Rotation Examples

Since the elasticity tensor is defined with respect to a given crystal orientation which may be different than the simulation coordinate frame, one may wish to apply a rotation to the elasticity tensor. Some example use cases include simulating a specific crystal plane in a 2D simulation or embedding a secondary phase in a matrix phase. The rotation ensures the correct stress is generated when a given strain is applied. Strain is calculated in the "sample" or "simulation" reference frame and so the proper "sample to crystal" rotation must be applied. As shown in Eq. (1), a rotation matrix is needed for this operation, which can be built with Euler angles or entered in the input file directly.

Rotation About An Axis

Suppose we wish to rotate the elasticity tensor about the z-axis by 30 degrees. The rotation matrix for rotating a vector by 30 degrees about the z-axis (an "active" rotation matrix) is $(13)var element = document.getElementById("moose-equation-431f4840-8e00-4bf0-98d6-1b17a3f7f1a5");katex.render(" R_z = \\begin{bmatrix} \\frac{\\sqrt{3}}{2} & -\\frac{1}{2} & 0 \\\\ \\frac{1}{2} & \\frac{\\sqrt{3}}{2} & 0 \\\\ 0 & 0 & 1 \\end{bmatrix} \\approx \\begin{bmatrix} 0.8660254 & -0.5 & 0 \\\\ 0.5 & 0.8660254 & 0 \\\\ 0 & 0 & 1 \\end{bmatrix}", element, {displayMode:true,throwOnError:false});$ Such a rotation can be implemented by directly supplying the rotation matrix in the input file using the rotation_matrix parameter in ComputeElasticityTensor.

Example Input File Syntax

[./elasticity_matrix]
  type = ComputeElasticityTensor
  block = 0
  base_name = 'rotation_matrix'
  fill_method = symmetric9
  C_ijkl = '1111 1122 1133 2222 2233 3333 2323 1313 1212'
  # rotation matrix for rotating a vector 30 degrees about the z-axis
  rotation_matrix = '0.8660254 -0.5       0.
                       0.5        0.8660254 0
                       0          0         1'
[../]

Note that the same rotation can be applied using Euler angles. MOOSE expects the "passive" (Bunge) convention, so the input angle is -30 degrees. Also note that since the $var element = document.getElementById("moose-equation-8bfb972e-c62a-4a31-a2c3-07899d9445ab");katex.render("Z_1 X_2 Z_3", element, {displayMode:false,throwOnError:false});$ convention is used, and only a single rotation is needed, the angle could be entered as either euler_angle_1 or euler_angle_3.

Example Input File Syntax

[./elasticity_euler]
  type = ComputeElasticityTensor
  block = 0
  base_name = 'euler'
  fill_method = symmetric9
  C_ijkl = '1111 1122 1133 2222 2233 3333 2323 1313 1212'
  euler_angle_1 = -30. # same as above but opposite direction because _transpose_ gets built from these angles
  euler_angle_2 = 0.
  euler_angle_3 = 0.
[../]

Orientation Relationship Rotation

Rather than a specific axis-angle rotation, sometimes the elasticity tensor must be rotated to satisfy a particular orientation relationship. In this case, the basis vectors of the rotated coordinate system are known, and the corresponding rotation matrix can be built using the unit basis vectors as rows of the rotation matrix. For example suppose we have the following rotation matrix that can be used in the case where the $var element = document.getElementById("moose-equation-d2028f7b-0a81-48bf-9319-43d4ac983b20");katex.render("\\left<111\\right>", element, {displayMode:false,throwOnError:false});$ direction of our rotated or "crystal" system points along the z-axis of our simulation or "sample" system. $(14)var element = document.getElementById("moose-equation-e7eb54ef-1f4b-43b7-8b1a-0df14d471cc2");katex.render(" R = \\begin{bmatrix} \\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{6}}{6} & \\frac{\\sqrt{3}}{3} \\\\ -\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{6}}{6} & \\frac{\\sqrt{3}}{3} \\\\ 0 & -\\frac{\\sqrt{6}}{3} & \\frac{\\sqrt{3}}{3} \\end{bmatrix} \\approx \\begin{bmatrix} 0.70710678 & 0.40824829 & 0.57735027 \\\\ -0.70710678 & 0.40824829 & 0.57735027 \\\\ 0 & -0.81649658 & 0.57735027 \\end{bmatrix}", element, {displayMode:true,throwOnError:false});$ To verify, we apply this rotation matrix to the $var element = document.getElementById("moose-equation-b4dffad4-30fb-49e0-bdc4-df46e4139fec");katex.render("\\hat{z}=\\left<001\\right>", element, {displayMode:false,throwOnError:false});$ direction of our "sample" or simulation frame: $var element = document.getElementById("moose-equation-66879097-c471-4aee-91bf-39f197321cfd");katex.render("R\\hat{z}=\\left<111\\right>", element, {displayMode:false,throwOnError:false});$ , meaning it correctly converts directions from "sample" to "crystal" frame, which is a "passive" rotation.

Example Input File Syntax

[./elasticity_matrix]
  type = ComputeElasticityTensor
  block = 0
  base_name = 'rotation_matrix'
  fill_method = symmetric9
  C_ijkl = '1111 1122 1133 2222 2233 3333 2323 1313 1212'
  # rotation matrix for rotating a vector
  #   1. 45 degrees about z-axis
  #   2. ~54.7 degrees (arccos(1/sqrt(3)) radians) about x-axis
  # then taking the tranpose to give sample-to-crystal rotation,
  # ie. R*([0,0,1]) = [1,1,1], meaning the <001> direction of the sample
  # (or simulation) frame points along the <111> direction of the crystal
  rotation_matrix = '0.70710678  0.40824829  0.57735027
                      -0.70710678  0.40824829  0.57735027
                       0.         -0.81649658  0.57735027'
[../]

The rotation matrix in Eq. (14) can also be built in an "active" sense by doing a 45 degree rotation about the z-axis and then a ~54.7 degree ( $var element = document.getElementById("moose-equation-c431516c-3cd1-44fc-8f36-a2aaa69e64e8");katex.render("\\arccos\\left(1/\\sqrt{3}\\right)", element, {displayMode:false,throwOnError:false});$ radians) rotation about the x-axis, then taking the transpose. Therefore these are the corresponding Euler angles to be used since we rotated the elasticity tensor by the "passive" matrix rather than the "active" matrix in the previous example. However, where more than 1 rotation is needed, the order of rotations matter. Since the Euler angle convention in MOOSE uses "extrinsic" rotations, the order must be reversed.

Example Input File Syntax

[./elasticity_euler]
  type = ComputeElasticityTensor
  block = 0
  base_name = 'euler'
  fill_method = symmetric9
  C_ijkl = '1111 1122 1133 2222 2233 3333 2323 1313 1212'
  # the angles here are the same as used to build the rotation matrix above because
  # we build the _transpose_ from euler angles in MOOSE, but we also transposed
  # the matrix for this example, so it goes back to the original;
  # the reversed order is due to the "extrinsic" convention used by MOOSE
  euler_angle_1 = 0.
  euler_angle_2 = 54.73561032
  euler_angle_3 = 45.
[../]

Input Parameters

C_ijklStiffness tensor for material
C++ Type:std::vector<double>
Controllable:No
Description:Stiffness tensor for material

Required Parameters

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
Controllable:No
Description:Optional parameter that allows the user to define multiple mechanics material systems on the same block, i.e. for multiple phases
blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
boundaryThe list of boundaries (ids or names) from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The list of boundaries (ids or names) from the mesh where this object applies
computeTrueWhen false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
Default:True
C++ Type:bool
Controllable:No
Description:When false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
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 computeQpProperties() 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
Controllable:No
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 computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
declare_suffixAn optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Controllable:No
Description:An optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.
elasticity_tensor_prefactorOptional function to use as a scalar prefactor on the elasticity tensor.
C++ Type:FunctionName
Controllable:No
Description:Optional function to use as a scalar prefactor on the elasticity tensor.
euler_angle_10Euler angle in direction 1
Default:0
C++ Type:double
Controllable:No
Description:Euler angle in direction 1
euler_angle_20Euler angle in direction 2
Default:0
C++ Type:double
Controllable:No
Description:Euler angle in direction 2
euler_angle_30Euler angle in direction 3
Default:0
C++ Type:double
Controllable:No
Description:Euler angle in direction 3
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, orthotropic
Controllable:No
Description:The fill method
prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Controllable:No
Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
rotation_matrixRotation matrix to apply to elasticity tensor.
C++ Type:libMesh::TensorValue<double>
Controllable:No
Description:Rotation matrix to apply to elasticity tensor.

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:Yes
Description:Set the enabled status of the MooseObject.
implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Controllable:No
Description:Determines whether this object is calculated using an implicit or explicit form
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Controllable:No
Description:The seed for the master random number generator
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
Controllable:No
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.

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<std::string>
Controllable:No
Description:List of material properties, from this material, to output (outputs must also be defined to an output type)
outputsnone Vector of output names where you would like to restrict the output of variables(s) associated with this object
Default:none
C++ Type:std::vector<OutputName>
Controllable:No
Description:Vector of output names where you would like to restrict the output of variables(s) associated with this object

Outputs Parameters

References

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

William S Slaughter. The Linearized Theory of Elasticity. Springer Science & Business Media, 2012.

(moose/modules/combined/test/tests/linear_elasticity/tensor.i)

# This input file is designed to test the RankTwoAux and RankFourAux
# auxkernels, which report values out of the Tensors used in materials
# properties.

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 2
  ny = 2
  nz = 0
  xmin = 0
  xmax = 2
  ymin = 0
  ymax = 2
  zmin = 0
  zmax = 0
  elem_type = QUAD4
[]

[Variables]
  [./diffused]
     [./InitialCondition]
      type = RandomIC
     [../]
  [../]
[]

[AuxVariables]
  [./C11]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./C12]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./C13]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./C14]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./C15]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./C16]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./C22]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./C23]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./C24]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./C25]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./C26]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./C33]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./C34]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./C35]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./C36]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./C44]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./C45]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./C46]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./C55]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./C56]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./C66]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[Modules/TensorMechanics/Master/All]
  strain = SMALL
  add_variables = true
  generate_output = 'stress_xx stress_yy stress_zz stress_xy stress_yz stress_zx'
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = diffused
  [../]
[]

[AuxKernels]
  [./matl_C11]
    type = RankFourAux
    rank_four_tensor = elasticity_tensor
    index_i = 0
    index_j = 0
    index_k = 0
    index_l = 0
    variable = C11
  [../]
  [./matl_C12]
    type = RankFourAux
    rank_four_tensor = elasticity_tensor
    index_i = 0
    index_j = 0
    index_k = 1
    index_l = 1
    variable = C12
  [../]
  [./matl_C13]
    type = RankFourAux
    rank_four_tensor = elasticity_tensor
    index_i = 0
    index_j = 0
    index_k = 2
    index_l = 2
    variable = C13
  [../]
  [./matl_C14]
    type = RankFourAux
    rank_four_tensor = elasticity_tensor
    index_i = 0
    index_j = 0
    index_k = 1
    index_l = 2
    variable = C14
  [../]
  [./matl_C15]
    type = RankFourAux
    rank_four_tensor = elasticity_tensor
    index_i = 0
    index_j = 0
    index_k = 0
    index_l = 2
    variable = C15
  [../]
  [./matl_C16]
    type = RankFourAux
    rank_four_tensor = elasticity_tensor
    index_i = 0
    index_j = 0
    index_k = 0
    index_l = 1
    variable = C16
  [../]
  [./matl_C22]
    type = RankFourAux
    rank_four_tensor = elasticity_tensor
    index_i = 1
    index_j = 1
    index_k = 1
    index_l = 1
    variable = C22
  [../]
  [./matl_C23]
    type = RankFourAux
    rank_four_tensor = elasticity_tensor
    index_i = 1
    index_j = 1
    index_k = 2
    index_l = 2
    variable = C23
  [../]
  [./matl_C24]
    type = RankFourAux
    rank_four_tensor = elasticity_tensor
    index_i = 1
    index_j = 1
    index_k = 1
    index_l = 2
    variable = C24
  [../]
  [./matl_C25]
    type = RankFourAux
    rank_four_tensor = elasticity_tensor
    index_i = 1
    index_j = 1
    index_k = 0
    index_l = 2
    variable = C25
  [../]
  [./matl_C26]
    type = RankFourAux
    rank_four_tensor = elasticity_tensor
    index_i = 1
    index_j = 1
    index_k = 0
    index_l = 1
    variable = C26
  [../]
 [./matl_C33]
    type = RankFourAux
    rank_four_tensor = elasticity_tensor
    index_i = 2
    index_j = 2
    index_k = 2
    index_l = 2
    variable = C33
  [../]
  [./matl_C34]
    type = RankFourAux
    rank_four_tensor = elasticity_tensor
    index_i = 2
    index_j = 2
    index_k = 1
    index_l = 2
    variable = C34
  [../]
  [./matl_C35]
    type = RankFourAux
    rank_four_tensor = elasticity_tensor
    index_i = 2
    index_j = 2
    index_k = 0
    index_l = 2
    variable = C35
  [../]
  [./matl_C36]
    type = RankFourAux
    rank_four_tensor = elasticity_tensor
    index_i = 2
    index_j = 2
    index_k = 0
    index_l = 1
    variable = C36
  [../]
  [./matl_C44]
    type = RankFourAux
    rank_four_tensor = elasticity_tensor
    index_i = 1
    index_j = 2
    index_k = 1
    index_l = 2
    variable = C44
  [../]
  [./matl_C45]
    type = RankFourAux
    rank_four_tensor = elasticity_tensor
    index_i = 1
    index_j = 2
    index_k = 0
    index_l = 2
    variable = C45
  [../]
  [./matl_C46]
    type = RankFourAux
    rank_four_tensor = elasticity_tensor
    index_i = 1
    index_j = 2
    index_k = 0
    index_l = 1
    variable = C46
  [../]
  [./matl_C55]
    type = RankFourAux
    rank_four_tensor = elasticity_tensor
    index_i = 0
    index_j = 2
    index_k = 0
    index_l = 2
    variable = C55
  [../]
  [./matl_C56]
    type = RankFourAux
    rank_four_tensor = elasticity_tensor
    index_i = 0
    index_j = 2
    index_k = 0
    index_l = 1
    variable = C56
  [../]
  [./matl_C66]
    type = RankFourAux
    rank_four_tensor = elasticity_tensor
    index_i = 0
    index_j = 1
    index_k = 0
    index_l = 1
    variable = C66
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeElasticityTensor
    fill_method = symmetric21
    C_ijkl ='1111 1122 1133 1123 1113 1112 2222 2233 2223 2213 2212 3333 3323 3313 3312 2323 2313 2312 1313 1312 1212'
  [../]
  [./stress]
    type = ComputeLinearElasticStress
  [../]
[]

[BCs]
  [./bottom]
    type = DirichletBC
    variable = diffused
    boundary = '1'
    value = 1
  [../]
  [./top]
    type = DirichletBC
    variable = diffused
    boundary = '2'
    value = 0
  [../]
  [./disp_x_BC]
    type = DirichletBC
    variable = disp_x
    boundary = '0 2'
    value = 0.5
  [../]
  [./disp_x_BC2]
    type = DirichletBC
    variable = disp_x
    boundary = '1 3'
    value = 0.01
  [../]
  [./disp_y_BC]
    type = DirichletBC
    variable = disp_y
    boundary = '0 2'
    value = 0.8
  [../]
  [./disp_y_BC2]
    type = DirichletBC
    variable = disp_y
    boundary = '1 3'
    value = 0.02
  [../]
[]

[Executioner]
  type = Steady
  solve_type = 'PJFNK'
[]

[Outputs]
  exodus = true
[]

(moose/modules/tensor_mechanics/test/tests/finite_strain_elastic/finite_strain_elastic_new_test.i)

[Mesh]
  type = GeneratedMesh
  dim = 3
  elem_type = HEX8
[]

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[Functions]
  [./tdisp]
    type = ParsedFunction
    expression = '0.01 * t'
  [../]
[]

[Modules]
  [./TensorMechanics]
    [./Master]
      [./all]
        strain = FINITE
        add_variables = true
      [../]
    [../]
  [../]
[]

[BCs]
  [./symmy]
    type = DirichletBC
    variable = disp_y
    boundary = bottom
    value = 0
  [../]
  [./symmx]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0
  [../]
  [./symmz]
    type = DirichletBC
    variable = disp_z
    boundary = back
    value = 0
  [../]
  [./tdisp]
    type = FunctionDirichletBC
    variable = disp_z
    boundary = front
    function = tdisp
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeElasticityTensor
    C_ijkl = '1.684e5 0.176e5 0.176e5 1.684e5 0.176e5 1.684e5 0.754e5 0.754e5 0.754e5'
    fill_method = symmetric9
  [../]
  [./stress]
    type = ComputeFiniteStrainElasticStress
  [../]
[]

[Preconditioning]
  [./smp]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Transient
  dt = 0.05

  #Preconditioned JFNK (default)
  solve_type = 'PJFNK'

  petsc_options_iname = -pc_hypre_type
  petsc_options_value = boomeramg
  nl_abs_tol = 1e-10
  nl_rel_step_tol = 1e-10
  dtmax = 10.0
  nl_rel_tol = 1e-10
  end_time = 1
  dtmin = 0.05
  num_steps = 10
  nl_abs_step_tol = 1e-10
[]

[Outputs]
  exodus = true
[]

(moose/modules/tensor_mechanics/test/tests/finite_strain_elastic_anisotropy/3d_bar_orthotropic_full_rotation.i)

[Mesh]
  [generated_mesh]
    type = GeneratedMeshGenerator
    dim = 3
    xmin = 0
    xmax = 2
    ymin = 0
    ymax = 10
    zmin = 0
    zmax = 2
    nx = 1
    ny = 1
    nz = 1
    elem_type = HEX8
  []
  [corner]
    type = ExtraNodesetGenerator
    new_boundary = 101
    coord = '0 0 0'
    input = generated_mesh
  []
  [side]
    type = ExtraNodesetGenerator
    new_boundary = 102
    coord = '2 0 0'
    input = corner
  []
[]

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[Modules/TensorMechanics/Master]
  [all]
    strain = FINITE
    add_variables = true
    use_finite_deform_jacobian = true
    volumetric_locking_correction = false
    generate_output = 'stress_xx stress_yy stress_zz stress_xy stress_xz'
  []
[]

[Materials]
  [stress]
    type = ComputeFiniteStrainElasticStress
  []
  [elasticity_tensor]
    type = ComputeElasticityTensor
    fill_method = orthotropic
    C_ijkl = '2.0e3 2.0e5 2.0e3 0.71428571e3 0.71428571e3 0.71428571e3 0.4 0.2 0.004 0.004 0.2 0.4'
  []
[]

[BCs]
  [fix_z]
    type = DirichletBC
    variable = disp_z
    boundary = bottom
    value = 0
  []

  [rot_y]
    type = DisplacementAboutAxis
    boundary = bottom
    function = t
    angle_units = degrees
    axis_origin = '0. 0. 0.'
    axis_direction = '0. 0. 1.'
    component = 1
    variable = disp_y
  []
  #
  [rot_x]
    type = DisplacementAboutAxis
    boundary = bottom
    function = t
    angle_units = degrees
    axis_origin = '0. 0. 0.'
    axis_direction = '0. 0. 1.'
    component = 0
    variable = disp_x
  []

  [rot_y90]
    type = DisplacementAboutAxis
    boundary = bottom
    function = 360
    angle_units = degrees
    axis_origin = '0. 0. 0.'
    axis_direction = '0. 0. 1.'
    component = 1
    variable = disp_y
  []
  #
  [rot_x90]
    type = DisplacementAboutAxis
    boundary = bottom
    function = 360
    angle_units = degrees
    axis_origin = '0. 0. 0.'
    axis_direction = '0. 0. 1.'
    component = 0
    variable = disp_x
  []

  [press]
    boundary = top
    function = '-1.0*(t-360)*10.0'
    use_displaced_mesh = true
    displacements = 'disp_x disp_y disp_z'
    type = Pressure
    variable = disp_y
  []

[]

[Controls]
  [c1]
    type = TimePeriod
    enable_objects = 'BCs::rot_x BCs::rot_y'
    disable_objects = 'BCs::rot_x90 BCs::rot_y90 BCs::press'
    start_time = '0'
    end_time = '360'
  []
  [c190plus]
    type = TimePeriod
    enable_objects = 'BCs::rot_x90 BCs::rot_y90 BCs::press'
    disable_objects = 'BCs::rot_x BCs::rot_y '
    start_time = '360'
    end_time = '660'
  []
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-ksp_gmres_restart'
  petsc_options_value = '101'

  line_search = 'none'

  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-08
  nl_max_its = 50

  l_tol = 1e-4
  l_max_its = 50
  start_time = 0.0

  dt = 5
  dtmin = 5

  num_steps = 132
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Outputs]
  exodus = true
[]

(moose/modules/tensor_mechanics/test/tests/isotropic_elasticity_tensor/2D-axisymmetric_rz_test.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  elem_type = QUAD8
[]

[GlobalParams]
  displacements = 'disp_r disp_z'
[]

[Problem]
  coord_type = RZ
[]

[Modules/TensorMechanics/Master]
  [./all]
    strain = SMALL
    add_variables = true
  [../]
[]

[AuxVariables]
  [./stress_theta]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[AuxKernels]
  [./stress_theta]
    type = RankTwoAux
    rank_two_tensor = stress
    index_i = 2
    index_j = 2
    variable = stress_theta
    execute_on = timestep_end
  [../]
[]

[Materials]
  [./elasticity_tensor]
    #Material constants selected to match isotropic lambda and shear modulus case
    type = ComputeElasticityTensor
    C_ijkl = '1022726 113636 113636 1022726 454545'
    fill_method = axisymmetric_rz
  [../]
  [./elastic_stress]
    type = ComputeLinearElasticStress
  [../]
[]

[BCs]
# pin particle along symmetry planes
  [./no_disp_r]
    type = DirichletBC
    variable = disp_r
    boundary = left
    value = 0.0
  [../]

  [./no_disp_z]
    type = DirichletBC
    variable = disp_z
    boundary = bottom
    value = 0.0
  [../]

# exterior and internal pressures
  [./exterior_pressure_r]
    type = Pressure
    variable = disp_r
    boundary = right
    factor = 200000
  [../]
[]

[Debug]
  show_var_residual_norms = true
[]

[Executioner]
  type = Transient

  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
  petsc_options_value = '  201               hypre    boomeramg      10'

  line_search = 'none'

  #Preconditioned JFNK (default)
  solve_type = 'PJFNK'

  nl_rel_tol = 5e-9
  nl_abs_tol = 1e-10
  nl_max_its = 15

  l_tol = 1e-3
  l_max_its = 50

  start_time = 0.0
  end_time = 1
  num_steps = 1000

  dtmax = 5e6
  dtmin = 1

  [./TimeStepper]
    type = IterationAdaptiveDT
    dt = 1
    optimal_iterations = 6
    iteration_window = 0
    linear_iteration_ratio = 100
  [../]

  [./Predictor]
    type = SimplePredictor
    scale = 1.0
  [../]

[]

[Postprocessors]
  [./dt]
    type = TimestepSize
  [../]
[]

[Outputs]
  file_base = 2D-axisymmetric_rz_test_out
  exodus = true
[]

(moose/modules/tensor_mechanics/test/tests/elasticitytensor/rotation_matrix_1_rotation.i)

# This input file is designed to rotate an elasticity tensor both with euler angles
# and a rotation matrix. The rotated tensor components should match between the
# two methods.

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 20
  xmax = 1
[]

[AuxVariables]
  [./C1111_aux_matrix]  # C11
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./C1122_aux_matrix]  # C12
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./C1133_aux_matrix]  # C13
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./C1112_aux_matrix]  # C16
    order = CONSTANT
    family = MONOMIAL
  [../]

  [./C1111_aux_euler]  # C11
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./C1122_aux_euler]  # C12
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./C1133_aux_euler]  # C13
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./C1112_aux_euler]  # C16
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[AuxKernels]
  [./matl_C1111_matrix]  # C11
    type = RankFourAux
    rank_four_tensor = rotation_matrix_elasticity_tensor
    index_i = 0
    index_j = 0
    index_k = 0
    index_l = 0
    variable = C1111_aux_matrix
    execute_on = initial
  [../]
  [./matl_C1122_matrix]  # C12
    type = RankFourAux
    rank_four_tensor = rotation_matrix_elasticity_tensor
    index_i = 0
    index_j = 0
    index_k = 1
    index_l = 1
    variable = C1122_aux_matrix
    execute_on = initial
  [../]
  [./matl_C1133_matrix]  # C13
    type = RankFourAux
    rank_four_tensor = rotation_matrix_elasticity_tensor
    index_i = 0
    index_j = 0
    index_k = 2
    index_l = 2
    variable = C1133_aux_matrix
    execute_on = initial
  [../]
  [./matl_C1112_matrix]  # C16
    type = RankFourAux
    rank_four_tensor = rotation_matrix_elasticity_tensor
    index_i = 0
    index_j = 0
    index_k = 0
    index_l = 1
    variable = C1112_aux_matrix
    execute_on = initial
  [../]

  [./matl_C1111_euler]  # C11
    type = RankFourAux
    rank_four_tensor = euler_elasticity_tensor
    index_i = 0
    index_j = 0
    index_k = 0
    index_l = 0
    variable = C1111_aux_euler
    execute_on = initial
  [../]
  [./matl_C1122_euler]  # C12
    type = RankFourAux
    rank_four_tensor = euler_elasticity_tensor
    index_i = 0
    index_j = 0
    index_k = 1
    index_l = 1
    variable = C1122_aux_euler
    execute_on = initial
  [../]
  [./matl_C1133_euler]  # C13
    type = RankFourAux
    rank_four_tensor = euler_elasticity_tensor
    index_i = 0
    index_j = 0
    index_k = 2
    index_l = 2
    variable = C1133_aux_euler
    execute_on = initial
  [../]
  [./matl_C1112_euler]  # C16
    type = RankFourAux
    rank_four_tensor = euler_elasticity_tensor
    index_i = 0
    index_j = 0
    index_k = 0
    index_l = 1
    variable = C1112_aux_euler
    execute_on = initial
  [../]
[]

[Materials]
  [./elasticity_matrix]
    type = ComputeElasticityTensor
    block = 0
    base_name = 'rotation_matrix'
    fill_method = symmetric9
    C_ijkl = '1111 1122 1133 2222 2233 3333 2323 1313 1212'
    # rotation matrix for rotating a vector 30 degrees about the z-axis
    rotation_matrix = '0.8660254 -0.5       0.
                       0.5        0.8660254 0
                       0          0         1'
  [../]
  [./elasticity_euler]
    type = ComputeElasticityTensor
    block = 0
    base_name = 'euler'
    fill_method = symmetric9
    C_ijkl = '1111 1122 1133 2222 2233 3333 2323 1313 1212'
    euler_angle_1 = -30.  # same as above but opposite direction because _transpose_ gets built from these angles
    euler_angle_2 = 0.
    euler_angle_3 = 0.
  [../]
[]

[Problem]
  kernel_coverage_check = false
  solve = false
[]

[Executioner]
  type = Steady
[]

[Postprocessors]
  # corresponding values in "matrix" and "euler" postprocessors should match
  [./C11_matrix]
    type = ElementAverageValue
    variable = C1111_aux_matrix
    execute_on = 'INITIAL TIMESTEP_END'
  [../]
  [./C12_matrix]
    type = ElementAverageValue
    variable = C1122_aux_matrix
    execute_on = 'INITIAL TIMESTEP_END'
  [../]
  [./C13_matrix]
    type = ElementAverageValue
    variable = C1133_aux_matrix
    execute_on = 'INITIAL TIMESTEP_END'
  [../]
  [./C16_matrix]
    type = ElementAverageValue
    variable = C1112_aux_matrix
    execute_on = 'INITIAL TIMESTEP_END'
  [../]

  [./C11_euler]
    type = ElementAverageValue
    variable = C1111_aux_euler
    execute_on = 'INITIAL TIMESTEP_END'
  [../]
  [./C12_euler]
    type = ElementAverageValue
    variable = C1122_aux_euler
    execute_on = 'INITIAL TIMESTEP_END'
  [../]
  [./C13_euler]
    type = ElementAverageValue
    variable = C1133_aux_euler
    execute_on = 'INITIAL TIMESTEP_END'
  [../]
  [./C16_euler]
    type = ElementAverageValue
    variable = C1112_aux_euler
    execute_on = 'INITIAL TIMESTEP_END'
  [../]
[]

[Outputs]
  exodus = true
[]

(moose/modules/tensor_mechanics/test/tests/elasticitytensor/rotation_matrix_1_rotation.i)

# This input file is designed to rotate an elasticity tensor both with euler angles
# and a rotation matrix. The rotated tensor components should match between the
# two methods.

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 20
  xmax = 1
[]

[AuxVariables]
  [./C1111_aux_matrix]  # C11
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./C1122_aux_matrix]  # C12
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./C1133_aux_matrix]  # C13
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./C1112_aux_matrix]  # C16
    order = CONSTANT
    family = MONOMIAL
  [../]

  [./C1111_aux_euler]  # C11
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./C1122_aux_euler]  # C12
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./C1133_aux_euler]  # C13
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./C1112_aux_euler]  # C16
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[AuxKernels]
  [./matl_C1111_matrix]  # C11
    type = RankFourAux
    rank_four_tensor = rotation_matrix_elasticity_tensor
    index_i = 0
    index_j = 0
    index_k = 0
    index_l = 0
    variable = C1111_aux_matrix
    execute_on = initial
  [../]
  [./matl_C1122_matrix]  # C12
    type = RankFourAux
    rank_four_tensor = rotation_matrix_elasticity_tensor
    index_i = 0
    index_j = 0
    index_k = 1
    index_l = 1
    variable = C1122_aux_matrix
    execute_on = initial
  [../]
  [./matl_C1133_matrix]  # C13
    type = RankFourAux
    rank_four_tensor = rotation_matrix_elasticity_tensor
    index_i = 0
    index_j = 0
    index_k = 2
    index_l = 2
    variable = C1133_aux_matrix
    execute_on = initial
  [../]
  [./matl_C1112_matrix]  # C16
    type = RankFourAux
    rank_four_tensor = rotation_matrix_elasticity_tensor
    index_i = 0
    index_j = 0
    index_k = 0
    index_l = 1
    variable = C1112_aux_matrix
    execute_on = initial
  [../]

  [./matl_C1111_euler]  # C11
    type = RankFourAux
    rank_four_tensor = euler_elasticity_tensor
    index_i = 0
    index_j = 0
    index_k = 0
    index_l = 0
    variable = C1111_aux_euler
    execute_on = initial
  [../]
  [./matl_C1122_euler]  # C12
    type = RankFourAux
    rank_four_tensor = euler_elasticity_tensor
    index_i = 0
    index_j = 0
    index_k = 1
    index_l = 1
    variable = C1122_aux_euler
    execute_on = initial
  [../]
  [./matl_C1133_euler]  # C13
    type = RankFourAux
    rank_four_tensor = euler_elasticity_tensor
    index_i = 0
    index_j = 0
    index_k = 2
    index_l = 2
    variable = C1133_aux_euler
    execute_on = initial
  [../]
  [./matl_C1112_euler]  # C16
    type = RankFourAux
    rank_four_tensor = euler_elasticity_tensor
    index_i = 0
    index_j = 0
    index_k = 0
    index_l = 1
    variable = C1112_aux_euler
    execute_on = initial
  [../]
[]

[Materials]
  [./elasticity_matrix]
    type = ComputeElasticityTensor
    block = 0
    base_name = 'rotation_matrix'
    fill_method = symmetric9
    C_ijkl = '1111 1122 1133 2222 2233 3333 2323 1313 1212'
    # rotation matrix for rotating a vector 30 degrees about the z-axis
    rotation_matrix = '0.8660254 -0.5       0.
                       0.5        0.8660254 0
                       0          0         1'
  [../]
  [./elasticity_euler]
    type = ComputeElasticityTensor
    block = 0
    base_name = 'euler'
    fill_method = symmetric9
    C_ijkl = '1111 1122 1133 2222 2233 3333 2323 1313 1212'
    euler_angle_1 = -30.  # same as above but opposite direction because _transpose_ gets built from these angles
    euler_angle_2 = 0.
    euler_angle_3 = 0.
  [../]
[]

[Problem]
  kernel_coverage_check = false
  solve = false
[]

[Executioner]
  type = Steady
[]

[Postprocessors]
  # corresponding values in "matrix" and "euler" postprocessors should match
  [./C11_matrix]
    type = ElementAverageValue
    variable = C1111_aux_matrix
    execute_on = 'INITIAL TIMESTEP_END'
  [../]
  [./C12_matrix]
    type = ElementAverageValue
    variable = C1122_aux_matrix
    execute_on = 'INITIAL TIMESTEP_END'
  [../]
  [./C13_matrix]
    type = ElementAverageValue
    variable = C1133_aux_matrix
    execute_on = 'INITIAL TIMESTEP_END'
  [../]
  [./C16_matrix]
    type = ElementAverageValue
    variable = C1112_aux_matrix
    execute_on = 'INITIAL TIMESTEP_END'
  [../]

  [./C11_euler]
    type = ElementAverageValue
    variable = C1111_aux_euler
    execute_on = 'INITIAL TIMESTEP_END'
  [../]
  [./C12_euler]
    type = ElementAverageValue
    variable = C1122_aux_euler
    execute_on = 'INITIAL TIMESTEP_END'
  [../]
  [./C13_euler]
    type = ElementAverageValue
    variable = C1133_aux_euler
    execute_on = 'INITIAL TIMESTEP_END'
  [../]
  [./C16_euler]
    type = ElementAverageValue
    variable = C1112_aux_euler
    execute_on = 'INITIAL TIMESTEP_END'
  [../]
[]

[Outputs]
  exodus = true
[]

(moose/modules/tensor_mechanics/test/tests/elasticitytensor/rotation_matrix_2_rotations.i)

# This input file is designed to rotate an elasticity tensor both with euler angles
# and a rotation matrix. The rotated tensor components should match between the
# two methods.

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 20
  xmax = 1
[]

[AuxVariables]
  [./C1111_aux_matrix]  # C11
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./C1122_aux_matrix]  # C12
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./C1133_aux_matrix]  # C13
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./C1112_aux_matrix]  # C16
    order = CONSTANT
    family = MONOMIAL
  [../]

  [./C1111_aux_euler]  # C11
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./C1122_aux_euler]  # C12
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./C1133_aux_euler]  # C13
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./C1112_aux_euler]  # C16
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[AuxKernels]
  [./matl_C1111_matrix]  # C11
    type = RankFourAux
    rank_four_tensor = rotation_matrix_elasticity_tensor
    index_i = 0
    index_j = 0
    index_k = 0
    index_l = 0
    variable = C1111_aux_matrix
    execute_on = initial
  [../]
  [./matl_C1122_matrix]  # C12
    type = RankFourAux
    rank_four_tensor = rotation_matrix_elasticity_tensor
    index_i = 0
    index_j = 0
    index_k = 1
    index_l = 1
    variable = C1122_aux_matrix
    execute_on = initial
  [../]
  [./matl_C1133_matrix]  # C13
    type = RankFourAux
    rank_four_tensor = rotation_matrix_elasticity_tensor
    index_i = 0
    index_j = 0
    index_k = 2
    index_l = 2
    variable = C1133_aux_matrix
    execute_on = initial
  [../]
  [./matl_C1112_matrix]  # C16
    type = RankFourAux
    rank_four_tensor = rotation_matrix_elasticity_tensor
    index_i = 0
    index_j = 0
    index_k = 0
    index_l = 1
    variable = C1112_aux_matrix
    execute_on = initial
  [../]

  [./matl_C1111_euler]  # C11
    type = RankFourAux
    rank_four_tensor = euler_elasticity_tensor
    index_i = 0
    index_j = 0
    index_k = 0
    index_l = 0
    variable = C1111_aux_euler
    execute_on = initial
  [../]
  [./matl_C1122_euler]  # C12
    type = RankFourAux
    rank_four_tensor = euler_elasticity_tensor
    index_i = 0
    index_j = 0
    index_k = 1
    index_l = 1
    variable = C1122_aux_euler
    execute_on = initial
  [../]
  [./matl_C1133_euler]  # C13
    type = RankFourAux
    rank_four_tensor = euler_elasticity_tensor
    index_i = 0
    index_j = 0
    index_k = 2
    index_l = 2
    variable = C1133_aux_euler
    execute_on = initial
  [../]
  [./matl_C1112_euler]  # C16
    type = RankFourAux
    rank_four_tensor = euler_elasticity_tensor
    index_i = 0
    index_j = 0
    index_k = 0
    index_l = 1
    variable = C1112_aux_euler
    execute_on = initial
  [../]
[]

[Materials]
  [./elasticity_matrix]
    type = ComputeElasticityTensor
    block = 0
    base_name = 'rotation_matrix'
    fill_method = symmetric9
    C_ijkl = '1111 1122 1133 2222 2233 3333 2323 1313 1212'
    # rotation matrix for rotating a vector
    #   1. 45 degrees about z-axis
    #   2. ~54.7 degrees (arccos(1/sqrt(3)) radians) about x-axis
    # then taking the tranpose to give sample-to-crystal rotation,
    # ie. R*([0,0,1]) = [1,1,1], meaning the <001> direction of the sample
    # (or simulation) frame points along the <111> direction of the crystal
    rotation_matrix = '0.70710678  0.40824829  0.57735027
                      -0.70710678  0.40824829  0.57735027
                       0.         -0.81649658  0.57735027'
  [../]
  [./elasticity_euler]
    type = ComputeElasticityTensor
    block = 0
    base_name = 'euler'
    fill_method = symmetric9
    C_ijkl = '1111 1122 1133 2222 2233 3333 2323 1313 1212'
    # the angles here are the same as used to build the rotation matrix above because
    # we build the _transpose_ from euler angles in MOOSE, but we also transposed
    # the matrix for this example, so it goes back to the original;
    # the reversed order is due to the "extrinsic" convention used by MOOSE
    euler_angle_1 = 0.
    euler_angle_2 = 54.73561032
    euler_angle_3 = 45.
  [../]
[]

[Problem]
  kernel_coverage_check = false
  solve = false
[]

[Executioner]
  type = Steady
[]

[Postprocessors]
  # corresponding values in "matrix" and "euler" postprocessors should match
  [./C11_matrix]
    type = ElementAverageValue
    variable = C1111_aux_matrix
    execute_on = 'INITIAL TIMESTEP_END'
  [../]
  [./C12_matrix]
    type = ElementAverageValue
    variable = C1122_aux_matrix
    execute_on = 'INITIAL TIMESTEP_END'
  [../]
  [./C13_matrix]
    type = ElementAverageValue
    variable = C1133_aux_matrix
    execute_on = 'INITIAL TIMESTEP_END'
  [../]
  [./C16_matrix]
    type = ElementAverageValue
    variable = C1112_aux_matrix
    execute_on = 'INITIAL TIMESTEP_END'
  [../]

  [./C11_euler]
    type = ElementAverageValue
    variable = C1111_aux_euler
    execute_on = 'INITIAL TIMESTEP_END'
  [../]
  [./C12_euler]
    type = ElementAverageValue
    variable = C1122_aux_euler
    execute_on = 'INITIAL TIMESTEP_END'
  [../]
  [./C13_euler]
    type = ElementAverageValue
    variable = C1133_aux_euler
    execute_on = 'INITIAL TIMESTEP_END'
  [../]
  [./C16_euler]
    type = ElementAverageValue
    variable = C1112_aux_euler
    execute_on = 'INITIAL TIMESTEP_END'
  [../]
[]

[Outputs]
  exodus = true
[]

(moose/modules/tensor_mechanics/test/tests/elasticitytensor/rotation_matrix_2_rotations.i)

# This input file is designed to rotate an elasticity tensor both with euler angles
# and a rotation matrix. The rotated tensor components should match between the
# two methods.

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 20
  xmax = 1
[]

[AuxVariables]
  [./C1111_aux_matrix]  # C11
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./C1122_aux_matrix]  # C12
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./C1133_aux_matrix]  # C13
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./C1112_aux_matrix]  # C16
    order = CONSTANT
    family = MONOMIAL
  [../]

  [./C1111_aux_euler]  # C11
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./C1122_aux_euler]  # C12
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./C1133_aux_euler]  # C13
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./C1112_aux_euler]  # C16
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[AuxKernels]
  [./matl_C1111_matrix]  # C11
    type = RankFourAux
    rank_four_tensor = rotation_matrix_elasticity_tensor
    index_i = 0
    index_j = 0
    index_k = 0
    index_l = 0
    variable = C1111_aux_matrix
    execute_on = initial
  [../]
  [./matl_C1122_matrix]  # C12
    type = RankFourAux
    rank_four_tensor = rotation_matrix_elasticity_tensor
    index_i = 0
    index_j = 0
    index_k = 1
    index_l = 1
    variable = C1122_aux_matrix
    execute_on = initial
  [../]
  [./matl_C1133_matrix]  # C13
    type = RankFourAux
    rank_four_tensor = rotation_matrix_elasticity_tensor
    index_i = 0
    index_j = 0
    index_k = 2
    index_l = 2
    variable = C1133_aux_matrix
    execute_on = initial
  [../]
  [./matl_C1112_matrix]  # C16
    type = RankFourAux
    rank_four_tensor = rotation_matrix_elasticity_tensor
    index_i = 0
    index_j = 0
    index_k = 0
    index_l = 1
    variable = C1112_aux_matrix
    execute_on = initial
  [../]

  [./matl_C1111_euler]  # C11
    type = RankFourAux
    rank_four_tensor = euler_elasticity_tensor
    index_i = 0
    index_j = 0
    index_k = 0
    index_l = 0
    variable = C1111_aux_euler
    execute_on = initial
  [../]
  [./matl_C1122_euler]  # C12
    type = RankFourAux
    rank_four_tensor = euler_elasticity_tensor
    index_i = 0
    index_j = 0
    index_k = 1
    index_l = 1
    variable = C1122_aux_euler
    execute_on = initial
  [../]
  [./matl_C1133_euler]  # C13
    type = RankFourAux
    rank_four_tensor = euler_elasticity_tensor
    index_i = 0
    index_j = 0
    index_k = 2
    index_l = 2
    variable = C1133_aux_euler
    execute_on = initial
  [../]
  [./matl_C1112_euler]  # C16
    type = RankFourAux
    rank_four_tensor = euler_elasticity_tensor
    index_i = 0
    index_j = 0
    index_k = 0
    index_l = 1
    variable = C1112_aux_euler
    execute_on = initial
  [../]
[]

[Materials]
  [./elasticity_matrix]
    type = ComputeElasticityTensor
    block = 0
    base_name = 'rotation_matrix'
    fill_method = symmetric9
    C_ijkl = '1111 1122 1133 2222 2233 3333 2323 1313 1212'
    # rotation matrix for rotating a vector
    #   1. 45 degrees about z-axis
    #   2. ~54.7 degrees (arccos(1/sqrt(3)) radians) about x-axis
    # then taking the tranpose to give sample-to-crystal rotation,
    # ie. R*([0,0,1]) = [1,1,1], meaning the <001> direction of the sample
    # (or simulation) frame points along the <111> direction of the crystal
    rotation_matrix = '0.70710678  0.40824829  0.57735027
                      -0.70710678  0.40824829  0.57735027
                       0.         -0.81649658  0.57735027'
  [../]
  [./elasticity_euler]
    type = ComputeElasticityTensor
    block = 0
    base_name = 'euler'
    fill_method = symmetric9
    C_ijkl = '1111 1122 1133 2222 2233 3333 2323 1313 1212'
    # the angles here are the same as used to build the rotation matrix above because
    # we build the _transpose_ from euler angles in MOOSE, but we also transposed
    # the matrix for this example, so it goes back to the original;
    # the reversed order is due to the "extrinsic" convention used by MOOSE
    euler_angle_1 = 0.
    euler_angle_2 = 54.73561032
    euler_angle_3 = 45.
  [../]
[]

[Problem]
  kernel_coverage_check = false
  solve = false
[]

[Executioner]
  type = Steady
[]

[Postprocessors]
  # corresponding values in "matrix" and "euler" postprocessors should match
  [./C11_matrix]
    type = ElementAverageValue
    variable = C1111_aux_matrix
    execute_on = 'INITIAL TIMESTEP_END'
  [../]
  [./C12_matrix]
    type = ElementAverageValue
    variable = C1122_aux_matrix
    execute_on = 'INITIAL TIMESTEP_END'
  [../]
  [./C13_matrix]
    type = ElementAverageValue
    variable = C1133_aux_matrix
    execute_on = 'INITIAL TIMESTEP_END'
  [../]
  [./C16_matrix]
    type = ElementAverageValue
    variable = C1112_aux_matrix
    execute_on = 'INITIAL TIMESTEP_END'
  [../]

  [./C11_euler]
    type = ElementAverageValue
    variable = C1111_aux_euler
    execute_on = 'INITIAL TIMESTEP_END'
  [../]
  [./C12_euler]
    type = ElementAverageValue
    variable = C1122_aux_euler
    execute_on = 'INITIAL TIMESTEP_END'
  [../]
  [./C13_euler]
    type = ElementAverageValue
    variable = C1133_aux_euler
    execute_on = 'INITIAL TIMESTEP_END'
  [../]
  [./C16_euler]
    type = ElementAverageValue
    variable = C1112_aux_euler
    execute_on = 'INITIAL TIMESTEP_END'
  [../]
[]

[Outputs]
  exodus = true
[]