- variableThe name of the variable that this object applies to
C++ Type:AuxVariableName
Unit:(no unit assumed)
Controllable:No
Description:The name of the variable that this object applies to
TotalFreeEnergy
buildconstruction:Undocumented Class
The TotalFreeEnergy has not been documented. The content listed below should be used as a starting point for documenting the class, which includes the typical automatic documentation associated with a MooseObject; however, what is contained is ultimately determined by what is necessary to make the documentation clear for users.
Total free energy (both the bulk and gradient parts), where the bulk free energy has been defined in a material
Overview
Example Input File Syntax
Input Parameters
- additional_free_energyCoupled variable holding additional free energy contributions to be summed up
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled variable holding additional free energy contributions to be summed up
- 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
- check_boundary_restrictedTrueWhether to check for multiple element sides on the boundary in the case of a boundary restricted, element aux variable. Setting this to false will allow contribution to a single element's elemental value(s) from multiple boundary sides on the same element (example: when the restricted boundary exists on two or more sides of an element, such as at a corner of a mesh
Default:True
C++ Type:bool
Controllable:No
Description:Whether to check for multiple element sides on the boundary in the case of a boundary restricted, element aux variable. Setting this to false will allow contribution to a single element's elemental value(s) from multiple boundary sides on the same element (example: when the restricted boundary exists on two or more sides of an element, such as at a corner of a mesh
- execute_onLINEAR TIMESTEP_ENDThe list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
Default:LINEAR TIMESTEP_END
C++ Type:ExecFlagEnum
Options:XFEM_MARK, FORWARD, ADJOINT, HOMOGENEOUS_FORWARD, ADJOINT_TIMESTEP_BEGIN, ADJOINT_TIMESTEP_END, NONE, INITIAL, LINEAR, LINEAR_CONVERGENCE, NONLINEAR, NONLINEAR_CONVERGENCE, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, MULTIAPP_FIXED_POINT_CONVERGENCE, FINAL, CUSTOM, PRE_DISPLACE
Controllable:No
Description:The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
- f_nameF Base name of the free energy function
Default:F
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description: Base name of the free energy function
- interfacial_varsVariable names that contribute to interfacial energy
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Variable names that contribute to interfacial energy
- kappa_namesVector of kappa names corresponding to each variable name in interfacial_vars in the same order.
C++ Type:std::vector<MaterialPropertyName>
Unit:(no unit assumed)
Controllable:No
Description:Vector of kappa names corresponding to each variable name in interfacial_vars in the same order.
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.
- search_methodnearest_node_connected_sidesChoice of search algorithm. All options begin by finding the nearest node in the primary boundary to a query point in the secondary boundary. In the default nearest_node_connected_sides algorithm, primary boundary elements are searched iff that nearest node is one of their nodes. This is fast to determine via a pregenerated node-to-elem map and is robust on conforming meshes. In the optional all_proximate_sides algorithm, primary boundary elements are searched iff they touch that nearest node, even if they are not topologically connected to it. This is more CPU-intensive but is necessary for robustness on any boundary surfaces which has disconnections (such as Flex IGA meshes) or non-conformity (such as hanging nodes in adaptively h-refined meshes).
Default:nearest_node_connected_sides
C++ Type:MooseEnum
Options:nearest_node_connected_sides, all_proximate_sides
Controllable:No
Description:Choice of search algorithm. All options begin by finding the nearest node in the primary boundary to a query point in the secondary boundary. In the default nearest_node_connected_sides algorithm, primary boundary elements are searched iff that nearest node is one of their nodes. This is fast to determine via a pregenerated node-to-elem map and is robust on conforming meshes. In the optional all_proximate_sides algorithm, primary boundary elements are searched iff they touch that nearest node, even if they are not topologically connected to it. This is more CPU-intensive but is necessary for robustness on any boundary surfaces which has disconnections (such as Flex IGA meshes) or non-conformity (such as hanging nodes in adaptively h-refined meshes).
- 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
- 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
Unit:(no unit assumed)
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.
- use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Default:False
C++ Type:bool
Controllable:No
Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Material Property Retrieval Parameters
Input Files
- (modules/combined/examples/publications/rapid_dev/fig7b.i)
- (modules/phase_field/examples/cahn-hilliard/Parsed_SplitCH.i)
- (modules/phase_field/examples/multiphase/DerivativeMultiPhaseMaterial.i)
- (modules/combined/examples/periodic_strain/global_strain_pfm.i)
- (modules/combined/examples/phase_field-mechanics/Pattern1.i)
- (modules/phase_field/test/tests/GrandPotentialPFM/GrandPotentialSintering_test.i)
- (modules/phase_field/tutorials/spinodal_decomposition/s5_energycurve.i)
- (modules/phase_field/test/tests/actions/conserved_forward_split_1var.i)
- (modules/combined/examples/publications/rapid_dev/fig8.i)
- (modules/phase_field/test/tests/SplitCH/forward_split_math_test.i)
- (modules/phase_field/examples/cahn-hilliard/Parsed_CH.i)
- (modules/phase_field/examples/measure_interface_energy/1Dinterface_energy.i)
- (modules/combined/examples/periodic_strain/global_strain_pfm_3D.i)
- (modules/combined/examples/mortar/eigenstrain_action.i)
- (modules/combined/examples/publications/rapid_dev/fig7a.i)
- (modules/combined/examples/mortar/eigenstrain.i)
- (modules/phase_field/test/tests/TotalFreeEnergy/TotalFreeEnergy_2var_test.i)
- (modules/phase_field/examples/rigidbodymotion/AC_CH_Multigrain.i)
- (modules/phase_field/test/tests/free_energy_material/CoupledValueFunctionFreeEnergy.i)
- (modules/phase_field/test/tests/MultiPhase/crosstermfreeenergy.i)
- (modules/phase_field/test/tests/TotalFreeEnergy/TotalFreeEnergy_test.i)
(modules/combined/examples/publications/rapid_dev/fig7b.i)
#
# Fig. 7 input for 10.1016/j.commatsci.2017.02.017
# D. Schwen et al./Computational Materials Science 132 (2017) 36-45
# Dashed black curve (2)
# Eigenstrain is globally applied. Single global elastic free energies.
# Supply the RADIUS parameter (10-35) on the command line to generate data
# for all curves in the plot.
#
[Mesh]
type = GeneratedMesh
dim = 1
nx = 32
xmin = 0
xmax = 100
second_order = true
coord_type = RSPHERICAL
[]
[GlobalParams]
displacements = 'disp_r'
[]
[Functions]
[./diff]
type = ParsedFunction
expression = '${RADIUS}-pos_c'
symbol_names = pos_c
symbol_values = pos_c
[../]
[]
# AuxVars to compute the free energy density for outputting
[AuxVariables]
[./local_energy]
order = CONSTANT
family = MONOMIAL
[../]
[./cross_energy]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
[./local_free_energy]
type = TotalFreeEnergy
variable = local_energy
interfacial_vars = 'c'
kappa_names = 'kappa_c'
execute_on = 'INITIAL TIMESTEP_END'
[../]
[]
[Variables]
# Solute concentration variable
[./c]
[./InitialCondition]
type = SmoothCircleIC
invalue = 1
outvalue = 0
x1 = 0
y1 = 0
radius = ${RADIUS}
int_width = 3
[../]
[../]
[./w]
[../]
# Phase order parameter
[./eta]
[./InitialCondition]
type = SmoothCircleIC
invalue = 1
outvalue = 0
x1 = 0
y1 = 0
radius = ${RADIUS}
int_width = 3
[../]
[../]
[./Fe_fit]
order = SECOND
[../]
[]
[Physics/SolidMechanics/QuasiStatic/all]
add_variables = true
eigenstrain_names = eigenstrain
[]
[Kernels]
# Split Cahn-Hilliard kernels
[./c_res]
type = SplitCHParsed
variable = c
f_name = F
coupled_variables = 'eta'
kappa_name = kappa_c
w = w
[../]
[./wres]
type = SplitCHWRes
variable = w
mob_name = M
[../]
[./time]
type = CoupledTimeDerivative
variable = w
v = c
[../]
# Allen-Cahn and Lagrange-multiplier constraint kernels for order parameter 1
[./detadt]
type = TimeDerivative
variable = eta
[../]
[./ACBulk1]
type = AllenCahn
variable = eta
coupled_variables = 'c'
mob_name = L
f_name = F
[../]
[./ACInterface]
type = ACInterface
variable = eta
mob_name = L
kappa_name = kappa_eta
[../]
[./Fe]
type = MaterialPropertyValue
prop_name = Fe
variable = Fe_fit
[../]
[./autoadjust]
type = MaskedBodyForce
variable = w
function = diff
mask = mask
[../]
[]
[Materials]
# declare a few constants, such as mobilities (L,M) and interface gradient prefactors (kappa*)
[./consts]
type = GenericConstantMaterial
prop_names = 'M L kappa_c kappa_eta'
prop_values = '1.0 1.0 0.5 1'
[../]
# forcing function mask
[./mask]
type = ParsedMaterial
property_name = mask
expression = grad/dt
material_property_names = 'grad dt'
[../]
[./grad]
type = VariableGradientMaterial
variable = c
prop = grad
[../]
[./time]
type = TimeStepMaterial
[../]
# global mechanical properties
[./elasticity_tensor]
type = ComputeElasticityTensor
C_ijkl = '1 1'
fill_method = symmetric_isotropic
[../]
[./stress]
type = ComputeLinearElasticStress
[../]
# eigenstrain as a function of phase
[./eigenstrain]
type = ComputeVariableEigenstrain
eigen_base = '0.05 0.05 0.05 0 0 0'
prefactor = h
args = eta
eigenstrain_name = eigenstrain
[../]
# switching functions
[./switching]
type = SwitchingFunctionMaterial
function_name = h
eta = eta
h_order = SIMPLE
[../]
[./barrier]
type = BarrierFunctionMaterial
eta = eta
[../]
# chemical free energies
[./chemical_free_energy_1]
type = DerivativeParsedMaterial
property_name = Fc1
expression = 'c^2'
coupled_variables = 'c'
derivative_order = 2
[../]
[./chemical_free_energy_2]
type = DerivativeParsedMaterial
property_name = Fc2
expression = '(1-c)^2'
coupled_variables = 'c'
derivative_order = 2
[../]
# global chemical free energy
[./chemical_free_energy]
type = DerivativeTwoPhaseMaterial
f_name = Fc
fa_name = Fc1
fb_name = Fc2
eta = eta
coupled_variables = 'c'
W = 4
[../]
# global elastic free energy
[./elastic_free_energy]
type = ElasticEnergyMaterial
f_name = Fe
coupled_variables = 'eta'
output_properties = Fe
outputs = 'all'
derivative_order = 2
[../]
# free energy
[./free_energy]
type = DerivativeSumMaterial
property_name = F
sum_materials = 'Fc Fe'
coupled_variables = 'c eta'
derivative_order = 2
[../]
[]
[BCs]
[./left_r]
type = DirichletBC
variable = disp_r
boundary = 'left'
value = 0
[../]
[]
[Preconditioning]
[./SMP]
type = SMP
full = true
[../]
[]
# We monitor the total free energy and the total solute concentration (should be constant)
[Postprocessors]
[./total_free_energy]
type = ElementIntegralVariablePostprocessor
variable = local_energy
execute_on = 'INITIAL TIMESTEP_END'
outputs = 'table console'
[../]
[./total_solute]
type = ElementIntegralVariablePostprocessor
variable = c
execute_on = 'INITIAL TIMESTEP_END'
outputs = 'table console'
[../]
[./pos_c]
type = FindValueOnLine
start_point = '0 0 0'
end_point = '100 0 0'
v = c
target = 0.582
tol = 1e-8
execute_on = 'INITIAL TIMESTEP_END'
outputs = 'table console'
[../]
[./pos_eta]
type = FindValueOnLine
start_point = '0 0 0'
end_point = '100 0 0'
v = eta
target = 0.5
tol = 1e-8
execute_on = 'INITIAL TIMESTEP_END'
outputs = 'table console'
[../]
[./c_min]
type = ElementExtremeValue
value_type = min
variable = c
execute_on = 'INITIAL TIMESTEP_END'
outputs = 'table console'
[../]
[]
[VectorPostprocessors]
[./line]
type = LineValueSampler
variable = 'Fe_fit c w'
start_point = '0 0 0'
end_point = '100 0 0'
num_points = 5000
sort_by = x
outputs = vpp
execute_on = 'INITIAL TIMESTEP_END'
[../]
[]
[Executioner]
type = Transient
scheme = bdf2
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -sub_pc_type'
petsc_options_value = 'asm lu'
l_max_its = 30
nl_max_its = 15
l_tol = 1.0e-4
nl_rel_tol = 1.0e-8
nl_abs_tol = 2.0e-9
start_time = 0.0
end_time = 100000.0
[./TimeStepper]
type = IterationAdaptiveDT
optimal_iterations = 8
iteration_window = 1
dt = 1
[../]
[./Adaptivity]
initial_adaptivity = 5
interval = 10
max_h_level = 5
refine_fraction = 0.9
coarsen_fraction = 0.1
[../]
[]
[Outputs]
print_linear_residuals = false
perf_graph = true
execute_on = 'INITIAL TIMESTEP_END'
[./table]
type = CSV
delimiter = ' '
file_base = radius_${RADIUS}/eigenstrain_pp
[../]
[./vpp]
type = CSV
delimiter = ' '
sync_times = '10 50 100 500 1000 5000 10000 50000 100000'
sync_only = true
time_data = true
file_base = radius_${RADIUS}/eigenstrain_vpp
[../]
[]
(modules/phase_field/examples/cahn-hilliard/Parsed_SplitCH.i)
#
# Example problem showing how to use the DerivativeParsedMaterial with SplitCHParsed.
# The free energy is identical to that from SplitCHMath, f_bulk = 1/4*(1-c)^2*(1+c)^2.
#
[Mesh]
type = GeneratedMesh
dim = 2
nx = 150
ny = 150
xmax = 60
ymax = 60
[]
[Modules]
[./PhaseField]
[./Conserved]
[./c]
free_energy = fbulk
mobility = M
kappa = kappa_c
solve_type = REVERSE_SPLIT
[../]
[../]
[../]
[]
[AuxVariables]
[./local_energy]
order = CONSTANT
family = MONOMIAL
[../]
[]
[ICs]
[./cIC]
type = RandomIC
variable = c
min = -0.1
max = 0.1
[../]
[]
[AuxKernels]
[./local_energy]
type = TotalFreeEnergy
variable = local_energy
f_name = fbulk
interfacial_vars = c
kappa_names = kappa_c
execute_on = timestep_end
[../]
[]
[BCs]
[./Periodic]
[./all]
auto_direction = 'x y'
[../]
[../]
[]
[Materials]
[./mat]
type = GenericConstantMaterial
prop_names = 'M kappa_c'
prop_values = '1.0 0.5'
[../]
[./free_energy]
type = DerivativeParsedMaterial
property_name = fbulk
coupled_variables = c
constant_names = W
constant_expressions = 1.0/2^2
expression = W*(1-c)^2*(1+c)^2
enable_jit = true
outputs = exodus
[../]
[]
[Postprocessors]
[./top]
type = SideIntegralVariablePostprocessor
variable = c
boundary = top
[../]
[./total_free_energy]
type = ElementIntegralVariablePostprocessor
variable = local_energy
[../]
[]
[Preconditioning]
[./cw_coupling]
type = SMP
full = true
[../]
[]
[Executioner]
type = Transient
solve_type = NEWTON
scheme = bdf2
petsc_options_iname = '-pc_type -sub_pc_type'
petsc_options_value = 'asm lu '
l_max_its = 30
l_tol = 1e-4
nl_max_its = 20
nl_rel_tol = 1e-9
dt = 2.0
end_time = 20.0
[]
[Outputs]
exodus = true
perf_graph = true
[]
(modules/phase_field/examples/multiphase/DerivativeMultiPhaseMaterial.i)
[Mesh]
type = GeneratedMesh
dim = 2
nx = 40
ny = 40
nz = 0
xmin = -12
xmax = 12
ymin = -12
ymax = 12
elem_type = QUAD4
[]
[GlobalParams]
# let's output all material properties for demonstration purposes
outputs = exodus
# prefactor on the penalty function kernels. The higher this value is, the
# more rigorously the constraint is enforced
penalty = 1e3
[]
#
# These AuxVariables hold the directly calculated free energy density in the
# simulation cell. They are provided for visualization purposes.
#
[AuxVariables]
[./local_energy]
order = CONSTANT
family = MONOMIAL
[../]
[./cross_energy]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
[./local_free_energy]
type = TotalFreeEnergy
variable = local_energy
interfacial_vars = 'c'
kappa_names = 'kappa_c'
additional_free_energy = cross_energy
[../]
#
# Helper kernel to cpompute the gradient contribution from interfaces of order
# parameters evolved using the ACMultiInterface kernel
#
[./cross_terms]
type = CrossTermGradientFreeEnergy
variable = cross_energy
interfacial_vars = 'eta1 eta2 eta3'
#
# The interface coefficient matrix. This should be symmetrical!
#
kappa_names = 'kappa11 kappa12 kappa13
kappa21 kappa22 kappa23
kappa31 kappa32 kappa33'
[../]
[]
[Variables]
[./c]
order = FIRST
family = LAGRANGE
#
# We set up a smooth cradial concentrtaion gradient
# The concentration will quickly change to adapt to the preset order
# parameters eta1, eta2, and eta3
#
[./InitialCondition]
type = SmoothCircleIC
x1 = 0.0
y1 = 0.0
radius = 5.0
invalue = 1.0
outvalue = 0.01
int_width = 10.0
[../]
[../]
[./eta1]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = FunctionIC
#
# Note: this initial conditions sets up a _sharp_ interface. Ideally
# we should start with a smooth interface with a width consistent
# with the kappa parameter supplied for the given interface.
#
function = 'r:=sqrt(x^2+y^2);if(r<=4,1,0)'
[../]
[../]
[./eta2]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = FunctionIC
function = 'r:=sqrt(x^2+y^2);if(r>4&r<=7,1,0)'
[../]
[../]
[./eta3]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = FunctionIC
function = 'r:=sqrt(x^2+y^2);if(r>7,1,0)'
[../]
[../]
[]
[Kernels]
#
# Cahn-Hilliard kernel for the concentration variable.
# Note that we are not using an interfcae kernel on this variable, but rather
# rely on the interface width enforced on the order parameters. This allows us
# to use a direct solve using the CahnHilliard kernel _despite_ only using first
# order elements.
#
[./c_res]
type = CahnHilliard
variable = c
f_name = F
coupled_variables = 'eta1 eta2 eta3'
[../]
[./time]
type = TimeDerivative
variable = c
[../]
#
# Order parameter eta1
# Each order parameter is acted on by 4 kernels:
# 1. The stock time derivative deta_i/dt kernel
# 2. The Allen-Cahn kernel that takes a Dervative Material for the free energy
# 3. A gradient interface kernel that includes cross terms
# see https://mooseframework.inl.gov/wiki/PhysicsModules/PhaseField/DevelopingModels/MultiPhaseModels/ACMultiInterface/
# 4. A penalty contribution that forces the interface contributions h(eta)
# to sum up to unity
#
[./deta1dt]
type = TimeDerivative
variable = eta1
[../]
[./ACBulk1]
type = AllenCahn
variable = eta1
coupled_variables = 'eta2 eta3 c'
mob_name = L1
f_name = F
[../]
[./ACInterface1]
type = ACMultiInterface
variable = eta1
etas = 'eta1 eta2 eta3'
mob_name = L1
kappa_names = 'kappa11 kappa12 kappa13'
[../]
[./penalty1]
type = SwitchingFunctionPenalty
variable = eta1
etas = 'eta1 eta2 eta3'
h_names = 'h1 h2 h3'
[../]
#
# Order parameter eta2
#
[./deta2dt]
type = TimeDerivative
variable = eta2
[../]
[./ACBulk2]
type = AllenCahn
variable = eta2
coupled_variables = 'eta1 eta3 c'
mob_name = L2
f_name = F
[../]
[./ACInterface2]
type = ACMultiInterface
variable = eta2
etas = 'eta1 eta2 eta3'
mob_name = L2
kappa_names = 'kappa21 kappa22 kappa23'
[../]
[./penalty2]
type = SwitchingFunctionPenalty
variable = eta2
etas = 'eta1 eta2 eta3'
h_names = 'h1 h2 h3'
[../]
#
# Order parameter eta3
#
[./deta3dt]
type = TimeDerivative
variable = eta3
[../]
[./ACBulk3]
type = AllenCahn
variable = eta3
coupled_variables = 'eta1 eta2 c'
mob_name = L3
f_name = F
[../]
[./ACInterface3]
type = ACMultiInterface
variable = eta3
etas = 'eta1 eta2 eta3'
mob_name = L3
kappa_names = 'kappa31 kappa32 kappa33'
[../]
[./penalty3]
type = SwitchingFunctionPenalty
variable = eta3
etas = 'eta1 eta2 eta3'
h_names = 'h1 h2 h3'
[../]
[]
[BCs]
[./Periodic]
[./All]
auto_direction = 'x y'
[../]
[../]
[]
[Materials]
# here we declare some of the model parameters: the mobilities and interface
# gradient prefactors. For this example we use arbitrary numbers. In an actual simulation
# physical mobilities would be used, and the interface gradient prefactors would
# be readjusted to the free energy magnitudes.
[./consts]
type = GenericConstantMaterial
prop_names = 'M kappa_c L1 L2 L3 kappa11 kappa12 kappa13 kappa21 kappa22 kappa23 kappa31 kappa32 kappa33'
prop_values = '0.2 0.75 1 1 1 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 '
[../]
# This material sums up the individual phase contributions. It is written to the output file
# (see GlobalParams section above) and can be used to check the constraint enforcement.
[./etasummat]
type = ParsedMaterial
property_name = etasum
material_property_names = 'h1 h2 h3'
expression = 'h1+h2+h3'
[../]
# The phase contribution factors for each material point are computed using the
# SwitchingFunctionMaterials. Each phase with an order parameter eta contributes h(eta)
# to the global free energy density. h is a function that switches smoothly from 0 to 1
[./switching1]
type = SwitchingFunctionMaterial
function_name = h1
eta = eta1
h_order = SIMPLE
[../]
[./switching2]
type = SwitchingFunctionMaterial
function_name = h2
eta = eta2
h_order = SIMPLE
[../]
[./switching3]
type = SwitchingFunctionMaterial
function_name = h3
eta = eta3
h_order = SIMPLE
[../]
# The barrier function adds a phase transformation energy barrier. It also
# Drives order parameters toward the [0:1] interval to avoid negative or larger than 1
# order parameters (these are set to 0 and 1 contribution by the switching functions
# above)
[./barrier]
type = MultiBarrierFunctionMaterial
etas = 'eta1 eta2 eta3'
[../]
# We use DerivativeParsedMaterials to specify three (very) simple free energy
# expressions for the three phases. All necessary derivatives are built automatically.
# In a real problem these expressions can be arbitrarily complex (or even provided
# by custom kernels).
[./phase_free_energy_1]
type = DerivativeParsedMaterial
property_name = F1
expression = '(c-1)^2'
coupled_variables = 'c'
[../]
[./phase_free_energy_2]
type = DerivativeParsedMaterial
property_name = F2
expression = '(c-0.5)^2'
coupled_variables = 'c'
[../]
[./phase_free_energy_3]
type = DerivativeParsedMaterial
property_name = F3
expression = 'c^2'
coupled_variables = 'c'
[../]
# The DerivativeMultiPhaseMaterial ties the phase free energies together into a global free energy.
# https://mooseframework.inl.gov/wiki/PhysicsModules/PhaseField/DevelopingModels/MultiPhaseModels/
[./free_energy]
type = DerivativeMultiPhaseMaterial
property_name = F
# we use a constant free energy (GeneriConstantmaterial property Fx)
fi_names = 'F1 F2 F3'
hi_names = 'h1 h2 h3'
etas = 'eta1 eta2 eta3'
coupled_variables = 'c'
W = 1
[../]
[]
[Postprocessors]
# The total free energy of the simulation cell to observe the energy reduction.
[./total_free_energy]
type = ElementIntegralVariablePostprocessor
variable = local_energy
[../]
# for testing we also monitor the total solute amount, which should be conserved.
[./total_solute]
type = ElementIntegralVariablePostprocessor
variable = c
[../]
[]
[Preconditioning]
# This preconditioner makes sure the Jacobian Matrix is fully populated. Our
# kernels compute all Jacobian matrix entries.
# This allows us to use the Newton solver below.
[./SMP]
type = SMP
full = true
[../]
[]
[Executioner]
type = Transient
scheme = 'bdf2'
# Automatic differentiation provedes a _full_ Jacobian in this example
# so we can safely use NEWTON for a fast solve
solve_type = 'NEWTON'
l_max_its = 15
l_tol = 1.0e-6
nl_max_its = 50
nl_rel_tol = 1.0e-6
nl_abs_tol = 1.0e-6
start_time = 0.0
end_time = 150.0
[./TimeStepper]
type = SolutionTimeAdaptiveDT
dt = 0.1
[../]
[]
[Debug]
# show_var_residual_norms = true
[]
[Outputs]
execute_on = 'timestep_end'
exodus = true
[./table]
type = CSV
delimiter = ' '
[../]
[]
(modules/combined/examples/periodic_strain/global_strain_pfm.i)
[Mesh]
[gen]
type = GeneratedMeshGenerator
dim = 2
nx = 50
ny = 50
xmin = -0.5
xmax = 0.5
ymin = -0.5
ymax = 0.5
[]
[./cnode]
input = gen
type = ExtraNodesetGenerator
coord = '0.0 0.0'
new_boundary = 100
[../]
[]
[Variables]
[./u_x]
[../]
[./u_y]
[../]
[./global_strain]
order = THIRD
family = SCALAR
[../]
[./c]
[./InitialCondition]
type = FunctionIC
function = 'sin(2*x*pi)*sin(2*y*pi)*0.05+0.6'
[../]
[../]
[./w]
[../]
[]
[AuxVariables]
[./local_energy]
order = CONSTANT
family = MONOMIAL
[../]
[./disp_x]
[../]
[./disp_y]
[../]
[./s00]
order = CONSTANT
family = MONOMIAL
[../]
[./s01]
order = CONSTANT
family = MONOMIAL
[../]
[./s10]
order = CONSTANT
family = MONOMIAL
[../]
[./s11]
order = CONSTANT
family = MONOMIAL
[../]
[./e00]
order = CONSTANT
family = MONOMIAL
[../]
[./e01]
order = CONSTANT
family = MONOMIAL
[../]
[./e10]
order = CONSTANT
family = MONOMIAL
[../]
[./e11]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
[./disp_x]
type = GlobalDisplacementAux
variable = disp_x
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 0
[../]
[./disp_y]
type = GlobalDisplacementAux
variable = disp_y
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 1
[../]
[./local_free_energy]
type = TotalFreeEnergy
execute_on = 'initial LINEAR'
variable = local_energy
interfacial_vars = 'c'
kappa_names = 'kappa_c'
[../]
[./s00]
type = RankTwoAux
variable = s00
rank_two_tensor = stress
index_i = 0
index_j = 0
[../]
[./s01]
type = RankTwoAux
variable = s01
rank_two_tensor = stress
index_i = 0
index_j = 1
[../]
[./s10]
type = RankTwoAux
variable = s10
rank_two_tensor = stress
index_i = 1
index_j = 0
[../]
[./s11]
type = RankTwoAux
variable = s11
rank_two_tensor = stress
index_i = 1
index_j = 1
[../]
[./e00]
type = RankTwoAux
variable = e00
rank_two_tensor = total_strain
index_i = 0
index_j = 0
[../]
[./e01]
type = RankTwoAux
variable = e01
rank_two_tensor = total_strain
index_i = 0
index_j = 1
[../]
[./e10]
type = RankTwoAux
variable = e10
rank_two_tensor = total_strain
index_i = 1
index_j = 0
[../]
[./e11]
type = RankTwoAux
variable = e11
rank_two_tensor = total_strain
index_i = 1
index_j = 1
[../]
[]
[GlobalParams]
derivative_order = 2
enable_jit = true
displacements = 'u_x u_y'
block = 0
[]
[Kernels]
[./TensorMechanics]
[../]
# Cahn-Hilliard kernels
[./c_dot]
type = CoupledTimeDerivative
variable = w
v = c
block = 0
[../]
[./c_res]
type = SplitCHParsed
variable = c
f_name = F
kappa_name = kappa_c
w = w
block = 0
[../]
[./w_res]
type = SplitCHWRes
variable = w
mob_name = M
block = 0
[../]
[]
[ScalarKernels]
[./global_strain]
type = GlobalStrain
variable = global_strain
global_strain_uo = global_strain_uo
[../]
[]
[BCs]
[./Periodic]
[./all]
auto_direction = 'x y'
variable = 'c w u_x u_y'
[../]
[../]
# fix center point location
[./centerfix_x]
type = DirichletBC
boundary = 100
variable = u_x
value = 0
[../]
[./centerfix_y]
type = DirichletBC
boundary = 100
variable = u_y
value = 0
[../]
[]
[Materials]
[./consts]
type = GenericConstantMaterial
prop_names = 'M kappa_c'
prop_values = '0.2 0.01 '
[../]
[./shear1]
type = GenericConstantRankTwoTensor
tensor_values = '0 0 0 0 0 0.5'
tensor_name = shear1
[../]
[./shear2]
type = GenericConstantRankTwoTensor
tensor_values = '0 0 0 0 0 -0.5'
tensor_name = shear2
[../]
[./expand3]
type = GenericConstantRankTwoTensor
tensor_values = '1 1 0 0 0 0'
tensor_name = expand3
[../]
[./weight1]
type = DerivativeParsedMaterial
expression = '0.3*c^2'
property_name = weight1
coupled_variables = c
[../]
[./weight2]
type = DerivativeParsedMaterial
expression = '0.3*(1-c)^2'
property_name = weight2
coupled_variables = c
[../]
[./weight3]
type = DerivativeParsedMaterial
expression = '4*(0.5-c)^2'
property_name = weight3
coupled_variables = c
[../]
[./elasticity_tensor]
type = ComputeElasticityTensor
C_ijkl = '1 1'
fill_method = symmetric_isotropic
[../]
[./strain]
type = ComputeSmallStrain
global_strain = global_strain
eigenstrain_names = eigenstrain
[../]
[./eigenstrain]
type = CompositeEigenstrain
tensors = 'shear1 shear2 expand3'
weights = 'weight1 weight2 weight3'
coupled_variables = c
eigenstrain_name = eigenstrain
[../]
[./global_strain]
type = ComputeGlobalStrain
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
[../]
[./stress]
type = ComputeLinearElasticStress
[../]
# chemical free energies
[./chemical_free_energy]
type = DerivativeParsedMaterial
property_name = Fc
expression = '4*c^2*(1-c)^2'
coupled_variables = 'c'
outputs = exodus
output_properties = Fc
[../]
# elastic free energies
[./elastic_free_energy]
type = ElasticEnergyMaterial
f_name = Fe
coupled_variables = 'c'
outputs = exodus
output_properties = Fe
[../]
# free energy (chemical + elastic)
[./free_energy]
type = DerivativeSumMaterial
block = 0
property_name = F
sum_materials = 'Fc Fe'
coupled_variables = 'c'
[../]
[]
[UserObjects]
[./global_strain_uo]
type = GlobalStrainUserObject
execute_on = 'Initial Linear Nonlinear'
[../]
[]
[Postprocessors]
[./total_free_energy]
type = ElementIntegralVariablePostprocessor
execute_on = 'initial TIMESTEP_END'
variable = local_energy
[../]
[./total_solute]
type = ElementIntegralVariablePostprocessor
execute_on = 'initial TIMESTEP_END'
variable = c
[../]
[./min]
type = ElementExtremeValue
execute_on = 'initial TIMESTEP_END'
value_type = min
variable = c
[../]
[./max]
type = ElementExtremeValue
execute_on = 'initial TIMESTEP_END'
value_type = max
variable = c
[../]
[]
[Preconditioning]
[./SMP]
type = SMP
full = true
[../]
[]
[Executioner]
type = Transient
scheme = bdf2
solve_type = 'PJFNK'
line_search = basic
petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_ksp_type -sub_pc_type -pc_asm_overlap'
petsc_options_value = 'asm 31 preonly lu 1'
l_max_its = 30
nl_max_its = 12
l_tol = 1.0e-4
nl_rel_tol = 1.0e-8
nl_abs_tol = 1.0e-10
start_time = 0.0
end_time = 2.0
[./TimeStepper]
type = IterationAdaptiveDT
dt = 0.01
growth_factor = 1.5
cutback_factor = 0.8
optimal_iterations = 9
iteration_window = 2
[../]
[]
[Outputs]
execute_on = 'timestep_end'
print_linear_residuals = false
exodus = true
[./table]
type = CSV
delimiter = ' '
[../]
[]
(modules/combined/examples/phase_field-mechanics/Pattern1.i)
#
# Pattern example 1
#
# Phase changes driven by a combination mechanical (elastic) and chemical
# driving forces. In this three phase system a matrix phase, an oversized and
# an undersized precipitate phase compete. The chemical free energy favors a
# phase separation into either precipitate phase. A mix of both precipitate
# emerges to balance lattice expansion and contraction.
#
# This example demonstrates the use of
# * ACMultiInterface
# * SwitchingFunctionConstraintEta and SwitchingFunctionConstraintLagrange
# * DerivativeParsedMaterial
# * ElasticEnergyMaterial
# * DerivativeMultiPhaseMaterial
# * MultiPhaseStressMaterial
# which are the components to se up a phase field model with an arbitrary number
# of phases
#
[Mesh]
type = GeneratedMesh
dim = 2
nx = 80
ny = 80
nz = 0
xmin = -20
xmax = 20
ymin = -20
ymax = 20
zmin = 0
zmax = 0
elem_type = QUAD4
[]
[GlobalParams]
# CahnHilliard needs the third derivatives
derivative_order = 3
enable_jit = true
displacements = 'disp_x disp_y'
[]
# AuxVars to compute the free energy density for outputting
[AuxVariables]
[./local_energy]
order = CONSTANT
family = MONOMIAL
[../]
[./cross_energy]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
[./local_free_energy]
type = TotalFreeEnergy
variable = local_energy
interfacial_vars = 'c'
kappa_names = 'kappa_c'
additional_free_energy = cross_energy
[../]
[./cross_terms]
type = CrossTermGradientFreeEnergy
variable = cross_energy
interfacial_vars = 'eta1 eta2 eta3'
kappa_names = 'kappa11 kappa12 kappa13
kappa21 kappa22 kappa23
kappa31 kappa32 kappa33'
[../]
[]
[Variables]
# Solute concentration variable
[./c]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = 0
max = 0.8
seed = 1235
[../]
[../]
# Order parameter for the Matrix
[./eta1]
order = FIRST
family = LAGRANGE
initial_condition = 0.5
[../]
# Order parameters for the 2 different inclusion orientations
[./eta2]
order = FIRST
family = LAGRANGE
initial_condition = 0.1
[../]
[./eta3]
order = FIRST
family = LAGRANGE
initial_condition = 0.1
[../]
# Mesh displacement
[./disp_x]
order = FIRST
family = LAGRANGE
[../]
[./disp_y]
order = FIRST
family = LAGRANGE
[../]
# Lagrange-multiplier
[./lambda]
order = FIRST
family = LAGRANGE
initial_condition = 1.0
[../]
[]
[Kernels]
# Set up stress divergence kernels
[./TensorMechanics]
[../]
# Cahn-Hilliard kernels
[./c_res]
type = CahnHilliard
variable = c
f_name = F
coupled_variables = 'eta1 eta2 eta3'
[../]
[./time]
type = TimeDerivative
variable = c
[../]
# Allen-Cahn and Lagrange-multiplier constraint kernels for order parameter 1
[./deta1dt]
type = TimeDerivative
variable = eta1
[../]
[./ACBulk1]
type = AllenCahn
variable = eta1
coupled_variables = 'eta2 eta3 c'
mob_name = L1
f_name = F
[../]
[./ACInterface1]
type = ACMultiInterface
variable = eta1
etas = 'eta1 eta2 eta3'
mob_name = L1
kappa_names = 'kappa11 kappa12 kappa13'
[../]
[./lagrange1]
type = SwitchingFunctionConstraintEta
variable = eta1
h_name = h1
lambda = lambda
[../]
# Allen-Cahn and Lagrange-multiplier constraint kernels for order parameter 2
[./deta2dt]
type = TimeDerivative
variable = eta2
[../]
[./ACBulk2]
type = AllenCahn
variable = eta2
coupled_variables = 'eta1 eta3 c'
mob_name = L2
f_name = F
[../]
[./ACInterface2]
type = ACMultiInterface
variable = eta2
etas = 'eta1 eta2 eta3'
mob_name = L2
kappa_names = 'kappa21 kappa22 kappa23'
[../]
[./lagrange2]
type = SwitchingFunctionConstraintEta
variable = eta2
h_name = h2
lambda = lambda
[../]
# Allen-Cahn and Lagrange-multiplier constraint kernels for order parameter 3
[./deta3dt]
type = TimeDerivative
variable = eta3
[../]
[./ACBulk3]
type = AllenCahn
variable = eta3
coupled_variables = 'eta1 eta2 c'
mob_name = L3
f_name = F
[../]
[./ACInterface3]
type = ACMultiInterface
variable = eta3
etas = 'eta1 eta2 eta3'
mob_name = L3
kappa_names = 'kappa31 kappa32 kappa33'
[../]
[./lagrange3]
type = SwitchingFunctionConstraintEta
variable = eta3
h_name = h3
lambda = lambda
[../]
# Lagrange-multiplier constraint kernel for lambda
[./lagrange]
type = SwitchingFunctionConstraintLagrange
variable = lambda
etas = 'eta1 eta2 eta3'
h_names = 'h1 h2 h3'
epsilon = 1e-6
[../]
[]
[Materials]
# declare a few constants, such as mobilities (L,M) and interface gradient prefactors (kappa*)
[./consts]
type = GenericConstantMaterial
prop_names = 'M kappa_c L1 L2 L3 kappa11 kappa12 kappa13 kappa21 kappa22 kappa23 kappa31 kappa32 kappa33'
prop_values = '0.2 0 1 1 1 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 '
[../]
# We use this to output the level of constraint enforcement
# ideally it should be 0 everywhere, if the constraint is fully enforced
[./etasummat]
type = ParsedMaterial
property_name = etasum
coupled_variables = 'eta1 eta2 eta3'
material_property_names = 'h1 h2 h3'
expression = 'h1+h2+h3-1'
outputs = exodus
[../]
# This parsed material creates a single property for visualization purposes.
# It will be 0 for phase 1, -1 for phase 2, and 1 for phase 3
[./phasemap]
type = ParsedMaterial
property_name = phase
coupled_variables = 'eta2 eta3'
expression = 'if(eta3>0.5,1,0)-if(eta2>0.5,1,0)'
outputs = exodus
[../]
# matrix phase
[./elasticity_tensor_1]
type = ComputeElasticityTensor
base_name = phase1
C_ijkl = '3 3'
fill_method = symmetric_isotropic
[../]
[./strain_1]
type = ComputeSmallStrain
base_name = phase1
displacements = 'disp_x disp_y'
[../]
[./stress_1]
type = ComputeLinearElasticStress
base_name = phase1
[../]
# oversized phase
[./elasticity_tensor_2]
type = ComputeElasticityTensor
base_name = phase2
C_ijkl = '7 7'
fill_method = symmetric_isotropic
[../]
[./strain_2]
type = ComputeSmallStrain
base_name = phase2
displacements = 'disp_x disp_y'
eigenstrain_names = eigenstrain
[../]
[./stress_2]
type = ComputeLinearElasticStress
base_name = phase2
[../]
[./eigenstrain_2]
type = ComputeEigenstrain
base_name = phase2
eigen_base = '0.02'
eigenstrain_name = eigenstrain
[../]
# undersized phase
[./elasticity_tensor_3]
type = ComputeElasticityTensor
base_name = phase3
C_ijkl = '7 7'
fill_method = symmetric_isotropic
[../]
[./strain_3]
type = ComputeSmallStrain
base_name = phase3
displacements = 'disp_x disp_y'
eigenstrain_names = eigenstrain
[../]
[./stress_3]
type = ComputeLinearElasticStress
base_name = phase3
[../]
[./eigenstrain_3]
type = ComputeEigenstrain
base_name = phase3
eigen_base = '-0.05'
eigenstrain_name = eigenstrain
[../]
# switching functions
[./switching1]
type = SwitchingFunctionMaterial
function_name = h1
eta = eta1
h_order = SIMPLE
[../]
[./switching2]
type = SwitchingFunctionMaterial
function_name = h2
eta = eta2
h_order = SIMPLE
[../]
[./switching3]
type = SwitchingFunctionMaterial
function_name = h3
eta = eta3
h_order = SIMPLE
[../]
[./barrier]
type = MultiBarrierFunctionMaterial
etas = 'eta1 eta2 eta3'
[../]
# chemical free energies
[./chemical_free_energy_1]
type = DerivativeParsedMaterial
property_name = Fc1
expression = '4*c^2'
coupled_variables = 'c'
derivative_order = 2
[../]
[./chemical_free_energy_2]
type = DerivativeParsedMaterial
property_name = Fc2
expression = '(c-0.9)^2-0.4'
coupled_variables = 'c'
derivative_order = 2
[../]
[./chemical_free_energy_3]
type = DerivativeParsedMaterial
property_name = Fc3
expression = '(c-0.9)^2-0.5'
coupled_variables = 'c'
derivative_order = 2
[../]
# elastic free energies
[./elastic_free_energy_1]
type = ElasticEnergyMaterial
base_name = phase1
f_name = Fe1
derivative_order = 2
coupled_variables = 'c' # should be empty
[../]
[./elastic_free_energy_2]
type = ElasticEnergyMaterial
base_name = phase2
f_name = Fe2
derivative_order = 2
coupled_variables = 'c' # should be empty
[../]
[./elastic_free_energy_3]
type = ElasticEnergyMaterial
base_name = phase3
f_name = Fe3
derivative_order = 2
coupled_variables = 'c' # should be empty
[../]
# phase free energies (chemical + elastic)
[./phase_free_energy_1]
type = DerivativeSumMaterial
property_name = F1
sum_materials = 'Fc1 Fe1'
coupled_variables = 'c'
derivative_order = 2
[../]
[./phase_free_energy_2]
type = DerivativeSumMaterial
property_name = F2
sum_materials = 'Fc2 Fe2'
coupled_variables = 'c'
derivative_order = 2
[../]
[./phase_free_energy_3]
type = DerivativeSumMaterial
property_name = F3
sum_materials = 'Fc3 Fe3'
coupled_variables = 'c'
derivative_order = 2
[../]
# global free energy
[./free_energy]
type = DerivativeMultiPhaseMaterial
f_name = F
fi_names = 'F1 F2 F3'
hi_names = 'h1 h2 h3'
etas = 'eta1 eta2 eta3'
coupled_variables = 'c'
W = 3
[../]
# Generate the global stress from the phase stresses
[./global_stress]
type = MultiPhaseStressMaterial
phase_base = 'phase1 phase2 phase3'
h = 'h1 h2 h3'
[../]
[]
[BCs]
# the boundary conditions on the displacement enforce periodicity
# at zero total shear and constant volume
[./bottom_y]
type = DirichletBC
variable = disp_y
boundary = 'bottom'
value = 0
[../]
[./top_y]
type = DirichletBC
variable = disp_y
boundary = 'top'
value = 0
[../]
[./left_x]
type = DirichletBC
variable = disp_x
boundary = 'left'
value = 0
[../]
[./right_x]
type = DirichletBC
variable = disp_x
boundary = 'right'
value = 0
[../]
[./Periodic]
[./disp_x]
auto_direction = 'y'
[../]
[./disp_y]
auto_direction = 'x'
[../]
# all other phase field variables are fully periodic
[./c]
auto_direction = 'x y'
[../]
[./eta1]
auto_direction = 'x y'
[../]
[./eta2]
auto_direction = 'x y'
[../]
[./eta3]
auto_direction = 'x y'
[../]
[./lambda]
auto_direction = 'x y'
[../]
[../]
[]
[Preconditioning]
[./SMP]
type = SMP
full = true
[../]
[]
# We monitor the total free energy and the total solute concentration (should be constant)
[Postprocessors]
[./total_free_energy]
type = ElementIntegralVariablePostprocessor
variable = local_energy
[../]
[./total_solute]
type = ElementIntegralVariablePostprocessor
variable = c
[../]
[]
[Executioner]
type = Transient
scheme = bdf2
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -sub_pc_type'
petsc_options_value = 'asm ilu'
l_max_its = 30
nl_max_its = 10
l_tol = 1.0e-4
nl_rel_tol = 1.0e-8
nl_abs_tol = 1.0e-10
start_time = 0.0
num_steps = 200
[./TimeStepper]
type = SolutionTimeAdaptiveDT
dt = 0.1
[../]
[]
[Outputs]
execute_on = 'timestep_end'
exodus = true
[./table]
type = CSV
delimiter = ' '
[../]
[]
[Debug]
# show_var_residual_norms = true
[]
(modules/phase_field/test/tests/GrandPotentialPFM/GrandPotentialSintering_test.i)
#input file to test the materials GrandPotentialTensorMaterial
[Mesh]
type = GeneratedMesh
dim = 2
nx = 17
ny = 17
xmin = 0
xmax = 680
ymin = 0
ymax = 680
uniform_refine = 1
[]
[GlobalParams]
op_num = 4
var_name_base = gr
int_width = 40
[]
[Variables]
[./w]
[../]
[./phi]
[../]
[./PolycrystalVariables]
[../]
[]
[AuxVariables]
[./bnds]
[../]
[./T]
order = CONSTANT
family = MONOMIAL
[../]
[./F_loc]
order = CONSTANT
family = MONOMIAL
[../]
[]
[ICs]
[./phi_IC]
type = SpecifiedSmoothCircleIC
variable = phi
x_positions = '190 490 190 490'
y_positions = '190 190 490 490'
z_positions = ' 0 0 0 0'
radii = '150 150 150 150'
invalue = 0
outvalue = 1
[../]
[./gr0_IC]
type = SmoothCircleIC
variable = gr0
x1 = 190
y1 = 190
z1 = 0
radius = 150
invalue = 1
outvalue = 0
[../]
[./gr1_IC]
type = SmoothCircleIC
variable = gr1
x1 = 490
y1 = 190
z1 = 0
radius = 150
invalue = 1
outvalue = 0
[../]
[./gr2_IC]
type = SmoothCircleIC
variable = gr2
x1 = 190
y1 = 490
z1 = 0
radius = 150
invalue = 1
outvalue = 0
[../]
[./gr3_IC]
type = SmoothCircleIC
variable = gr3
x1 = 490
y1 = 490
z1 = 0
radius = 150
invalue = 1
outvalue = 0
[../]
[]
[Functions]
[./f_T]
type = ConstantFunction
value = 1600
[../]
[]
[Materials]
# Free energy coefficients for parabolic curves
[./ks]
type = ParsedMaterial
property_name = ks
coupled_variables = 'T'
constant_names = 'a b'
constant_expressions = '-0.0025 157.16'
expression = 'a*T + b'
[../]
[./kv]
type = ParsedMaterial
property_name = kv
material_property_names = 'ks'
expression = '10*ks'
[../]
# Diffusivity and mobilities
[./chiD]
type = GrandPotentialTensorMaterial
f_name = chiD
solid_mobility = L
void_mobility = Lv
chi = chi
surface_energy = 19.7
c = phi
T = T
D0 = 2.0e11
GBmob0 = 1.4759e9
Q = 2.77
Em = 2.40
bulkindex = 1
gbindex = 20
surfindex = 100
outputs = exodus
[../]
# Equilibrium vacancy concentration
[./cs_eq]
type = DerivativeParsedMaterial
property_name = cs_eq
coupled_variables = 'gr0 gr1 gr2 gr3 T'
constant_names = 'Ef c_GB kB'
constant_expressions = '2.69 0.189 8.617343e-5'
expression = 'bnds:=gr0^2 + gr1^2 + gr2^2 + gr3^2; exp(-Ef/kB/T) + 4.0 * c_GB * (1 - bnds)^2'
[../]
# Everything else
[./sintering]
type = GrandPotentialSinteringMaterial
chemical_potential = w
void_op = phi
Temperature = T
surface_energy = 19.7
grainboundary_energy = 9.86
void_energy_coefficient = kv
solid_energy_coefficient = ks
equilibrium_vacancy_concentration = cs_eq
solid_energy_model = PARABOLIC
[../]
# Concentration is only meant for output
[./c]
type = ParsedMaterial
property_name = c
material_property_names = 'hs rhos hv rhov'
constant_names = 'Va'
constant_expressions = '0.04092'
expression = 'Va*(hs*rhos + hv*rhov)'
outputs = exodus
[../]
[./f_bulk]
type = ParsedMaterial
property_name = f_bulk
coupled_variables = 'phi gr0 gr1 gr2 gr3'
material_property_names = 'mu gamma'
expression = 'mu*(phi^4/4-phi^2/2 + gr0^4/4-gr0^2/2 + gr1^4/4-gr1^2/2
+ gr2^4/4-gr2^2/2 + gr3^4/4-gr3^2/2
+ gamma*(phi^2*(gr0^2+gr1^2+gr2^2+gr3^2) + gr0^2*(gr1^2+gr2^2+gr3^2)
+ gr1^2*(gr2^2 + gr3^2) + gr2^2*gr3^2) + 0.25)'
outputs = exodus
[../]
[./f_switch]
type = ParsedMaterial
property_name = f_switch
coupled_variables = 'w'
material_property_names = 'chi'
expression = '0.5*w^2*chi'
outputs = exodus
[../]
[./f0]
type = ParsedMaterial
property_name = f0
material_property_names = 'f_bulk f_switch'
expression = 'f_bulk + f_switch'
[../]
[]
[Kernels]
[./dt_gr0]
type = TimeDerivative
variable = gr0
[../]
[./dt_gr1]
type = TimeDerivative
variable = gr1
[../]
[./dt_gr2]
type = TimeDerivative
variable = gr2
[../]
[./dt_gr3]
type = TimeDerivative
variable = gr3
[../]
[./dt_phi]
type = TimeDerivative
variable = phi
[../]
[./dt_w]
type = TimeDerivative
variable = w
[../]
[]
[AuxKernels]
[./bnds_aux]
type = BndsCalcAux
variable = bnds
execute_on = 'initial timestep_end'
[../]
[./T_aux]
type = FunctionAux
variable = T
function = f_T
[../]
[./F_aux]
type = TotalFreeEnergy
variable = F_loc
f_name = f0
interfacial_vars = 'phi gr0 gr1 gr2 gr3'
kappa_names = 'kappa kappa kappa kappa kappa'
[../]
[]
[Executioner]
type = Transient
scheme = bdf2
solve_type = JFNK
dt = 1
num_steps = 1
[]
[Outputs]
exodus = true
[]
(modules/phase_field/tutorials/spinodal_decomposition/s5_energycurve.i)
#
# Example simulation of an iron-chromium alloy at 500 C. Equilibrium
# concentrations are at 23.6 and 82.3 mol% Cr. Kappa value, free energy equation,
# and mobility equation were provided by Lars Hoglund. Solved using the split
# form of the Cahn-Hilliard equation.
[Mesh]
type = GeneratedMesh
dim = 2
elem_type = QUAD4
nx = 25
ny = 25
nz = 0
xmin = 0
xmax = 25
ymin = 0
ymax = 25
zmin = 0
zmax = 0
uniform_refine = 2
[]
[Variables]
[./c] # Mole fraction of Cr (unitless)
order = FIRST
family = LAGRANGE
scaling = 1e+04
[../]
[./w] # Chemical potential (eV/mol)
order = FIRST
family = LAGRANGE
[../]
[]
[AuxVariables]
[./f_density] # Local energy density (eV/mol)
order = CONSTANT
family = MONOMIAL
[../]
[]
[ICs]
[./concentrationIC] # 46.774 mol% Cr with variations
type = RandomIC
min = 0.44774
max = 0.48774
seed = 210
variable = c
[../]
[]
[BCs]
[./Periodic]
[./c_bcs]
auto_direction = 'x y'
[../]
[../]
[]
[Kernels]
[./w_dot]
variable = w
v = c
type = CoupledTimeDerivative
[../]
[./coupled_res]
variable = w
type = SplitCHWRes
mob_name = M
[../]
[./coupled_parsed]
variable = c
type = SplitCHParsed
f_name = f_loc
kappa_name = kappa_c
w = w
[../]
[]
[AuxKernels]
# Calculates the energy density by combining the local and gradient energies
[./f_density] # (eV/mol/nm^2)
type = TotalFreeEnergy
variable = f_density
f_name = 'f_loc'
kappa_names = 'kappa_c'
interfacial_vars = c
[../]
[]
[Materials]
# d is a scaling factor that makes it easier for the solution to converge
# without changing the results. It is defined in each of the first three
# materials and must have the same value in each one.
[./kappa] # Gradient energy coefficient (eV nm^2/mol)
type = GenericFunctionMaterial
prop_names = 'kappa_c'
prop_values = '8.125e-16*6.24150934e+18*1e+09^2*1e-27'
# kappa_c *eV_J*nm_m^2* d
[../]
[./mobility] # Mobility (nm^2 mol/eV/s)
# NOTE: This is a fitted equation, so only 'Conv' has units
type = DerivativeParsedMaterial
property_name = M
coupled_variables = c
constant_names = 'Acr Bcr Ccr Dcr
Ecr Fcr Gcr
Afe Bfe Cfe Dfe
Efe Ffe Gfe
nm_m eV_J d'
constant_expressions = '-32.770969 -25.8186669 -3.29612744 17.669757
37.6197853 20.6941796 10.8095813
-31.687117 -26.0291774 0.2286581 24.3633544
44.3334237 8.72990497 20.956768
1e+09 6.24150934e+18 1e-27'
expression = 'nm_m^2/eV_J/d*((1-c)^2*c*10^
(Acr*c+Bcr*(1-c)+Ccr*c*log(c)+Dcr*(1-c)*log(1-c)+
Ecr*c*(1-c)+Fcr*c*(1-c)*(2*c-1)+Gcr*c*(1-c)*(2*c-1)^2)
+c^2*(1-c)*10^
(Afe*c+Bfe*(1-c)+Cfe*c*log(c)+Dfe*(1-c)*log(1-c)+
Efe*c*(1-c)+Ffe*c*(1-c)*(2*c-1)+Gfe*c*(1-c)*(2*c-1)^2))'
derivative_order = 1
outputs = exodus
[../]
[./local_energy] # Local free energy function (eV/mol)
type = DerivativeParsedMaterial
property_name = f_loc
coupled_variables = c
constant_names = 'A B C D E F G eV_J d'
constant_expressions = '-2.446831e+04 -2.827533e+04 4.167994e+03 7.052907e+03
1.208993e+04 2.568625e+03 -2.354293e+03
6.24150934e+18 1e-27'
expression = 'eV_J*d*(A*c+B*(1-c)+C*c*log(c)+D*(1-c)*log(1-c)+
E*c*(1-c)+F*c*(1-c)*(2*c-1)+G*c*(1-c)*(2*c-1)^2)'
derivative_order = 2
[../]
[./precipitate_indicator] # Returns 1/625 if precipitate
type = ParsedMaterial
property_name = prec_indic
coupled_variables = c
expression = if(c>0.6,0.0016,0)
[../]
[]
[Postprocessors]
[./step_size] # Size of the time step
type = TimestepSize
[../]
[./iterations] # Number of iterations needed to converge timestep
type = NumNonlinearIterations
[../]
[./nodes] # Number of nodes in mesh
type = NumNodes
[../]
[./evaluations] # Cumulative residual calculations for simulation
type = NumResidualEvaluations
[../]
[./total_energy] # Total free energy at each timestep
type = ElementIntegralVariablePostprocessor
variable = f_density
execute_on = 'initial timestep_end'
[../]
[./num_features] # Number of precipitates formed
type = FeatureFloodCount
variable = c
threshold = 0.6
[../]
[./precipitate_area] # Fraction of surface devoted to precipitates
type = ElementIntegralMaterialProperty
mat_prop = prec_indic
[../]
[./active_time] # Time computer spent on simulation
type = PerfGraphData
section_name = "Root"
data_type = total
[../]
[]
[Preconditioning]
[./coupled]
type = SMP
full = true
[../]
[]
[Executioner]
type = Transient
solve_type = NEWTON
l_max_its = 30
l_tol = 1e-6
nl_max_its = 50
nl_abs_tol = 1e-9
end_time = 604800 # 7 days
petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_ksp_type
-sub_pc_type -pc_asm_overlap'
petsc_options_value = 'asm 31 preonly
ilu 1'
[./TimeStepper]
type = IterationAdaptiveDT
dt = 10
cutback_factor = 0.8
growth_factor = 1.5
optimal_iterations = 7
[../]
[./Adaptivity]
coarsen_fraction = 0.1
refine_fraction = 0.7
max_h_level = 2
[../]
[]
[Outputs]
exodus = true
console = true
csv = true
[./console]
type = Console
max_rows = 10
[../]
[]
(modules/phase_field/test/tests/actions/conserved_forward_split_1var.i)
[Mesh]
type = GeneratedMesh
dim = 2
nx = 30
ny = 30
xmax = 25.0
ymax = 25.0
elem_type = QUAD
[]
[Debug]
show_actions = true
[]
[Modules]
[./PhaseField]
[./Conserved]
[./c]
solve_type = FORWARD_SPLIT
mobility = 1.0
kappa = kappa_c
free_energy = F
[../]
[../]
[../]
[]
[ICs]
[./c_IC]
type = CrossIC
variable = c
x1 = 0.0
x2 = 25.0
y1 = 0.0
y2 = 25.0
[../]
[]
[AuxVariables]
[./local_energy]
family = MONOMIAL
order = CONSTANT
[../]
[]
[AuxKernels]
[./local_energy]
type = TotalFreeEnergy
variable = local_energy
f_name = F
kappa_names = kappa_c
interfacial_vars = c
[../]
[]
[Materials]
[./kappa_c]
type = GenericConstantMaterial
prop_names = kappa_c
prop_values = 2.0
[../]
[./free_energy]
type = DerivativeParsedMaterial
coupled_variables = c
expression = '(1 - c)^2 * (1 + c)^2'
property_name = F
[../]
[]
[Postprocessors]
[./total_free_energy]
type = ElementIntegralVariablePostprocessor
variable = local_energy
[../]
[./total_c]
type = ElementIntegralVariablePostprocessor
variable = c
execute_on = 'initial TIMESTEP_END'
[../]
[]
[Preconditioning]
[./SMP]
type = SMP
full = true
[../]
[]
[Executioner]
type = Transient
scheme = 'bdf2'
solve_type = 'NEWTON'
l_max_its = 30
l_tol = 1.0e-4
nl_max_its = 10
nl_rel_tol = 1.0e-10
start_time = 0.0
num_steps = 5
dt = 0.7
[]
[Outputs]
perf_graph = true
exodus = true
[]
(modules/combined/examples/publications/rapid_dev/fig8.i)
#
# Fig. 8 input for 10.1016/j.commatsci.2017.02.017
# D. Schwen et al./Computational Materials Science 132 (2017) 36-45
# Two growing particles with differnet anisotropic Eigenstrains
#
[Mesh]
[./gen]
type = GeneratedMeshGenerator
dim = 2
nx = 80
ny = 40
xmin = -20
xmax = 20
ymin = 0
ymax = 20
elem_type = QUAD4
[../]
[./cnode]
type = ExtraNodesetGenerator
input = gen
coord = '0.0 0.0'
new_boundary = 100
tolerance = 0.1
[../]
[]
[GlobalParams]
# CahnHilliard needs the third derivatives
derivative_order = 3
enable_jit = true
displacements = 'disp_x disp_y'
int_width = 1
[]
# AuxVars to compute the free energy density for outputting
[AuxVariables]
[./local_energy]
order = CONSTANT
family = MONOMIAL
[../]
[./cross_energy]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
[./local_free_energy]
type = TotalFreeEnergy
variable = local_energy
interfacial_vars = 'c'
kappa_names = 'kappa_c'
additional_free_energy = cross_energy
execute_on = 'INITIAL TIMESTEP_END'
[../]
[./cross_terms]
type = CrossTermGradientFreeEnergy
variable = cross_energy
interfacial_vars = 'eta1 eta2 eta3'
kappa_names = 'kappa11 kappa12 kappa13
kappa21 kappa22 kappa23
kappa31 kappa32 kappa33'
execute_on = 'INITIAL TIMESTEP_END'
[../]
[]
# particle x positions and radius
P1X=8
P2X=-4
PR=2
[Variables]
# Solute concentration variable
[./c]
[./InitialCondition]
type = SpecifiedSmoothCircleIC
x_positions = '${P1X} ${P2X}'
y_positions = '0 0'
z_positions = '0 0'
radii = '${PR} ${PR}'
outvalue = 0.5
invalue = 0.9
[../]
[../]
[./w]
[../]
# Order parameter for the Matrix
[./eta1]
[./InitialCondition]
type = SpecifiedSmoothCircleIC
x_positions = '${P1X} ${P2X}'
y_positions = '0 0'
z_positions = '0 0'
radii = '${PR} ${PR}'
outvalue = 1.0
invalue = 0.0
[../]
[../]
# Order parameters for the 2 different inclusion orientations
[./eta2]
[./InitialCondition]
type = SmoothCircleIC
x1 = ${P2X}
y1 = 0
radius = ${PR}
invalue = 1.0
outvalue = 0.0
[../]
[../]
[./eta3]
[./InitialCondition]
type = SmoothCircleIC
x1 = ${P1X}
y1 = 0
radius = ${PR}
invalue = 1.0
outvalue = 0.0
[../]
[../]
# Lagrange-multiplier
[./lambda]
initial_condition = 1.0
[../]
[]
[Physics/SolidMechanics/QuasiStatic/all]
add_variables = true
strain = SMALL
eigenstrain_names = eigenstrain
[]
[Kernels]
# Split Cahn-Hilliard kernels
[./c_res]
type = SplitCHParsed
variable = c
f_name = F
coupled_variables = 'eta1 eta2 eta3'
kappa_name = kappa_c
w = w
[../]
[./wres]
type = SplitCHWRes
variable = w
mob_name = M
[../]
[./time]
type = CoupledTimeDerivative
variable = w
v = c
[../]
# Allen-Cahn and Lagrange-multiplier constraint kernels for order parameter 1
[./deta1dt]
type = TimeDerivative
variable = eta1
[../]
[./ACBulk1]
type = AllenCahn
variable = eta1
coupled_variables = 'eta2 eta3 c'
mob_name = L1
f_name = F
[../]
[./ACInterface1]
type = ACMultiInterface
variable = eta1
etas = 'eta1 eta2 eta3'
mob_name = L1
kappa_names = 'kappa11 kappa12 kappa13'
[../]
[./lagrange1]
type = SwitchingFunctionConstraintEta
variable = eta1
h_name = h1
lambda = lambda
[../]
# Allen-Cahn and Lagrange-multiplier constraint kernels for order parameter 2
[./deta2dt]
type = TimeDerivative
variable = eta2
[../]
[./ACBulk2]
type = AllenCahn
variable = eta2
coupled_variables = 'eta1 eta3 c'
mob_name = L2
f_name = F
[../]
[./ACInterface2]
type = ACMultiInterface
variable = eta2
etas = 'eta1 eta2 eta3'
mob_name = L2
kappa_names = 'kappa21 kappa22 kappa23'
[../]
[./lagrange2]
type = SwitchingFunctionConstraintEta
variable = eta2
h_name = h2
lambda = lambda
[../]
# Allen-Cahn and Lagrange-multiplier constraint kernels for order parameter 3
[./deta3dt]
type = TimeDerivative
variable = eta3
[../]
[./ACBulk3]
type = AllenCahn
variable = eta3
coupled_variables = 'eta1 eta2 c'
mob_name = L3
f_name = F
[../]
[./ACInterface3]
type = ACMultiInterface
variable = eta3
etas = 'eta1 eta2 eta3'
mob_name = L3
kappa_names = 'kappa31 kappa32 kappa33'
[../]
[./lagrange3]
type = SwitchingFunctionConstraintEta
variable = eta3
h_name = h3
lambda = lambda
[../]
# Lagrange-multiplier constraint kernel for lambda
[./lagrange]
type = SwitchingFunctionConstraintLagrange
variable = lambda
etas = 'eta1 eta2 eta3'
h_names = 'h1 h2 h3'
epsilon = 1e-6
[../]
[]
[Materials]
# declare a few constants, such as mobilities (L,M) and interface gradient prefactors (kappa*)
[./consts]
type = GenericConstantMaterial
block = 0
prop_names = 'M kappa_c L1 L2 L3 kappa11 kappa12 kappa13 kappa21 kappa22 kappa23 kappa31 kappa32 kappa33'
prop_values = '0.2 0.5 1 1 1 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 '
[../]
# We use this to output the level of constraint enforcement
# ideally it should be 0 everywhere, if the constraint is fully enforced
[./etasummat]
type = ParsedMaterial
property_name = etasum
coupled_variables = 'eta1 eta2 eta3'
material_property_names = 'h1 h2 h3'
expression = 'h1+h2+h3-1'
outputs = exodus
[../]
# This parsed material creates a single property for visualization purposes.
# It will be 0 for phase 1, -1 for phase 2, and 1 for phase 3
[./phasemap]
type = ParsedMaterial
property_name = phase
coupled_variables = 'eta2 eta3'
expression = 'if(eta3>0.5,1,0)-if(eta2>0.5,1,0)'
outputs = exodus
[../]
# global mechanical properties
[./elasticity_tensor]
type = ComputeElasticityTensor
C_ijkl = '400 400'
fill_method = symmetric_isotropic
[../]
[./stress]
type = ComputeLinearElasticStress
[../]
# eigenstrain
[./eigenstrain_2]
type = GenericConstantRankTwoTensor
tensor_name = s2
tensor_values = '0 -0.05 0 0 0 0'
[../]
[./eigenstrain_3]
type = GenericConstantRankTwoTensor
tensor_name = s3
tensor_values = '-0.05 0 0 0 0 0'
[../]
[./eigenstrain]
type = CompositeEigenstrain
weights = 'h2 h3'
tensors = 's2 s3'
coupled_variables = 'eta2 eta3'
eigenstrain_name = eigenstrain
[../]
# switching functions
[./switching1]
type = SwitchingFunctionMaterial
function_name = h1
eta = eta1
h_order = SIMPLE
[../]
[./switching2]
type = SwitchingFunctionMaterial
function_name = h2
eta = eta2
h_order = SIMPLE
[../]
[./switching3]
type = SwitchingFunctionMaterial
function_name = h3
eta = eta3
h_order = SIMPLE
[../]
[./barrier]
type = MultiBarrierFunctionMaterial
etas = 'eta1 eta2 eta3'
[../]
# chemical free energies
[./chemical_free_energy_1]
type = DerivativeParsedMaterial
property_name = Fc1
expression = '4*c^2'
coupled_variables = 'c'
derivative_order = 2
[../]
[./chemical_free_energy_2]
type = DerivativeParsedMaterial
property_name = Fc2
expression = '(c-0.9)^2-0.4'
coupled_variables = 'c'
derivative_order = 2
[../]
[./chemical_free_energy_3]
type = DerivativeParsedMaterial
property_name = Fc3
expression = '(c-0.9)^2-0.5'
coupled_variables = 'c'
derivative_order = 2
[../]
# global chemical free energy
[./chemical_free_energy]
type = DerivativeMultiPhaseMaterial
f_name = Fc
fi_names = 'Fc1 Fc2 Fc3'
hi_names = 'h1 h2 h3'
etas = 'eta1 eta2 eta3'
coupled_variables = 'c'
W = 3
[../]
# global elastic free energy
[./elastic_free_energy]
type = ElasticEnergyMaterial
f_name = Fe
coupled_variables = 'eta2 eta3'
outputs = exodus
output_properties = Fe
derivative_order = 2
[../]
# Penalize phase 2 and 3 coexistence
[./multi_phase_penalty]
type = DerivativeParsedMaterial
property_name = Fp
expression = '50*(eta2*eta3)^2'
coupled_variables = 'eta2 eta3'
derivative_order = 2
outputs = exodus
output_properties = Fp
[../]
# free energy
[./free_energy]
type = DerivativeSumMaterial
property_name = F
sum_materials = 'Fc Fe Fp'
coupled_variables = 'c eta1 eta2 eta3'
derivative_order = 2
[../]
[]
[BCs]
# fix center point location
[./centerfix_x]
type = DirichletBC
boundary = 100
variable = disp_x
value = 0
[../]
# fix side point x coordinate to inhibit rotation
[./angularfix]
type = DirichletBC
boundary = bottom
variable = disp_y
value = 0
[../]
[]
[Preconditioning]
[./SMP]
type = SMP
full = true
[../]
[]
# We monitor the total free energy and the total solute concentration (should be constant)
[Postprocessors]
[./total_free_energy]
type = ElementIntegralVariablePostprocessor
variable = local_energy
execute_on = 'INITIAL TIMESTEP_END'
[../]
[./total_solute]
type = ElementIntegralVariablePostprocessor
variable = c
execute_on = 'INITIAL TIMESTEP_END'
[../]
[]
[Executioner]
type = Transient
scheme = bdf2
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -sub_pc_type'
petsc_options_value = 'asm lu'
l_max_its = 30
nl_max_its = 10
l_tol = 1.0e-4
nl_rel_tol = 1.0e-8
nl_abs_tol = 1.0e-10
start_time = 0.0
end_time = 12.0
[./TimeStepper]
type = IterationAdaptiveDT
optimal_iterations = 8
iteration_window = 1
dt = 0.01
[../]
[]
[Outputs]
print_linear_residuals = false
execute_on = 'INITIAL TIMESTEP_END'
exodus = true
[./table]
type = CSV
delimiter = ' '
[../]
[]
[Debug]
# show_var_residual_norms = true
[]
(modules/phase_field/test/tests/SplitCH/forward_split_math_test.i)
[Mesh]
type = GeneratedMesh
dim = 2
nx = 30
ny = 30
xmax = 25.0
ymax = 25.0
elem_type = QUAD
[]
[Variables]
[./c]
[../]
[./w]
[../]
[]
[ICs]
[./c_IC]
type = CrossIC
variable = c
x1 = 0
x2 = 25
y1 = 0
y2 = 25
[../]
[]
[Kernels]
[./cdot]
type = TimeDerivative
variable = c
[../]
[./grad_w]
type = MatDiffusion
variable = c
v = w
diffusivity = 1.0
[../]
[./grad_c]
type = MatDiffusion
variable = w
v = c
diffusivity = 2.0
[../]
[./w2]
type = CoupledMaterialDerivative
variable = w
v = c
f_name = F
[../]
[./w3]
type = CoefReaction
variable = w
coefficient = -1.0
[../]
[]
[AuxVariables]
[./local_energy]
family = MONOMIAL
order = CONSTANT
[../]
[]
[AuxKernels]
[./local_energy]
type = TotalFreeEnergy
variable = local_energy
f_name = F
kappa_names = kappa_c
interfacial_vars = c
[../]
[]
[Materials]
[./kappa_c]
type = GenericConstantMaterial
prop_names = kappa_c
prop_values = 2.0
[../]
[./free_energy]
type = DerivativeParsedMaterial
coupled_variables = c
expression = '(1 - c)^2 * (1 + c)^2'
property_name = F
[../]
[]
[Postprocessors]
[./total_free_energy]
type = ElementIntegralVariablePostprocessor
variable = local_energy
[../]
[./total_c]
type = ElementIntegralVariablePostprocessor
variable = c
execute_on = 'initial TIMESTEP_END'
[../]
[]
[Preconditioning]
[./SMP]
type = SMP
full = true
[../]
[]
[Executioner]
type = Transient
scheme = 'bdf2'
solve_type = 'NEWTON'
l_max_its = 30
l_tol = 1.0e-4
nl_max_its = 10
nl_rel_tol = 1.0e-10
start_time = 0.0
num_steps = 5
dt = 0.7
[]
[Outputs]
exodus = true
[]
(modules/phase_field/examples/cahn-hilliard/Parsed_CH.i)
#
# Example problem showing how to use the DerivativeParsedMaterial with CahnHilliard.
# The free energy is identical to that from CHMath, f_bulk = 1/4*(1-c)^2*(1+c)^2.
#
[Mesh]
type = GeneratedMesh
dim = 2
nx = 100
ny = 100
xmax = 60
ymax = 60
[]
[Modules]
[./PhaseField]
[./Conserved]
[./c]
free_energy = fbulk
mobility = M
kappa = kappa_c
solve_type = DIRECT
[../]
[../]
[../]
[]
[AuxVariables]
[./local_energy]
order = CONSTANT
family = MONOMIAL
[../]
[]
[ICs]
[./cIC]
type = RandomIC
variable = c
min = -0.1
max = 0.1
[../]
[]
[AuxKernels]
[./local_energy]
type = TotalFreeEnergy
variable = local_energy
f_name = fbulk
interfacial_vars = c
kappa_names = kappa_c
execute_on = timestep_end
[../]
[]
[BCs]
[./Periodic]
[./all]
auto_direction = 'x y'
[../]
[../]
[]
[Materials]
[./mat]
type = GenericConstantMaterial
prop_names = 'M kappa_c'
prop_values = '1.0 0.5'
[../]
[./free_energy]
type = DerivativeParsedMaterial
property_name = fbulk
coupled_variables = c
constant_names = W
constant_expressions = 1.0/2^2
expression = W*(1-c)^2*(1+c)^2
enable_jit = true
[../]
[]
[Postprocessors]
[./top]
type = SideIntegralVariablePostprocessor
variable = c
boundary = top
[../]
[./total_free_energy]
type = ElementIntegralVariablePostprocessor
variable = local_energy
[../]
[]
[Executioner]
type = Transient
solve_type = NEWTON
scheme = bdf2
# Alternative preconditioning using the additive Schwartz method and LU decomposition
#petsc_options_iname = '-pc_type -sub_ksp_type -sub_pc_type'
#petsc_options_value = 'asm preonly lu '
# Preconditioning options using Hypre (algebraic multi-grid)
petsc_options_iname = '-pc_type -pc_hypre_type'
petsc_options_value = 'hypre boomeramg'
l_max_its = 30
l_tol = 1e-4
nl_max_its = 20
nl_rel_tol = 1e-9
dt = 2.0
end_time = 20.0
[]
[Outputs]
exodus = true
perf_graph = true
[]
(modules/phase_field/examples/measure_interface_energy/1Dinterface_energy.i)
[Mesh]
type = GeneratedMesh
dim = 1
nx = 100
xmax = 100
xmin = 0
elem_type = EDGE
[]
[AuxVariables]
[./local_energy]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
[./local_free_energy]
type = TotalFreeEnergy
variable = local_energy
kappa_names = kappa_c
interfacial_vars = c
[../]
[]
[Variables]
[./c]
order = FIRST
family = LAGRANGE
scaling = 1e1
[./InitialCondition]
type = RampIC
variable = c
value_left = 0
value_right = 1
[../]
[../]
[./w]
order = FIRST
family = LAGRANGE
[../]
[]
[Kernels]
[./c_res]
type = SplitCHParsed
variable = c
f_name = F
kappa_name = kappa_c
w = w
[../]
[./w_res]
type = SplitCHWRes
variable = w
mob_name = M
[../]
[./time]
type = CoupledTimeDerivative
variable = w
v = c
[../]
[]
[Functions]
[./Int_energy]
type = ParsedFunction
symbol_values = 'total_solute Cleft Cright Fleft Fright volume'
expression = '((total_solute-Cleft*volume)/(Cright-Cleft))*Fright+(volume-(total_solute-Cleft*volume)/(Cright-Cleft))*Fleft'
symbol_names = 'total_solute Cleft Cright Fleft Fright volume'
[../]
[./Diff]
type = ParsedFunction
symbol_values = 'total_free_energy total_no_int'
symbol_names = 'total_free_energy total_no_int'
expression = total_free_energy-total_no_int
[../]
[]
[Materials]
[./consts]
type = GenericConstantMaterial
prop_names = 'kappa_c M'
prop_values = '25 150'
[../]
[./Free_energy]
type = DerivativeParsedMaterial
property_name = F
expression = 'c^2*(c-1)^2'
coupled_variables = c
derivative_order = 2
[../]
[]
[Postprocessors]
# The total free energy of the simulation cell to observe the energy reduction.
[./total_free_energy]
type = ElementIntegralVariablePostprocessor
variable = local_energy
[../]
# for testing we also monitor the total solute amount, which should be conserved,
# gives Cavg in % for this problem.
[./total_solute]
type = ElementIntegralVariablePostprocessor
variable = c
[../]
# Get simulation cell size (1D volume) from postprocessor
[./volume]
type = ElementIntegralMaterialProperty
mat_prop = 1
[../]
# Find concentration in each phase using SideAverageValue
[./Cleft]
type = SideAverageValue
boundary = left
variable = c
[../]
[./Cright]
type = SideAverageValue
boundary = right
variable = c
[../]
# Find local energy in each phase by checking boundaries
[./Fleft]
type = SideAverageValue
boundary = left
variable = local_energy
[../]
[./Fright]
type = SideAverageValue
boundary = right
variable = local_energy
[../]
# Use concentrations and energies to find total free energy without any interface,
# only applies once equilibrium is reached!!
# Difference between energy with and without interface
# gives interface energy per unit area.
[./total_no_int]
type = FunctionValuePostprocessor
function = Int_energy
[../]
[./Energy_of_Interface]
type = FunctionValuePostprocessor
function = Diff
[../]
[]
[Preconditioning]
# This preconditioner makes sure the Jacobian Matrix is fully populated. Our
# kernels compute all Jacobian matrix entries.
# This allows us to use the Newton solver below.
[./SMP]
type = SMP
full = true
[../]
[]
[Executioner]
type = Transient
scheme = 'bdf2'
# Automatic differentiation provides a _full_ Jacobian in this example
# so we can safely use NEWTON for a fast solve
solve_type = 'NEWTON'
l_max_its = 15
l_tol = 1.0e-6
nl_max_its = 15
nl_rel_tol = 1.0e-10
nl_abs_tol = 1.0e-4
start_time = 0.0
# make sure that the result obtained for the interfacial free energy is fully converged
end_time = 40
[./TimeStepper]
type = SolutionTimeAdaptiveDT
dt = 0.5
[../]
[]
[Outputs]
gnuplot = true
csv = true
[./exodus]
type = Exodus
show = 'c local_energy'
execute_on = 'failed initial nonlinear timestep_end final'
[../]
[./console]
type = Console
execute_on = 'FAILED INITIAL NONLINEAR TIMESTEP_END final'
[../]
perf_graph = true
[]
(modules/combined/examples/periodic_strain/global_strain_pfm_3D.i)
[Mesh]
[gen]
type = GeneratedMeshGenerator
dim = 3
nx = 20
ny = 20
nz = 20
xmin = -0.5
xmax = 0.5
ymin = -0.5
ymax = 0.5
zmin = -0.5
zmax = 0.5
[]
[./cnode]
input = gen
type = ExtraNodesetGenerator
coord = '0.0 0.0 0.0'
new_boundary = 100
[../]
[]
[Variables]
[./u_x]
[../]
[./u_y]
[../]
[./u_z]
[../]
[./global_strain]
order = SIXTH
family = SCALAR
[../]
[./c]
[./InitialCondition]
type = FunctionIC
function = 'sin(2*x*pi)*sin(2*y*pi)*sin(2*z*pi)*0.05+0.6'
[../]
[../]
[./w]
[../]
[]
[AuxVariables]
[./local_energy]
order = CONSTANT
family = MONOMIAL
[../]
[./disp_x]
[../]
[./disp_y]
[../]
[./disp_z]
[../]
[./s00]
order = CONSTANT
family = MONOMIAL
[../]
[./s01]
order = CONSTANT
family = MONOMIAL
[../]
[./s10]
order = CONSTANT
family = MONOMIAL
[../]
[./s11]
order = CONSTANT
family = MONOMIAL
[../]
[./e00]
order = CONSTANT
family = MONOMIAL
[../]
[./e01]
order = CONSTANT
family = MONOMIAL
[../]
[./e10]
order = CONSTANT
family = MONOMIAL
[../]
[./e11]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
[./disp_x]
type = GlobalDisplacementAux
variable = disp_x
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 0
[../]
[./disp_y]
type = GlobalDisplacementAux
variable = disp_y
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 1
[../]
[./disp_z]
type = GlobalDisplacementAux
variable = disp_z
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 2
[../]
[./local_free_energy]
type = TotalFreeEnergy
execute_on = 'initial LINEAR'
variable = local_energy
interfacial_vars = 'c'
kappa_names = 'kappa_c'
[../]
[./s00]
type = RankTwoAux
variable = s00
rank_two_tensor = stress
index_i = 0
index_j = 0
[../]
[./s01]
type = RankTwoAux
variable = s01
rank_two_tensor = stress
index_i = 0
index_j = 1
[../]
[./s10]
type = RankTwoAux
variable = s10
rank_two_tensor = stress
index_i = 1
index_j = 0
[../]
[./s11]
type = RankTwoAux
variable = s11
rank_two_tensor = stress
index_i = 1
index_j = 1
[../]
[./e00]
type = RankTwoAux
variable = e00
rank_two_tensor = total_strain
index_i = 0
index_j = 0
[../]
[./e01]
type = RankTwoAux
variable = e01
rank_two_tensor = total_strain
index_i = 0
index_j = 1
[../]
[./e10]
type = RankTwoAux
variable = e10
rank_two_tensor = total_strain
index_i = 1
index_j = 0
[../]
[./e11]
type = RankTwoAux
variable = e11
rank_two_tensor = total_strain
index_i = 1
index_j = 1
[../]
[]
[GlobalParams]
derivative_order = 2
enable_jit = true
displacements = 'u_x u_y u_z'
block = 0
[]
[Kernels]
[./TensorMechanics]
[../]
# Cahn-Hilliard kernels
[./c_dot]
type = CoupledTimeDerivative
variable = w
v = c
block = 0
[../]
[./c_res]
type = SplitCHParsed
variable = c
f_name = F
kappa_name = kappa_c
w = w
block = 0
[../]
[./w_res]
type = SplitCHWRes
variable = w
mob_name = M
block = 0
[../]
[]
[ScalarKernels]
[./global_strain]
type = GlobalStrain
variable = global_strain
global_strain_uo = global_strain_uo
[../]
[]
[BCs]
[./Periodic]
[./all]
auto_direction = 'x y z'
variable = 'c w u_x u_y u_z'
[../]
[../]
# fix center point location
[./centerfix_x]
type = DirichletBC
boundary = 100
variable = u_x
value = 0
[../]
[./centerfix_y]
type = DirichletBC
boundary = 100
variable = u_y
value = 0
[../]
[./centerfix_z]
type = DirichletBC
boundary = 100
variable = u_z
value = 0
[../]
[]
[Materials]
[./consts]
type = GenericConstantMaterial
prop_names = 'M kappa_c'
prop_values = '0.2 0.01 '
[../]
[./shear1]
type = GenericConstantRankTwoTensor
tensor_values = '0 0 0 0.5 0.5 0.5'
tensor_name = shear1
[../]
[./shear2]
type = GenericConstantRankTwoTensor
tensor_values = '0 0 0 -0.5 -0.5 -0.5'
tensor_name = shear2
[../]
[./expand3]
type = GenericConstantRankTwoTensor
tensor_values = '1 1 1 0 0 0'
tensor_name = expand3
[../]
[./weight1]
type = DerivativeParsedMaterial
expression = '0.3*c^2'
property_name = weight1
coupled_variables = c
[../]
[./weight2]
type = DerivativeParsedMaterial
expression = '0.3*(1-c)^2'
property_name = weight2
coupled_variables = c
[../]
[./weight3]
type = DerivativeParsedMaterial
expression = '4*(0.5-c)^2'
property_name = weight3
coupled_variables = c
[../]
[./elasticity_tensor]
type = ComputeElasticityTensor
C_ijkl = '1 1'
fill_method = symmetric_isotropic
[../]
[./strain]
type = ComputeSmallStrain
global_strain = global_strain
eigenstrain_names = eigenstrain
[../]
[./eigenstrain]
type = CompositeEigenstrain
tensors = 'shear1 shear2 expand3'
weights = 'weight1 weight2 weight3'
coupled_variables = c
eigenstrain_name = eigenstrain
[../]
[./global_strain]
type = ComputeGlobalStrain
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
[../]
[./stress]
type = ComputeLinearElasticStress
[../]
# chemical free energies
[./chemical_free_energy]
type = DerivativeParsedMaterial
property_name = Fc
expression = '4*c^2*(1-c)^2'
coupled_variables = 'c'
outputs = exodus
output_properties = Fc
[../]
# elastic free energies
[./elastic_free_energy]
type = ElasticEnergyMaterial
f_name = Fe
coupled_variables = 'c'
outputs = exodus
output_properties = Fe
[../]
# free energy (chemical + elastic)
[./free_energy]
type = DerivativeSumMaterial
block = 0
property_name = F
sum_materials = 'Fc Fe'
coupled_variables = 'c'
[../]
[]
[UserObjects]
[./global_strain_uo]
type = GlobalStrainUserObject
execute_on = 'Initial Linear Nonlinear'
[../]
[]
[Postprocessors]
[./total_free_energy]
type = ElementIntegralVariablePostprocessor
execute_on = 'initial TIMESTEP_END'
variable = local_energy
[../]
[./total_solute]
type = ElementIntegralVariablePostprocessor
execute_on = 'initial TIMESTEP_END'
variable = c
[../]
[./min]
type = ElementExtremeValue
execute_on = 'initial TIMESTEP_END'
value_type = min
variable = c
[../]
[./max]
type = ElementExtremeValue
execute_on = 'initial TIMESTEP_END'
value_type = max
variable = c
[../]
[]
[Preconditioning]
[./SMP]
type = SMP
full = true
[../]
[]
[Executioner]
type = Transient
scheme = bdf2
solve_type = 'PJFNK'
line_search = basic
petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_ksp_type -sub_pc_type -pc_asm_overlap'
petsc_options_value = 'asm 31 preonly lu 1'
l_max_its = 30
nl_max_its = 12
l_tol = 1.0e-4
nl_rel_tol = 1.0e-8
nl_abs_tol = 1.0e-10
start_time = 0.0
end_time = 2.0
[./TimeStepper]
type = IterationAdaptiveDT
dt = 0.01
growth_factor = 1.5
cutback_factor = 0.8
optimal_iterations = 9
iteration_window = 2
[../]
[]
[Outputs]
execute_on = 'timestep_end'
print_linear_residuals = false
exodus = true
[./table]
type = CSV
delimiter = ' '
[../]
[]
(modules/combined/examples/mortar/eigenstrain_action.i)
#
# Eigenstrain with Mortar gradient periodicity
#
[Mesh]
[gen]
type = GeneratedMeshGenerator
dim = 2
nx = 50
ny = 50
xmin = -0.5
xmax = 0.5
ymin = -0.5
ymax = 0.5
[]
[./cnode]
input = gen
type = ExtraNodesetGenerator
coord = '0.0 0.0'
new_boundary = 100
[../]
[./anode]
input = cnode
type = ExtraNodesetGenerator
coord = '0.0 0.5'
new_boundary = 101
[../]
[]
[Modules/PhaseField/MortarPeriodicity]
[./strain]
variable = 'disp_x disp_y'
periodicity = gradient
periodic_directions = 'x y'
[../]
[]
[GlobalParams]
derivative_order = 2
enable_jit = true
displacements = 'disp_x disp_y'
[]
# AuxVars to compute the free energy density for outputting
[AuxVariables]
[./local_energy]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
[./local_free_energy]
type = TotalFreeEnergy
block = 0
execute_on = 'initial LINEAR'
variable = local_energy
interfacial_vars = 'c'
kappa_names = 'kappa_c'
[../]
[]
[Variables]
# Solute concentration variable
[./c]
[./InitialCondition]
type = RandomIC
min = 0.49
max = 0.51
[../]
block = 0
[../]
[./w]
block = 0
[../]
# Mesh displacement
[./disp_x]
block = 0
[../]
[./disp_y]
block = 0
[../]
[]
[Kernels]
# Set up stress divergence kernels
[./TensorMechanics]
[../]
# Cahn-Hilliard kernels
[./c_dot]
type = CoupledTimeDerivative
variable = w
v = c
[../]
[./c_res]
type = SplitCHParsed
variable = c
f_name = F
kappa_name = kappa_c
w = w
[../]
[./w_res]
type = SplitCHWRes
variable = w
mob_name = M
[../]
[]
[Materials]
# declare a few constants, such as mobilities (L,M) and interface gradient prefactors (kappa*)
[./consts]
type = GenericConstantMaterial
block = '0'
prop_names = 'M kappa_c'
prop_values = '0.2 0.01 '
[../]
[./shear1]
type = GenericConstantRankTwoTensor
block = 0
tensor_values = '0 0 0 0 0 0.5'
tensor_name = shear1
[../]
[./shear2]
type = GenericConstantRankTwoTensor
block = 0
tensor_values = '0 0 0 0 0 -0.5'
tensor_name = shear2
[../]
[./expand3]
type = GenericConstantRankTwoTensor
block = 0
tensor_values = '1 1 0 0 0 0'
tensor_name = expand3
[../]
[./weight1]
type = DerivativeParsedMaterial
block = 0
expression = '0.3*c^2'
property_name = weight1
coupled_variables = c
[../]
[./weight2]
type = DerivativeParsedMaterial
block = 0
expression = '0.3*(1-c)^2'
property_name = weight2
coupled_variables = c
[../]
[./weight3]
type = DerivativeParsedMaterial
block = 0
expression = '4*(0.5-c)^2'
property_name = weight3
coupled_variables = c
[../]
# matrix phase
[./elasticity_tensor]
type = ComputeElasticityTensor
block = 0
C_ijkl = '1 1'
fill_method = symmetric_isotropic
[../]
[./strain]
type = ComputeSmallStrain
block = 0
displacements = 'disp_x disp_y'
[../]
[./eigenstrain]
type = CompositeEigenstrain
block = 0
tensors = 'shear1 shear2 expand3'
weights = 'weight1 weight2 weight3'
coupled_variables = c
eigenstrain_name = eigenstrain
[../]
[./stress]
type = ComputeLinearElasticStress
block = 0
[../]
# chemical free energies
[./chemical_free_energy]
type = DerivativeParsedMaterial
block = 0
property_name = Fc
expression = '4*c^2*(1-c)^2'
coupled_variables = 'c'
outputs = exodus
output_properties = Fc
[../]
# elastic free energies
[./elastic_free_energy]
type = ElasticEnergyMaterial
f_name = Fe
block = 0
coupled_variables = 'c'
outputs = exodus
output_properties = Fe
[../]
# free energy (chemical + elastic)
[./free_energy]
type = DerivativeSumMaterial
block = 0
property_name = F
sum_materials = 'Fc Fe'
coupled_variables = 'c'
[../]
[]
[BCs]
[./Periodic]
[./up_down]
primary = top
secondary = bottom
translation = '0 -1 0'
variable = 'c w'
[../]
[./left_right]
primary = left
secondary = right
translation = '1 0 0'
variable = 'c w'
[../]
[../]
# fix center point location
[./centerfix_x]
type = DirichletBC
boundary = 100
variable = disp_x
value = 0
[../]
[./centerfix_y]
type = DirichletBC
boundary = 100
variable = disp_y
value = 0
[../]
# fix side point x coordinate to inhibit rotation
[./angularfix]
type = DirichletBC
boundary = 101
variable = disp_x
value = 0
[../]
[]
[Preconditioning]
[./SMP]
type = SMP
full = true
[../]
[]
# We monitor the total free energy and the total solute concentration (should be constant)
[Postprocessors]
[./total_free_energy]
type = ElementIntegralVariablePostprocessor
block = 0
execute_on = 'initial TIMESTEP_END'
variable = local_energy
[../]
[./total_solute]
type = ElementIntegralVariablePostprocessor
block = 0
execute_on = 'initial TIMESTEP_END'
variable = c
[../]
[./min]
type = ElementExtremeValue
block = 0
execute_on = 'initial TIMESTEP_END'
value_type = min
variable = c
[../]
[./max]
type = ElementExtremeValue
block = 0
execute_on = 'initial TIMESTEP_END'
value_type = max
variable = c
[../]
[]
[Executioner]
type = Transient
scheme = bdf2
solve_type = 'PJFNK'
line_search = basic
# mortar currently does not support MPI parallelization
petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_shift_amount'
petsc_options_value = ' lu NONZERO 1e-10'
l_max_its = 30
nl_max_its = 12
l_tol = 1.0e-4
nl_rel_tol = 1.0e-8
nl_abs_tol = 1.0e-10
start_time = 0.0
num_steps = 200
[./TimeStepper]
type = SolutionTimeAdaptiveDT
dt = 0.01
[../]
[]
[Outputs]
execute_on = 'timestep_end'
print_linear_residuals = false
exodus = true
[./table]
type = CSV
delimiter = ' '
[../]
[]
(modules/combined/examples/publications/rapid_dev/fig7a.i)
#
# Fig. 7 input for 10.1016/j.commatsci.2017.02.017
# D. Schwen et al./Computational Materials Science 132 (2017) 36-45
# Solid gray curve (1)
# Eigenstrain and elastic energies ar computed per phase and then interpolated.
# Supply the RADIUS parameter (10-35) on the command line to generate data
# for all curves in the plot.
#
[Mesh]
type = GeneratedMesh
dim = 1
nx = 32
xmin = 0
xmax = 100
second_order = true
coord_type = RSPHERICAL
[]
[GlobalParams]
displacements = 'disp_r'
[]
[Functions]
[./diff]
type = ParsedFunction
expression = '${RADIUS}-pos_c'
symbol_names = pos_c
symbol_values = pos_c
[../]
[]
# AuxVars to compute the free energy density for outputting
[AuxVariables]
[./local_energy]
order = CONSTANT
family = MONOMIAL
[../]
[./cross_energy]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
[./local_free_energy]
type = TotalFreeEnergy
variable = local_energy
interfacial_vars = 'c'
kappa_names = 'kappa_c'
execute_on = 'INITIAL TIMESTEP_END'
[../]
[]
[Variables]
# Solute concentration variable
[./c]
[./InitialCondition]
type = SmoothCircleIC
invalue = 1
outvalue = 0
x1 = 0
y1 = 0
radius = ${RADIUS}
int_width = 3
[../]
[../]
[./w]
[../]
# Phase order parameter
[./eta]
[./InitialCondition]
type = SmoothCircleIC
invalue = 1
outvalue = 0
x1 = 0
y1 = 0
radius = ${RADIUS}
int_width = 3
[../]
[../]
# Mesh displacement
[./disp_r]
order = SECOND
[../]
[./Fe_fit]
order = SECOND
[../]
[]
[Kernels]
# Set up stress divergence kernels
[./TensorMechanics]
[../]
# Split Cahn-Hilliard kernels
[./c_res]
type = SplitCHParsed
variable = c
f_name = F
coupled_variables = 'eta'
kappa_name = kappa_c
w = w
[../]
[./wres]
type = SplitCHWRes
variable = w
mob_name = M
[../]
[./time]
type = CoupledTimeDerivative
variable = w
v = c
[../]
# Allen-Cahn and Lagrange-multiplier constraint kernels for order parameter 1
[./detadt]
type = TimeDerivative
variable = eta
[../]
[./ACBulk1]
type = AllenCahn
variable = eta
coupled_variables = 'c'
mob_name = L
f_name = F
[../]
[./ACInterface]
type = ACInterface
variable = eta
mob_name = L
kappa_name = kappa_eta
[../]
[./Fe]
type = MaterialPropertyValue
prop_name = Fe
variable = Fe_fit
[../]
[./autoadjust]
type = MaskedBodyForce
variable = w
function = diff
mask = mask
[../]
[]
[Materials]
# declare a few constants, such as mobilities (L,M) and interface gradient prefactors (kappa*)
[./consts]
type = GenericConstantMaterial
prop_names = 'M L kappa_c kappa_eta'
prop_values = '1.0 1.0 0.5 1'
[../]
# forcing function mask
[./mask]
type = ParsedMaterial
property_name = mask
expression = grad/dt
material_property_names = 'grad dt'
[../]
[./grad]
type = VariableGradientMaterial
variable = c
prop = grad
[../]
[./time]
type = TimeStepMaterial
[../]
# global mechanical properties
[./elasticity_tensor_1]
type = ComputeElasticityTensor
C_ijkl = '1 1'
base_name = phase1
fill_method = symmetric_isotropic
[../]
[./elasticity_tensor_2]
type = ComputeElasticityTensor
C_ijkl = '1 1'
base_name = phase2
fill_method = symmetric_isotropic
[../]
[./strain_1]
type = ComputeRSphericalSmallStrain
base_name = phase1
[../]
[./strain_2]
type = ComputeRSphericalSmallStrain
base_name = phase2
eigenstrain_names = eigenstrain
[../]
[./stress_1]
type = ComputeLinearElasticStress
base_name = phase1
[../]
[./stress_2]
type = ComputeLinearElasticStress
base_name = phase2
[../]
# eigenstrain per phase
[./eigenstrain2]
type = ComputeEigenstrain
eigen_base = '0.05 0.05 0.05 0 0 0'
base_name = phase2
eigenstrain_name = eigenstrain
[../]
# switching functions
[./switching]
type = SwitchingFunctionMaterial
function_name = h
eta = eta
h_order = SIMPLE
[../]
[./barrier]
type = BarrierFunctionMaterial
eta = eta
[../]
# chemical free energies
[./chemical_free_energy_1]
type = DerivativeParsedMaterial
property_name = Fc1
expression = 'c^2'
coupled_variables = 'c'
derivative_order = 2
[../]
[./chemical_free_energy_2]
type = DerivativeParsedMaterial
property_name = Fc2
expression = '(1-c)^2'
coupled_variables = 'c'
derivative_order = 2
[../]
# elastic free energies
[./elastic_free_energy_1]
type = ElasticEnergyMaterial
f_name = Fe1
coupled_variables = ''
base_name = phase1
derivative_order = 2
[../]
[./elastic_free_energy_2]
type = ElasticEnergyMaterial
f_name = Fe2
coupled_variables = ''
base_name = phase2
derivative_order = 2
[../]
# per phase free energies
[./free_energy_1]
type = DerivativeSumMaterial
property_name = F1
sum_materials = 'Fc1 Fe1'
coupled_variables = 'c'
derivative_order = 2
[../]
[./free_energy_2]
type = DerivativeSumMaterial
property_name = F2
sum_materials = 'Fc2 Fe2'
coupled_variables = 'c'
derivative_order = 2
[../]
# global chemical free energy
[./global_free_energy]
type = DerivativeTwoPhaseMaterial
f_name = F
fa_name = F1
fb_name = F2
eta = eta
coupled_variables = 'c'
W = 4
[../]
# global stress
[./global_stress]
type = TwoPhaseStressMaterial
base_A = phase1
base_B = phase2
[../]
[./elastic_free_energy]
type = DerivativeTwoPhaseMaterial
f_name = Fe
fa_name = Fe1
fb_name = Fe2
eta = eta
coupled_variables = 'c'
W = 0
[../]
[]
[BCs]
[./left_r]
type = DirichletBC
variable = disp_r
boundary = 'left'
value = 0
[../]
[]
[Preconditioning]
[./SMP]
type = SMP
full = true
[../]
[]
# We monitor the total free energy and the total solute concentration (should be constant)
[Postprocessors]
[./total_free_energy]
type = ElementIntegralVariablePostprocessor
variable = local_energy
execute_on = 'INITIAL TIMESTEP_END'
outputs = 'table console'
[../]
[./total_solute]
type = ElementIntegralVariablePostprocessor
variable = c
execute_on = 'INITIAL TIMESTEP_END'
outputs = 'table console'
[../]
[./pos_c]
type = FindValueOnLine
start_point = '0 0 0'
end_point = '100 0 0'
v = c
target = 0.582
tol = 1e-8
execute_on = 'INITIAL TIMESTEP_END'
outputs = 'table console'
[../]
[./pos_eta]
type = FindValueOnLine
start_point = '0 0 0'
end_point = '100 0 0'
v = eta
target = 0.5
tol = 1e-8
execute_on = 'INITIAL TIMESTEP_END'
outputs = 'table console'
[../]
[./c_min]
type = ElementExtremeValue
value_type = min
variable = c
execute_on = 'INITIAL TIMESTEP_END'
outputs = 'table console'
[../]
[]
[VectorPostprocessors]
[./line]
type = LineValueSampler
variable = 'Fe_fit c w'
start_point = '0 0 0'
end_point = '100 0 0'
num_points = 5000
sort_by = x
outputs = vpp
execute_on = 'INITIAL TIMESTEP_END'
[../]
[]
[Executioner]
type = Transient
scheme = bdf2
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -sub_pc_type'
petsc_options_value = 'asm lu'
l_max_its = 30
nl_max_its = 15
l_tol = 1.0e-4
nl_rel_tol = 1.0e-8
nl_abs_tol = 2.0e-9
start_time = 0.0
end_time = 100000.0
[./TimeStepper]
type = IterationAdaptiveDT
optimal_iterations = 7
iteration_window = 1
dt = 1
[../]
[./Adaptivity]
initial_adaptivity = 5
interval = 10
max_h_level = 5
refine_fraction = 0.9
coarsen_fraction = 0.1
[../]
[]
[Outputs]
print_linear_residuals = false
perf_graph = true
execute_on = 'INITIAL TIMESTEP_END'
[./table]
type = CSV
delimiter = ' '
file_base = radius_${RADIUS}/energy_pp
[../]
[./vpp]
type = CSV
delimiter = ' '
sync_times = '10 50 100 500 1000 5000 10000 50000 100000'
sync_only = true
time_data = true
file_base = radius_${RADIUS}/energy_vpp
[../]
[]
(modules/combined/examples/mortar/eigenstrain.i)
#
# Eigenstrain with Mortar gradient periodicity
#
[Mesh]
[gen]
type = GeneratedMeshGenerator
dim = 2
nx = 50
ny = 50
xmin = -0.5
xmax = 0.5
ymin = -0.5
ymax = 0.5
[]
[./cnode]
input = gen
type = ExtraNodesetGenerator
coord = '0.0 0.0'
new_boundary = 100
[../]
[./anode]
input = cnode
type = ExtraNodesetGenerator
coord = '0.0 0.5'
new_boundary = 101
[../]
[secondary_x]
input = anode
type = LowerDBlockFromSidesetGenerator
sidesets = '3'
new_block_id = 10
new_block_name = "secondary_x"
[]
[primary_x]
input = secondary_x
type = LowerDBlockFromSidesetGenerator
sidesets = '1'
new_block_id = 12
new_block_name = "primary_x"
[]
[secondary_y]
input = primary_x
type = LowerDBlockFromSidesetGenerator
sidesets = '0'
new_block_id = 11
new_block_name = "secondary_y"
[]
[primary_y]
input = secondary_y
type = LowerDBlockFromSidesetGenerator
sidesets = '2'
new_block_id = 13
new_block_name = "primary_y"
[]
[]
[GlobalParams]
derivative_order = 2
enable_jit = true
displacements = 'disp_x disp_y'
[]
# AuxVars to compute the free energy density for outputting
[AuxVariables]
[./local_energy]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
[./local_free_energy]
type = TotalFreeEnergy
block = 0
execute_on = 'initial LINEAR'
variable = local_energy
interfacial_vars = 'c'
kappa_names = 'kappa_c'
[../]
[]
[Variables]
# Solute concentration variable
[./c]
[./InitialCondition]
type = RandomIC
min = 0.49
max = 0.51
[../]
block = 0
[../]
[./w]
block = 0
[../]
# Mesh displacement
[./disp_x]
block = 0
[../]
[./disp_y]
block = 0
[../]
# Lagrange multipliers for gradient component periodicity
[./lm_left_right_xx]
order = FIRST
family = LAGRANGE
block = secondary_x
[../]
[./lm_left_right_xy]
order = FIRST
family = LAGRANGE
block = secondary_x
[../]
[./lm_left_right_yx]
order = FIRST
family = LAGRANGE
block = secondary_x
[../]
[./lm_left_right_yy]
order = FIRST
family = LAGRANGE
block = secondary_x
[../]
[./lm_up_down_xx]
order = FIRST
family = LAGRANGE
block = secondary_y
[../]
[./lm_up_down_xy]
order = FIRST
family = LAGRANGE
block = secondary_y
[../]
[./lm_up_down_yx]
order = FIRST
family = LAGRANGE
block = secondary_y
[../]
[./lm_up_down_yy]
order = FIRST
family = LAGRANGE
block = secondary_y
[../]
[]
[Constraints]
[./ud_disp_x_grad_x]
type = EqualGradientConstraint
variable = lm_up_down_xx
component = 0
secondary_variable = disp_x
secondary_boundary = bottom
primary_boundary = top
secondary_subdomain = secondary_y
primary_subdomain = primary_y
periodic = true
[../]
[./ud_disp_x_grad_y]
type = EqualGradientConstraint
variable = lm_up_down_xy
component = 1
secondary_variable = disp_x
secondary_boundary = bottom
primary_boundary = top
secondary_subdomain = secondary_y
primary_subdomain = primary_y
periodic = true
[../]
[./ud_disp_y_grad_x]
type = EqualGradientConstraint
variable = lm_up_down_yx
component = 0
secondary_variable = disp_y
secondary_boundary = bottom
primary_boundary = top
secondary_subdomain = secondary_y
primary_subdomain = primary_y
periodic = true
[../]
[./ud_disp_y_grad_y]
type = EqualGradientConstraint
variable = lm_up_down_yy
component = 1
secondary_variable = disp_y
secondary_boundary = bottom
primary_boundary = top
secondary_subdomain = secondary_y
primary_subdomain = primary_y
periodic = true
[../]
[./lr_disp_x_grad_x]
type = EqualGradientConstraint
variable = lm_left_right_xx
component = 0
secondary_variable = disp_x
secondary_boundary = left
primary_boundary = right
secondary_subdomain = secondary_x
primary_subdomain = primary_x
periodic = true
[../]
[./lr_disp_x_grad_y]
type = EqualGradientConstraint
variable = lm_left_right_xy
component = 1
secondary_variable = disp_x
secondary_boundary = left
primary_boundary = right
secondary_subdomain = secondary_x
primary_subdomain = primary_x
periodic = true
[../]
[./lr_disp_y_grad_x]
type = EqualGradientConstraint
variable = lm_left_right_yx
component = 0
secondary_variable = disp_y
secondary_boundary = left
primary_boundary = right
secondary_subdomain = secondary_x
primary_subdomain = primary_x
periodic = true
[../]
[./lr_disp_y_grad_y]
type = EqualGradientConstraint
variable = lm_left_right_yy
component = 1
secondary_variable = disp_y
secondary_boundary = left
primary_boundary = right
secondary_subdomain = secondary_x
primary_subdomain = primary_x
periodic = true
[../]
[]
[Kernels]
# Set up stress divergence kernels
[./TensorMechanics]
block = 0
[../]
# Cahn-Hilliard kernels
[./c_dot]
type = CoupledTimeDerivative
variable = w
v = c
block = 0
[../]
[./c_res]
type = SplitCHParsed
variable = c
f_name = F
kappa_name = kappa_c
w = w
block = 0
[../]
[./w_res]
type = SplitCHWRes
variable = w
mob_name = M
block = 0
[../]
[]
[Materials]
# declare a few constants, such as mobilities (L,M) and interface gradient prefactors (kappa*)
[./consts]
type = GenericConstantMaterial
block = '0 10 11'
prop_names = 'M kappa_c'
prop_values = '0.2 0.01 '
[../]
[./shear1]
type = GenericConstantRankTwoTensor
block = 0
tensor_values = '0 0 0 0 0 0.5'
tensor_name = shear1
[../]
[./shear2]
type = GenericConstantRankTwoTensor
block = 0
tensor_values = '0 0 0 0 0 -0.5'
tensor_name = shear2
[../]
[./expand3]
type = GenericConstantRankTwoTensor
block = 0
tensor_values = '1 1 0 0 0 0'
tensor_name = expand3
[../]
[./weight1]
type = DerivativeParsedMaterial
block = 0
expression = '0.3*c^2'
property_name = weight1
coupled_variables = c
[../]
[./weight2]
type = DerivativeParsedMaterial
block = 0
expression = '0.3*(1-c)^2'
property_name = weight2
coupled_variables = c
[../]
[./weight3]
type = DerivativeParsedMaterial
block = 0
expression = '4*(0.5-c)^2'
property_name = weight3
coupled_variables = c
[../]
# matrix phase
[./elasticity_tensor]
type = ComputeElasticityTensor
block = 0
C_ijkl = '1 1'
fill_method = symmetric_isotropic
[../]
[./strain]
type = ComputeSmallStrain
block = 0
displacements = 'disp_x disp_y'
eigenstrain_names = eigenstrain
[../]
[./eigenstrain]
type = CompositeEigenstrain
block = 0
tensors = 'shear1 shear2 expand3'
weights = 'weight1 weight2 weight3'
coupled_variables = c
eigenstrain_name = eigenstrain
[../]
[./stress]
type = ComputeLinearElasticStress
block = 0
[../]
# chemical free energies
[./chemical_free_energy]
type = DerivativeParsedMaterial
block = 0
property_name = Fc
expression = '4*c^2*(1-c)^2'
coupled_variables = 'c'
outputs = exodus
output_properties = Fc
[../]
# elastic free energies
[./elastic_free_energy]
type = ElasticEnergyMaterial
f_name = Fe
block = 0
coupled_variables = 'c'
outputs = exodus
output_properties = Fe
[../]
# free energy (chemical + elastic)
[./free_energy]
type = DerivativeSumMaterial
block = 0
property_name = F
sum_materials = 'Fc Fe'
coupled_variables = 'c'
[../]
[]
[BCs]
[./Periodic]
[./up_down]
primary = top
secondary = bottom
translation = '0 -1 0'
variable = 'c w'
[../]
[./left_right]
primary = left
secondary = right
translation = '1 0 0'
variable = 'c w'
[../]
[../]
# fix center point location
[./centerfix_x]
type = DirichletBC
boundary = 100
variable = disp_x
value = 0
[../]
[./centerfix_y]
type = DirichletBC
boundary = 100
variable = disp_y
value = 0
[../]
# fix side point x coordinate to inhibit rotation
[./angularfix]
type = DirichletBC
boundary = 101
variable = disp_x
value = 0
[../]
[]
[Preconditioning]
[./SMP]
type = SMP
full = true
[../]
[]
# We monitor the total free energy and the total solute concentration (should be constant)
[Postprocessors]
[./total_free_energy]
type = ElementIntegralVariablePostprocessor
block = 0
execute_on = 'initial TIMESTEP_END'
variable = local_energy
[../]
[./total_solute]
type = ElementIntegralVariablePostprocessor
block = 0
execute_on = 'initial TIMESTEP_END'
variable = c
[../]
[./min]
type = ElementExtremeValue
block = 0
execute_on = 'initial TIMESTEP_END'
value_type = min
variable = c
[../]
[./max]
type = ElementExtremeValue
block = 0
execute_on = 'initial TIMESTEP_END'
value_type = max
variable = c
[../]
[]
[Executioner]
type = Transient
scheme = bdf2
solve_type = 'PJFNK'
line_search = basic
# mortar currently does not support MPI parallelization
petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_shift_amount'
petsc_options_value = ' lu NONZERO 1e-10'
l_max_its = 30
nl_max_its = 12
l_tol = 1.0e-4
nl_rel_tol = 1.0e-8
nl_abs_tol = 1.0e-10
start_time = 0.0
num_steps = 200
[./TimeStepper]
type = SolutionTimeAdaptiveDT
dt = 0.01
[../]
[]
[Outputs]
execute_on = 'timestep_end'
print_linear_residuals = false
exodus = true
[./table]
type = CSV
delimiter = ' '
[../]
[]
(modules/phase_field/test/tests/TotalFreeEnergy/TotalFreeEnergy_2var_test.i)
[Mesh]
type = GeneratedMesh
dim = 2
nx = 10
ny = 10
nz = 0
xmin = 0
xmax = 1000
ymin = 0
ymax = 1000
zmin = 0
zmax = 0
elem_type = QUAD4
uniform_refine = 2
[]
[GlobalParams]
op_num = 2
var_name_base = gr
[]
[Variables]
[./PolycrystalVariables]
[../]
[]
[ICs]
[./PolycrystalICs]
[./BicrystalCircleGrainIC]
radius = 333.333
x = 500
y = 500
int_width = 60
[../]
[../]
[]
[AuxVariables]
[./bnds]
order = FIRST
family = LAGRANGE
[../]
[./local_energy]
order = CONSTANT
family = MONOMIAL
[../]
[]
[Kernels]
[./gr0dot]
type = TimeDerivative
variable = gr0
[../]
[./gr0bulk]
type = AllenCahn
variable = gr0
f_name = F
coupled_variables = gr1
[../]
[./gr0int]
type = ACInterface
variable = gr0
kappa_name = kappa_op
[../]
[./gr1dot]
type = TimeDerivative
variable = gr1
[../]
[./gr1bulk]
type = AllenCahn
variable = gr1
f_name = F
coupled_variables = gr0
[../]
[./gr1int]
type = ACInterface
variable = gr1
kappa_name = kappa_op
[../]
[]
[AuxKernels]
[./BndsCalc]
type = BndsCalcAux
variable = bnds
[../]
[./local_free_energy]
type = TotalFreeEnergy
variable = local_energy
kappa_names = 'kappa_op kappa_op'
interfacial_vars = 'gr0 gr1'
[../]
[]
[BCs]
[./Periodic]
[./All]
auto_direction = 'x y'
[../]
[../]
[]
[Materials]
[./Copper]
type = GBEvolution
T = 500 # K
wGB = 60 # nm
GBmob0 = 2.5e-6 # m^4/(Js) from Schoenfelder 1997
Q = 0.23 # Migration energy in eV
GBenergy = 0.708 # GB energy in J/m^2
[../]
[./free_energy]
type = DerivativeParsedMaterial
coupled_variables = 'gr0 gr1'
material_property_names = 'mu gamma_asymm'
expression = 'mu*( gr0^4/4.0 - gr0^2/2.0 + gr1^4/4.0 - gr1^2/2.0 + gamma_asymm*gr0^2*gr1^2) + 1.0/4.0'
derivative_order = 2
enable_jit = true
[../]
[]
[Postprocessors]
[./total_energy]
type = ElementIntegralVariablePostprocessor
variable = local_energy
[../]
[]
[Preconditioning]
[./SMP]
type = SMP
full = true
[../]
[]
[Executioner]
type = Transient
scheme = bdf2
solve_type = NEWTON
petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart'
petsc_options_value = 'hypre boomeramg 31'
l_tol = 1.0e-4
l_max_its = 30
nl_max_its = 30
nl_rel_tol = 1.0e-10
start_time = 0.0
num_steps = 7
dt = 80.0
[./Adaptivity]
initial_adaptivity = 2
refine_fraction = 0.8
coarsen_fraction = 0.05
max_h_level = 2
[../]
[]
[Outputs]
execute_on = 'timestep_end'
exodus = true
[]
(modules/phase_field/examples/rigidbodymotion/AC_CH_Multigrain.i)
# Tests the rigid body motion due to applied force of multiple particles.
# ***COPY AND PASTE THESE AS NEEDED***
# 'gr0 gr1 gr2 gr3 gr4 gr5 gr6 gr7 gr8 gr9 gr10 gr11 gr12 gr13 gr14 gr15 gr16 gr17 gr18 gr19'
# (gr0^2+gr1^2+gr2^2+gr3^2+gr4^2+gr5^2+gr6^2+gr7^2+gr8^2+gr9^2+gr10^2+gr11^2+gr12^2+gr13^2+gr14^2+gr15^2+gr16^2+gr17^2+gr18^2+gr19^2)
# (gr0^3+gr1^3+gr2^3+gr3^3+gr4^3+gr5^3+gr6^3+gr7^3+gr8^3+gr9^3+gr10^3+gr11^3+gr12^3+gr13^3+gr14^3+gr15^3+gr16^3+gr17^3+gr18^3+gr19^3)
[GlobalParams]
op_num = 4
var_name_base = gr
[]
[Mesh]
type = GeneratedMesh
dim = 2
nx = 15
ny = 15
xmin = 0
xmax = 600
ymin = 0
ymax = 600
elem_type = QUAD4
uniform_refine = 1
[]
[Variables]
[./c]
[../]
[./w]
[../]
[./PolycrystalVariables] # Automatically creates order parameter variables
[../]
[]
[AuxVariables]
[./bnds]
[../]
[./force]
order = CONSTANT
family = MONOMIAL
[../]
[./free_energy]
order = CONSTANT
family = MONOMIAL
[../]
[./unique_grains]
order = CONSTANT
family = MONOMIAL
[../]
[./var_indices]
order = CONSTANT
family = MONOMIAL
[../]
[./centroids]
order = CONSTANT
family = MONOMIAL
[../]
[]
[Functions]
[./load_x]
# Defines the force on the grains in the x-direction
type = ParsedFunction
expression = 0.005*cos(x*pi/600)
[../]
[./load_y]
# Defines the force on the grains in the y-direction
type = ConstantFunction
value = 0.002
[../]
[]
[Kernels]
[./RigidBodyMultiKernel]
# Creates all of the necessary Allen Cahn kernels automatically
c = c
f_name = f_loc
mob_name = L
kappa_name = kappa_gr
grain_force = grain_force
grain_volumes = grain_volumes
grain_tracker_object = grain_center
[../]
# Cahn Hilliard kernels
[./dt_w]
type = CoupledTimeDerivative
variable = w
v = c
[../]
[./CH_wres]
type = SplitCHWRes
variable = w
mob_name = M
[../]
[./CH_Parsed]
type = SplitCHParsed
variable = c
f_name = f_loc
w = w
kappa_name = kappa_c
coupled_variables = 'gr0 gr1 gr2 gr3' # Must be changed as op_num changes. Copy/paste from line 4
[../]
[./CH_RBM]
type = MultiGrainRigidBodyMotion
variable = w
c = c
v = 'gr0 gr1 gr2 gr3'
grain_force = grain_force
grain_volumes = grain_volumes
grain_tracker_object = grain_center
[../]
[]
[AuxKernels]
[./force_x]
type = FunctionAux
variable = force
function = load_x
[../]
[./force_y]
type = FunctionAux
variable = force
function = load_y
[../]
[./energy_density]
type = TotalFreeEnergy
variable = free_energy
f_name = f_loc
kappa_names = kappa_c
interfacial_vars = c
[../]
[./bnds]
type = BndsCalcAux
variable = bnds
[../]
[]
[BCs]
[./bcs]
#zero flux BC
type = NeumannBC
value = 0
variable = c
boundary = '0 1 2 3'
[../]
[]
[Materials]
[./constants]
type = GenericConstantMaterial
prop_names = 'kappa_gr kappa_c M L'
prop_values = '250 4000 4.5 60'
[../]
[./free_energy]
type = DerivativeParsedMaterial
property_name = f_loc
constant_names = 'A B'
constant_expressions = '450 1.5'
coupled_variables = 'c gr0 gr1 gr2 gr3' #Must be changed as op_num changes. Copy/paste from line 4
expression = 'A*c^2*(1-c)^2+B*(c^2+6*(1-c)*(gr0^2+gr1^2+gr2^2+gr3^2)
-4*(2-c)*(gr0^3+gr1^3+gr2^3+gr3^3)
+3*(gr0^2+gr1^2+gr2^2+gr3^2)^2)'
#Copy/paste from lines 5-6
derivative_order = 2
[../]
[./force_density]
type = ExternalForceDensityMaterial
c = c
k = 10.0
force_x = load_x
force_y = load_y
[../]
[]
[Postprocessors]
[./total_energy]
type = ElementIntegralVariablePostprocessor
variable = free_energy
execute_on = 'initial timestep_end'
[../]
[]
[VectorPostprocessors]
[./forces]
type = GrainForcesPostprocessor
grain_force = grain_force
[../]
[./grain_volumes]
type = FeatureVolumeVectorPostprocessor
flood_counter = grain_center
execute_on = 'initial timestep_begin'
[../]
[]
[UserObjects]
[./grain_center]
type = GrainTracker
outputs = none
compute_var_to_feature_map = true
execute_on = 'initial timestep_begin'
[../]
[./grain_force]
type = ComputeExternalGrainForceAndTorque
grain_data = grain_center
c = c
etas = 'gr0 gr1 gr2 gr3'
force_density = force_density_ext
execute_on = 'linear nonlinear'
[../]
[]
[Preconditioning]
[./coupled]
type = SMP
full = true
[../]
[]
[Executioner]
type = Transient
scheme = bdf2
solve_type = NEWTON
petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_ksp_type
-sub_pc_type -pc_asm_overlap'
petsc_options_value = 'asm 31 preonly
ilu 2'
l_tol = 1e-05
nl_max_its = 30
l_max_its = 30
nl_rel_tol = 1e-07
nl_abs_tol = 1e-09
start_time = 0.0
end_time = 4
dt = 0.05
[]
[Outputs]
exodus = true
perf_graph = true
[./display]
type = Console
max_rows = 12
[../]
[]
[ICs]
[./concentration_IC]
type = SpecifiedSmoothCircleIC
x_positions = '150 450 150 450'
y_positions = '150 150 450 450'
z_positions = '0 0 0 0'
radii = '120 120 120 120'
variable = c
invalue = 1.0
outvalue = 0.0
int_width = 25
[../]
[./gr0_IC]
type = SmoothCircleIC
variable = gr0
x1 = 150
y1 = 150
radius = 120
invalue = 1.0
outvalue = 0.0
int_width = 25
[../]
[./gr1_IC]
type = SmoothCircleIC
variable = gr1
x1 = 450
y1 = 150
radius = 120
invalue = 1.0
outvalue = 0.0
int_width = 25
[../]
[./gr2_IC]
type = SmoothCircleIC
variable = gr2
x1 = 150
y1 = 450
radius = 120
invalue = 1.0
outvalue = 0.0
int_width = 25
[../]
[./gr3_IC]
type = SmoothCircleIC
variable = gr3
x1 = 450
y1 = 450
radius = 120
invalue = 1.0
outvalue = 0.0
int_width = 25
[../]
[]
(modules/phase_field/test/tests/free_energy_material/CoupledValueFunctionFreeEnergy.i)
[Mesh]
type = GeneratedMesh
dim = 2
nx = 10
ny = 10
nz = 0
xmin = 0
xmax = 500
ymin = 0
ymax = 500
zmin = 0
zmax = 0
elem_type = QUAD4
[]
[GlobalParams]
op_num = 4
var_name_base = gr
[]
[Variables]
[PolycrystalVariables]
[]
[]
[Functions]
[grain_growth_energy]
type = PiecewiseMultilinear
data_file = grain_growth_energy.data
[]
[grain_growth_mu0]
type = PiecewiseMultilinear
data_file = grain_growth_mu0.data
[]
[grain_growth_mu1]
type = PiecewiseMultilinear
data_file = grain_growth_mu1.data
[]
[grain_growth_mu2]
type = PiecewiseMultilinear
data_file = grain_growth_mu2.data
[]
[grain_growth_mu3]
type = PiecewiseMultilinear
data_file = grain_growth_mu3.data
[]
[matrix]
type = ParsedFunction
expression = '1-x-y-z'
[]
[]
[ICs]
[gr1]
type = SmoothCircleIC
variable = gr1
x1 = 0
y1 = 0
radius = 150
int_width = 90
invalue = 1
outvalue = 0
[]
[gr2]
type = SmoothCircleIC
variable = gr2
x1 = 500
y1 = 0
radius = 120
int_width = 90
invalue = 1
outvalue = 0
[]
[gr3]
type = SmoothCircleIC
variable = gr3
x1 = 250
y1 = 500
radius = 300
int_width = 90
invalue = 1
outvalue = 0
[]
[gr0]
type = CoupledValueFunctionIC
variable = gr0
v = 'gr1 gr2 gr3'
function = matrix
[]
[]
[AuxVariables]
[bnds]
order = FIRST
family = LAGRANGE
[]
[local_energy]
order = CONSTANT
family = MONOMIAL
[]
[]
[Kernels]
[gr0dot]
type = TimeDerivative
variable = gr0
[]
[gr0bulk]
type = AllenCahn
variable = gr0
f_name = F
coupled_variables = 'gr1 gr2 gr3'
[]
[gr0int]
type = ACInterface
variable = gr0
kappa_name = kappa_op
[]
[gr1dot]
type = TimeDerivative
variable = gr1
[]
[gr1bulk]
type = AllenCahn
variable = gr1
f_name = F
coupled_variables = 'gr0 gr2 gr3'
[]
[gr1int]
type = ACInterface
variable = gr1
kappa_name = kappa_op
[]
[gr2dot]
type = TimeDerivative
variable = gr2
[]
[gr2bulk]
type = AllenCahn
variable = gr2
f_name = F
coupled_variables = 'gr0 gr1 gr3'
[]
[gr2int]
type = ACInterface
variable = gr2
kappa_name = kappa_op
[]
[gr3dot]
type = TimeDerivative
variable = gr3
[]
[gr3bulk]
type = AllenCahn
variable = gr3
f_name = F
coupled_variables = 'gr0 gr1 gr2'
[]
[gr3int]
type = ACInterface
variable = gr3
kappa_name = kappa_op
[]
[]
[AuxKernels]
[BndsCalc]
type = BndsCalcAux
variable = bnds
[]
[local_free_energy]
type = TotalFreeEnergy
variable = local_energy
kappa_names = 'kappa_op kappa_op kappa_op kappa_op'
interfacial_vars = 'gr0 gr1 gr2 gr3'
[]
[]
[Materials]
[Copper]
type = GBEvolution
T = 500 # K
wGB = 60 # nm
GBmob0 = 2.5e-6 # m^4/(Js) from Schoenfelder 1997
Q = 0.23 # Migration energy in eV
GBenergy = 0.708 # GB energy in J/m^2
[]
[Tabulated]
type = CoupledValueFunctionFreeEnergy
free_energy_function = grain_growth_energy
chemical_potential_functions = 'grain_growth_mu0 grain_growth_mu1 grain_growth_mu2 '
'grain_growth_mu3'
v = 'gr0 gr1 gr2 gr3'
[]
[]
[Postprocessors]
[total_energy]
type = ElementIntegralVariablePostprocessor
variable = local_energy
[]
[]
[Preconditioning]
[SMP]
type = SMP
coupled_groups = 'gr0,gr1 gr0,gr2 gr0,gr3'
[]
[]
[Executioner]
type = Transient
scheme = bdf2
solve_type = NEWTON
l_tol = 1.0e-4
l_max_its = 30
nl_max_its = 30
nl_rel_tol = 1.0e-9
start_time = 0.0
num_steps = 3
dt = 100.0
[]
[Outputs]
exodus = true
print_linear_residuals = false
perf_graph = true
[]
(modules/phase_field/test/tests/MultiPhase/crosstermfreeenergy.i)
[Mesh]
type = GeneratedMesh
dim = 2
nx = 20
ny = 20
nz = 0
xmin = -8
xmax = 8
ymin = -8
ymax = 8
elem_type = QUAD4
[]
[AuxVariables]
[./local_energy]
order = CONSTANT
family = MONOMIAL
[../]
[./cross_energy]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
[./local_free_energy]
type = TotalFreeEnergy
f_name = F0
variable = local_energy
additional_free_energy = cross_energy
[../]
[./cross_terms]
type = CrossTermGradientFreeEnergy
variable = cross_energy
interfacial_vars = 'eta1 eta2 eta3'
kappa_names = 'kappa11 kappa12 kappa13
kappa21 kappa22 kappa23
kappa31 kappa32 kappa33'
[../]
[]
[Variables]
[./eta1]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = SmoothCircleIC
x1 = 0.0
y1 = 5.0
radius = 5.0
invalue = 1.0
outvalue = 0.0
int_width = 10.0
[../]
[../]
[./eta2]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = SmoothCircleIC
x1 = -4.0
y1 = -2.0
radius = 5.0
invalue = 1.0
outvalue = 0.0
int_width = 10.0
[../]
[../]
[./eta3]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = SmoothCircleIC
x1 = 4.0
y1 = -2.0
radius = 5.0
invalue = 1.0
outvalue = 0.0
int_width = 10.0
[../]
[../]
[]
[Kernels]
[./dummy_diff1]
type = Diffusion
variable = eta1
[../]
[./dummy_time1]
type = TimeDerivative
variable = eta1
[../]
[./dummy_diff2]
type = Diffusion
variable = eta2
[../]
[./dummy_time2]
type = TimeDerivative
variable = eta2
[../]
[./dummy_diff3]
type = Diffusion
variable = eta3
[../]
[./dummy_tim3]
type = TimeDerivative
variable = eta3
[../]
[]
[Materials]
[./consts]
type = GenericConstantMaterial
prop_names = 'F0 kappa11 kappa12 kappa13 kappa21 kappa22 kappa23 kappa31 kappa32 kappa33'
prop_values = '0 11 12 13 12 22 23 13 23 33 '
[../]
[]
[Executioner]
type = Transient
dt = 0.001
num_steps = 1
[]
[Outputs]
execute_on = 'timestep_end'
[./out]
type = Exodus
hide = 'eta1 eta2 eta3 local_energy'
[../]
[]
(modules/phase_field/test/tests/TotalFreeEnergy/TotalFreeEnergy_test.i)
#
# Test the TotalFreeEnergy auxkernel, which outputs both the sum of the bulk and interfacial free energies. This test has only one variable.
#
[Mesh]
type = GeneratedMesh
dim = 2
nx = 30
ny = 30
nz = 0
xmin = 0
xmax = 250
ymin = 0
ymax = 250
zmin = 0
zmax = 0
elem_type = QUAD4
[]
[Variables]
[./c]
[../]
[./w]
[../]
[]
[AuxVariables]
[./local_free_energy]
order = CONSTANT
family = MONOMIAL
[../]
[]
[ICs]
[./cIC]
type = SmoothCircleIC
variable = c
x1 = 125.0
y1 = 125.0
radius = 60.0
invalue = 1.0
outvalue = 0.1
int_width = 30.0
[../]
[]
[Kernels]
[./c_res]
type = SplitCHParsed
variable = c
f_name = F
kappa_name = kappa_c
w = w
[../]
[./w_res]
type = SplitCHWRes
variable = w
mob_name = M
[../]
[./time]
type = CoupledTimeDerivative
variable = w
v = c
[../]
[]
[AuxKernels]
[./local_free_energy]
type = TotalFreeEnergy
variable = local_free_energy
kappa_names = kappa_c
interfacial_vars = c
[../]
[]
[Materials]
[./pfmobility]
type = GenericConstantMaterial
prop_names = 'M kappa_c'
prop_values = '1e-3 0.1'
[../]
[./free_energy]
type = DerivativeParsedMaterial
coupled_variables = c
constant_names = 'barr_height cv_eq'
constant_expressions = '0.1 1.0e-2'
expression = 16*barr_height*(c-cv_eq)^2*(1-cv_eq-c)^2
derivative_order = 2
[../]
[]
[Postprocessors]
[./total_free_energy]
type = ElementIntegralVariablePostprocessor
variable = local_free_energy
[../]
[]
[Preconditioning]
[./SMP]
type = SMP
full = true
[../]
[]
[Executioner]
type = Transient
scheme = bdf2
solve_type = NEWTON
petsc_options_iname = -pc_type
petsc_options_value = lu
l_max_its = 30
l_tol = 1.0e-4
nl_rel_tol = 1.0e-10
start_time = 0.0
num_steps = 6
dt = 200
[]
[Outputs]
execute_on = 'timestep_end'
exodus = true
[]