- first_order_varsA subset of variables that require first-order integration (velocity only) to be applied by this time integrator.
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:A subset of variables that require first-order integration (velocity only) to be applied by this time integrator.
- mass_matrix_tagmassThe tag for the mass matrix
Default:mass
C++ Type:TagName
Controllable:No
Description:The tag for the mass matrix
- second_order_varsA subset of variables that require second-order integration (velocity and acceleration) to be applied by this time integrator.
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:A subset of variables that require second-order integration (velocity and acceleration) to be applied by this time integrator.
- use_constant_massFalseIf set to true, will only compute the mass matrix in the first time step, and keep using it throughout the simulation.
Default:False
C++ Type:bool
Controllable:No
Description:If set to true, will only compute the mass matrix in the first time step, and keep using it throughout the simulation.
ExplicitMixedOrder
Implementation of explicit time integration without invoking any of the nonlinear solver.
Overview
ExplicitMixedOrder applies a time integrator for central difference in which the acceleration used for the solution update is calculated directly from the residual forces.
The formulation assumes a constant acceleration between midpoints. An average between the old and current time step is used to increment midpoint velocity to account for changing time steps, which is the same method used in Abaqus.
For example if, then,
When using Dirichlet BCs, one must use the (ExplicitDirichletBC,ExplicitFunctionDirichletBC) variations to enforce Dirichlet BC's properly.
Additionally, the time integrator must be used with MassMatrix, with a properly tagged mass matrix.
Example Input File Syntax
An example input file is shown below:
[GlobalParams]
displacements = 'disp_x disp_y'
[]
[Kernels]
[DynamicSolidMechanics]
displacements = 'disp_x disp_y'
[]
[massmatrix]
type = MassMatrix
density = 1
matrix_tags = 'system'
variable = disp_x
[]
[massmatrix_y]
type = MassMatrix
density = 1
matrix_tags = 'system'
variable = disp_y
[]
[]
[Executioner]
type = Transient
[TimeIntegrator]
type = CentralDifferenceDirect
mass_matrix_tag = 'system'
[]
[]
Input 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:No
Description:Set the enabled status of the MooseObject.
Advanced Parameters
Input Files
- (modules/contact/test/tests/explicit_dynamics/highvel.i)
- (modules/contact/test/tests/explicit_dynamics/deep_impact.i)
- (modules/contact/test/tests/explicit_dynamics/test_balance_optimized.i)
- (modules/contact/test/tests/explicit_dynamics/settlement.i)
- (modules/solid_mechanics/test/tests/dynamics/time_integration/direct_central_difference_multiVarBC.i)
- (modules/solid_mechanics/test/tests/dynamics/explicit_mms/mms_direct_combined.i)
- (modules/contact/test/tests/explicit_dynamics/test_balance.i)
- (modules/solid_mechanics/test/tests/dynamics/explicit_mms/mms_direct_second_order_with_ic.i)
- (modules/solid_mechanics/test/tests/dynamics/time_integration/direct_central_difference_varied_dt.i)
- (modules/solid_mechanics/test/tests/dynamics/time_integration/direct_central_difference.i)
(modules/contact/test/tests/explicit_dynamics/highvel.i)
# One element test to test the central difference time integrator in 3D.
[GlobalParams]
displacements = 'disp_x disp_y disp_z'
volumetric_locking_correction = true
[]
[Problem]
extra_tag_matrices = 'mass'
[]
[Mesh]
[block_one]
type = GeneratedMeshGenerator
dim = 3
nx = 3
ny = 3
nz = 3
xmin = 4.5
xmax = 5.5
ymin = 4.5
ymax = 5.5
zmin = 0.06
zmax = 1.06
boundary_name_prefix = 'ball'
[]
[block_two]
type = GeneratedMeshGenerator
dim = 3
nx = 2
ny = 2
nz = 2
xmin = 0.0
xmax = 10
ymin = 0.0
ymax = 10
zmin = -2
zmax = 0
boundary_name_prefix = 'base'
boundary_id_offset = 10
[]
[block_one_id]
type = SubdomainIDGenerator
input = block_one
subdomain_id = 1
[]
[block_two_id]
type = SubdomainIDGenerator
input = block_two
subdomain_id = 2
[]
[combine]
type = MeshCollectionGenerator
inputs = ' block_one_id block_two_id'
[]
[]
[AuxVariables]
[penetration]
[]
[]
[AuxKernels]
[penetration]
type = PenetrationAux
variable = penetration
boundary = ball_back
paired_boundary = base_front
quantity = distance
[]
[]
[Variables]
[disp_x]
[]
[disp_y]
[]
[disp_z]
[]
[]
[AuxVariables]
[gap_rate]
[]
[vel_x]
[]
[accel_x]
[]
[vel_y]
[]
[accel_y]
[]
[vel_z]
[]
[accel_z]
[]
[stress_zz]
family = MONOMIAL
order = CONSTANT
[]
[strain_zz]
family = MONOMIAL
order = CONSTANT
[]
[kinetic_energy_one]
order = CONSTANT
family = MONOMIAL
[]
[elastic_energy_one]
order = CONSTANT
family = MONOMIAL
[]
[kinetic_energy_two]
order = CONSTANT
family = MONOMIAL
[]
[elastic_energy_two]
order = CONSTANT
family = MONOMIAL
[]
[]
[AuxKernels]
[stress_zz]
type = RankTwoAux
rank_two_tensor = stress
index_i = 2
index_j = 2
variable = stress_zz
execute_on = 'TIMESTEP_END'
[]
[strain_zz]
type = RankTwoAux
rank_two_tensor = mechanical_strain
index_i = 2
index_j = 2
variable = strain_zz
[]
[accel_x]
type = TestNewmarkTI
variable = accel_x
displacement = disp_x
first = false
execute_on = 'LINEAR TIMESTEP_BEGIN TIMESTEP_END'
[]
[vel_x]
type = TestNewmarkTI
variable = vel_x
displacement = disp_x
execute_on = 'LINEAR TIMESTEP_BEGIN TIMESTEP_END'
[]
[accel_y]
type = TestNewmarkTI
variable = accel_y
displacement = disp_y
first = false
execute_on = 'LINEAR TIMESTEP_BEGIN TIMESTEP_END'
[]
[vel_y]
type = TestNewmarkTI
variable = vel_y
displacement = disp_x
execute_on = 'LINEAR TIMESTEP_BEGIN TIMESTEP_END'
[]
[accel_z]
type = TestNewmarkTI
variable = accel_z
displacement = disp_z
first = false
execute_on = 'LINEAR TIMESTEP_BEGIN TIMESTEP_END'
[]
[vel_z]
type = TestNewmarkTI
variable = vel_z
displacement = disp_z
execute_on = 'LINEAR TIMESTEP_BEGIN TIMESTEP_END'
[]
[kinetic_energy_one]
type = KineticEnergyAux
block = '1'
variable = kinetic_energy_one
newmark_velocity_x = vel_x
newmark_velocity_y = vel_y
newmark_velocity_z = vel_z
density = density
[]
[elastic_energy_one]
type = ElasticEnergyAux
variable = elastic_energy_one
block = '1'
[]
[kinetic_energy_two]
type = KineticEnergyAux
block = '2'
variable = kinetic_energy_two
newmark_velocity_x = vel_x
newmark_velocity_y = vel_y
newmark_velocity_z = vel_z
density = density
[]
[elastic_energy_two]
type = ElasticEnergyAux
variable = elastic_energy_two
block = '2'
[]
[]
[Kernels]
[DynamicTensorMechanics]
displacements = 'disp_x disp_y disp_z'
stiffness_damping_coefficient = 1.0e-3
generate_output = 'stress_zz strain_zz'
[]
[Mass_x]
type = MassMatrix
variable = disp_x
density = density
matrix_tags = 'mass'
[]
[Mass_y]
type = MassMatrix
variable = disp_y
density = density
matrix_tags = 'mass'
[]
[Mass_z]
type = MassMatrix
variable = disp_z
density = density
matrix_tags = 'mass'
[]
[gravity]
type = Gravity
variable = disp_z
value = -981
block = 1
[]
[]
[BCs]
[x_front]
type = ExplicitDirichletBC
variable = disp_x
boundary = 'ball_front'
value = 0.0
[]
[y_front]
type = ExplicitDirichletBC
variable = disp_y
boundary = 'ball_front'
value = 0.0
[]
[x_fixed]
type = ExplicitDirichletBC
variable = disp_x
boundary = 'base_back'
value = 0.0
[]
[y_fixed]
type = ExplicitDirichletBC
variable = disp_y
boundary = 'base_back'
value = 0.0
[]
[z_fixed]
type = ExplicitDirichletBC
variable = disp_z
boundary = 'base_back'
value = 0.0
[]
[z_fixed_front]
type = ExplicitDirichletBC
variable = disp_z
boundary = 'base_front'
value = 0.0
[]
[]
[ExplicitDynamicsContact]
[my_contact]
model = frictionless_balance
primary = base_front
secondary = ball_back
vel_x = 'vel_x'
vel_y = 'vel_y'
vel_z = 'vel_z'
verbose = true
[]
[]
[Materials]
[elasticity_tensor_block_one]
type = ComputeIsotropicElasticityTensor
youngs_modulus = 1e6
poissons_ratio = 0.0
block = 1
outputs = 'exodus'
output_properties = __all__
[]
[elasticity_tensor_block_two]
type = ComputeIsotropicElasticityTensor
youngs_modulus = 1e10
poissons_ratio = 0.0
block = 2
outputs = 'exodus'
output_properties = __all__
[]
[strain_block]
type = ComputeFiniteStrain # ComputeIncrementalSmallStrain
displacements = 'disp_x disp_y disp_z'
implicit = false
[]
[stress_block]
type = ComputeFiniteStrainElasticStress
[]
[density_one]
type = GenericConstantMaterial
prop_names = density
prop_values = 1e1
outputs = 'exodus'
output_properties = 'density'
block = '1'
[]
[density_two]
type = GenericConstantMaterial
prop_names = density
prop_values = 1e6
outputs = 'exodus'
output_properties = 'density'
block = '2'
[]
[wave_speed]
type = WaveSpeed
outputs = 'exodus'
output_properties = 'wave_speed'
[]
[]
[Executioner]
type = Transient
end_time = 0.03
dt = 2e-4
timestep_tolerance = 1e-6
[TimeIntegrator]
type = ExplicitMixedOrder
mass_matrix_tag = mass
second_order_vars = 'disp_x disp_y disp_z'
[]
[]
[Outputs]
interval = 2
exodus = true
csv = true
execute_on = 'TIMESTEP_END'
file_base = highvel_out
[]
[Postprocessors]
[accel_58z]
type = NodalVariableValue
nodeid = 1
variable = accel_z
[]
[vel_58z]
type = NodalVariableValue
nodeid = 1
variable = vel_z
[]
[critical_time_step]
type = CriticalTimeStep
[]
[contact_pressure_max]
type = NodalExtremeValue
variable = contact_pressure
block = '1 2'
value_type = max
[]
[penetration_max]
type = NodalExtremeValue
variable = penetration
block = '1 2'
value_type = max
[]
[total_kinetic_energy_one]
type = ElementIntegralVariablePostprocessor
variable = kinetic_energy_one
block = '1'
[]
[total_elastic_energy_one]
type = ElementIntegralVariablePostprocessor
variable = elastic_energy_one
block = '1'
[]
[total_kinetic_energy_two]
type = ElementIntegralVariablePostprocessor
variable = kinetic_energy_two
block = '2'
[]
[total_elastic_energy_two]
type = ElementIntegralVariablePostprocessor
variable = elastic_energy_two
block = '2'
[]
[]
(modules/contact/test/tests/explicit_dynamics/deep_impact.i)
# This test demonstrates explicit contact with MOOSE and includes optimizations
# to enhance performance.
[GlobalParams]
displacements = 'disp_x disp_y disp_z'
[]
[Problem]
extra_tag_matrices = 'mass'
[]
[Mesh]
[block_one]
type = GeneratedMeshGenerator
dim = 3
nx = 4
ny = 4
nz = 4
xmin = 4.5
xmax = 5.5
ymin = 4.5
ymax = 5.5
zmin = 0.0001
zmax = 1.0001
boundary_name_prefix = 'ball'
[]
[block_two]
type = GeneratedMeshGenerator
dim = 3
nx = 9
ny = 9
nz = 4
xmin = 3
xmax = 7
ymin = 3
ymax = 7
zmin = -2
zmax = 0
boundary_name_prefix = 'base'
boundary_id_offset = 10
[]
[block_one_id]
type = SubdomainIDGenerator
input = block_one
subdomain_id = 1
[]
[block_two_id]
type = SubdomainIDGenerator
input = block_two
subdomain_id = 2
[]
[combine]
type = MeshCollectionGenerator
inputs = ' block_one_id block_two_id'
[]
allow_renumbering = false
# patch_update_strategy = always
[]
[Variables]
[disp_x]
[]
[disp_y]
[]
[disp_z]
[]
[]
[AuxVariables]
[gap_rate]
[]
[vel_x]
[]
[accel_x]
[]
[vel_y]
[]
[accel_y]
[]
[vel_z]
[]
[accel_z]
[]
[]
[AuxKernels]
[accel_x]
type = TestNewmarkTI
variable = accel_x
displacement = disp_x
first = false
execute_on = 'TIMESTEP_END'
[]
[vel_x]
type = TestNewmarkTI
variable = vel_x
displacement = disp_x
execute_on = 'TIMESTEP_END'
[]
[accel_y]
type = TestNewmarkTI
variable = accel_y
displacement = disp_y
first = false
execute_on = 'TIMESTEP_END'
[]
[vel_y]
type = TestNewmarkTI
variable = vel_y
displacement = disp_x
execute_on = 'TIMESTEP_END'
[]
[accel_z]
type = TestNewmarkTI
variable = accel_z
displacement = disp_z
first = false
execute_on = 'TIMESTEP_END'
[]
[vel_z]
type = TestNewmarkTI
variable = vel_z
displacement = disp_z
execute_on = 'TIMESTEP_END'
[]
[]
[Kernels]
[DynamicTensorMechanics]
displacements = 'disp_x disp_y disp_z'
[]
[Mass_x]
type = MassMatrix
variable = disp_x
density = density
matrix_tags = 'mass'
[]
[Mass_y]
type = MassMatrix
variable = disp_y
density = density
matrix_tags = 'mass'
[]
[Mass_z]
type = MassMatrix
variable = disp_z
density = density
matrix_tags = 'mass'
[]
[]
[Kernels]
[gravity]
type = Gravity
variable = disp_z
value = -981.0
block = 1
[]
[]
[BCs]
[x_front]
type = ExplicitDirichletBC
variable = disp_x
boundary = 'ball_front'
value = 0.0
[]
[y_front]
type = ExplicitDirichletBC
variable = disp_y
boundary = 'ball_front'
value = 0.0
[]
[x_fixed]
type = ExplicitDirichletBC
variable = disp_x
boundary = 'base_back'
value = 0.0
[]
[y_fixed]
type = ExplicitDirichletBC
variable = disp_y
boundary = 'base_back'
value = 0.0
[]
[z_fixed]
type = ExplicitDirichletBC
variable = disp_z
boundary = 'base_back'
value = 0.0
[]
[]
[ExplicitDynamicsContact]
[my_contact]
model = frictionless_balance
primary = 'base_front ball_back'
secondary = 'ball_back base_front'
vel_x = 'vel_x'
vel_y = 'vel_y'
vel_z = 'vel_z'
[]
[]
[Materials]
[elasticity_tensor_block_one]
type = ComputeIsotropicElasticityTensor
youngs_modulus = 1e1
poissons_ratio = 0.3
block = 1
constant_on = SUBDOMAIN
[]
[elasticity_tensor_block_two]
type = ComputeIsotropicElasticityTensor
youngs_modulus = 1e7
poissons_ratio = 0.3
block = 2
constant_on = SUBDOMAIN
[]
[strain_block]
type = ComputeFiniteStrain
displacements = 'disp_x disp_y disp_z'
implicit = false
[]
[stress_block]
type = ComputeFiniteStrainElasticStress
[]
[density_one]
type = GenericConstantMaterial
prop_names = density
prop_values = 1e7
output_properties = 'density'
block = '1'
[]
[density_two]
type = GenericConstantMaterial
prop_names = density
prop_values = 1e3
output_properties = 'density'
block = '2'
[]
[wave_speed]
type = WaveSpeed
outputs = 'exodus'
output_properties = 'wave_speed'
[]
[]
[Executioner]
type = Transient
start_time = 0
end_time = 0.04
dt = 0.0001
timestep_tolerance = 1e-6
[TimeIntegrator]
type = ExplicitMixedOrder
mass_matrix_tag = 'mass'
use_constant_mass = true
second_order_vars = 'disp_x disp_y disp_z'
[]
skip_exception_check = true
[]
[Outputs]
interval = 100
exodus = true
[]
(modules/contact/test/tests/explicit_dynamics/test_balance_optimized.i)
[GlobalParams]
displacements = 'disp_x disp_y disp_z'
volumetric_locking_correction = true
[]
[Problem]
extra_tag_matrices = 'mass'
[]
[Mesh]
[block_one]
type = GeneratedMeshGenerator
dim = 3
nx = 3
ny = 3
nz = 3
xmin = 4.5
xmax = 5.5
ymin = 4.5
ymax = 5.5
zmin = 0.0001
zmax = 1.0001
boundary_name_prefix = 'ball'
[]
[block_two]
type = GeneratedMeshGenerator
dim = 3
nx = 2
ny = 2
nz = 2
xmin = 0.0
xmax = 10
ymin = 0.0
ymax = 10
zmin = -2
zmax = 0
boundary_name_prefix = 'base'
boundary_id_offset = 10
[]
[block_one_id]
type = SubdomainIDGenerator
input = block_one
subdomain_id = 1
[]
[block_two_id]
type = SubdomainIDGenerator
input = block_two
subdomain_id = 2
[]
[combine]
type = MeshCollectionGenerator
inputs = ' block_one_id block_two_id'
[]
allow_renumbering = false
patch_update_strategy = auto
[]
[Variables]
[disp_x]
[]
[disp_y]
[]
[disp_z]
[]
[]
[AuxVariables]
[gap_rate]
[]
[vel_x]
[]
[accel_x]
[]
[vel_y]
[]
[accel_y]
[]
[vel_z]
[]
[accel_z]
[]
[]
[AuxKernels]
[accel_x]
type = TestNewmarkTI
variable = accel_x
displacement = disp_x
first = false
execute_on = 'TIMESTEP_END'
[]
[vel_x]
type = TestNewmarkTI
variable = vel_x
displacement = disp_x
execute_on = 'TIMESTEP_END'
[]
[accel_y]
type = TestNewmarkTI
variable = accel_y
displacement = disp_y
first = false
execute_on = 'TIMESTEP_END'
[]
[vel_y]
type = TestNewmarkTI
variable = vel_y
displacement = disp_x
execute_on = 'TIMESTEP_END'
[]
[accel_z]
type = TestNewmarkTI
variable = accel_z
displacement = disp_z
first = false
execute_on = 'TIMESTEP_END'
[]
[vel_z]
type = TestNewmarkTI
variable = vel_z
displacement = disp_z
execute_on = 'TIMESTEP_END'
[]
[]
[Kernels]
[DynamicTensorMechanics]
displacements = 'disp_x disp_y disp_z'
volumetric_locking_correction = true
stiffness_damping_coefficient = 0.001
decomposition_method = EigenSolution
[]
[Mass_x]
type = MassMatrix
variable = disp_x
density = density
matrix_tags = 'mass'
[]
[Mass_y]
type = MassMatrix
variable = disp_y
density = density
matrix_tags = 'mass'
[]
[Mass_z]
type = MassMatrix
variable = disp_z
density = density
matrix_tags = 'mass'
[]
[]
[Kernels]
[gravity]
type = Gravity
variable = disp_z
value = -981.0
[]
[]
[BCs]
[x_front]
type = ExplicitDirichletBC
variable = disp_x
boundary = 'ball_front'
value = 0.0
[]
[y_front]
type = ExplicitDirichletBC
variable = disp_y
boundary = 'ball_front'
value = 0.0
[]
[x_fixed]
type = ExplicitDirichletBC
variable = disp_x
boundary = 'base_back'
value = 0.0
[]
[y_fixed]
type = ExplicitDirichletBC
variable = disp_y
boundary = 'base_back'
value = 0.0
[]
[z_fixed]
type = ExplicitDirichletBC
variable = disp_z
boundary = 'base_back'
value = 0.0
[]
[z_fixed_front]
type = ExplicitDirichletBC
variable = disp_z
boundary = 'base_front'
value = 0.0
[]
[]
[ExplicitDynamicsContact]
[my_contact]
model = frictionless_balance
primary = base_front
secondary = ball_back
vel_x = 'vel_x'
vel_y = 'vel_y'
vel_z = 'vel_z'
[]
[]
[Materials]
[elasticity_tensor_block_one]
type = ComputeIsotropicElasticityTensor
youngs_modulus = 1e6
poissons_ratio = 0.0
block = 1
constant_on = SUBDOMAIN
[]
[elasticity_tensor_block_two]
type = ComputeIsotropicElasticityTensor
youngs_modulus = 1e10
poissons_ratio = 0.0
block = 2
constant_on = SUBDOMAIN
[]
[strain_block]
type = ComputeFiniteStrain
displacements = 'disp_x disp_y disp_z'
implicit = false
[]
[stress_block]
type = ComputeFiniteStrainElasticStress
[]
[density_one]
type = GenericConstantMaterial
prop_names = density
prop_values = 1e1
output_properties = 'density'
block = '1'
[]
[density_two]
type = GenericConstantMaterial
prop_names = density
prop_values = 1e6
output_properties = 'density'
block = '2'
[]
[wave_speed]
type = WaveSpeed
outputs = 'exodus'
output_properties = 'wave_speed'
[]
[]
[Executioner]
type = Transient
start_time = 0
end_time = 0.0025
dt = 0.00001
timestep_tolerance = 1e-6
[TimeIntegrator]
type = ExplicitMixedOrder
mass_matrix_tag = 'mass'
use_constant_mass = true
second_order_vars = 'disp_x disp_y disp_z'
[]
[]
[Outputs]
interval = 10
exodus = true
csv = true
file_base = test_balance_out
[]
(modules/contact/test/tests/explicit_dynamics/settlement.i)
# One element test to test the central difference time integrator in 3D.
[GlobalParams]
displacements = 'disp_x disp_y disp_z'
volumetric_locking_correction = true
[]
[Problem]
extra_tag_matrices = 'mass'
[]
[Mesh]
[block_one]
type = GeneratedMeshGenerator
dim = 3
nx = 3
ny = 3
nz = 3
xmin = 4.5
xmax = 5.5
ymin = 4.5
ymax = 5.5
zmin = 0.0001
zmax = 1.0001
boundary_name_prefix = 'ball'
[]
[block_two]
type = GeneratedMeshGenerator
dim = 3
nx = 2
ny = 2
nz = 2
xmin = 0.0
xmax = 10
ymin = 0.0
ymax = 10
zmin = -2
zmax = 0
boundary_name_prefix = 'base'
boundary_id_offset = 10
[]
[block_one_id]
type = SubdomainIDGenerator
input = block_one
subdomain_id = 1
[]
[block_two_id]
type = SubdomainIDGenerator
input = block_two
subdomain_id = 2
[]
[combine]
type = MeshCollectionGenerator
inputs = ' block_one_id block_two_id'
[]
[]
[AuxVariables]
[penetration]
[]
[]
[AuxKernels]
[penetration]
type = PenetrationAux
variable = penetration
boundary = ball_back
paired_boundary = base_front
quantity = distance
[]
[]
[Variables]
[disp_x]
[]
[disp_y]
[]
[disp_z]
[]
[]
[AuxVariables]
[gap_rate]
[]
[vel_x]
[]
[accel_x]
[]
[vel_y]
[]
[accel_y]
[]
[vel_z]
[]
[accel_z]
[]
[stress_zz]
family = MONOMIAL
order = CONSTANT
[]
[strain_zz]
family = MONOMIAL
order = CONSTANT
[]
[kinetic_energy_one]
order = CONSTANT
family = MONOMIAL
[]
[elastic_energy_one]
order = CONSTANT
family = MONOMIAL
[]
[kinetic_energy_two]
order = CONSTANT
family = MONOMIAL
[]
[elastic_energy_two]
order = CONSTANT
family = MONOMIAL
[]
[]
[AuxKernels]
[stress_zz]
type = RankTwoAux
rank_two_tensor = stress
index_i = 2
index_j = 2
variable = stress_zz
execute_on = 'TIMESTEP_END'
[]
[strain_zz]
type = RankTwoAux
rank_two_tensor = mechanical_strain
index_i = 2
index_j = 2
variable = strain_zz
[]
[accel_x]
type = TestNewmarkTI
variable = accel_x
displacement = disp_x
first = false
execute_on = 'LINEAR TIMESTEP_BEGIN TIMESTEP_END'
[]
[vel_x]
type = TestNewmarkTI
variable = vel_x
displacement = disp_x
execute_on = 'LINEAR TIMESTEP_BEGIN TIMESTEP_END'
[]
[accel_y]
type = TestNewmarkTI
variable = accel_y
displacement = disp_y
first = false
execute_on = 'LINEAR TIMESTEP_BEGIN TIMESTEP_END'
[]
[vel_y]
type = TestNewmarkTI
variable = vel_y
displacement = disp_x
execute_on = 'LINEAR TIMESTEP_BEGIN TIMESTEP_END'
[]
[accel_z]
type = TestNewmarkTI
variable = accel_z
displacement = disp_z
first = false
execute_on = 'LINEAR TIMESTEP_BEGIN TIMESTEP_END'
[]
[vel_z]
type = TestNewmarkTI
variable = vel_z
displacement = disp_z
execute_on = 'LINEAR TIMESTEP_BEGIN TIMESTEP_END'
[]
[kinetic_energy_one]
type = KineticEnergyAux
block = '1'
variable = kinetic_energy_one
newmark_velocity_x = vel_x
newmark_velocity_y = vel_y
newmark_velocity_z = vel_z
density = density
[]
[elastic_energy_one]
type = ElasticEnergyAux
variable = elastic_energy_one
block = '1'
[]
[kinetic_energy_two]
type = KineticEnergyAux
block = '2'
variable = kinetic_energy_two
newmark_velocity_x = vel_x
newmark_velocity_y = vel_y
newmark_velocity_z = vel_z
density = density
[]
[elastic_energy_two]
type = ElasticEnergyAux
variable = elastic_energy_two
block = '2'
[]
[]
[Kernels]
[DynamicTensorMechanics]
displacements = 'disp_x disp_y disp_z'
stiffness_damping_coefficient = 9.5e-4
generate_output = 'stress_zz strain_zz'
[]
[Mass_x]
type = MassMatrix
variable = disp_x
density = density
matrix_tags = 'mass'
[]
[Mass_y]
type = MassMatrix
variable = disp_y
density = density
matrix_tags = 'mass'
[]
[Mass_z]
type = MassMatrix
variable = disp_z
density = density
matrix_tags = 'mass'
[]
[gravity]
type = Gravity
variable = disp_z
value = -98.10
block = 1
[]
[]
[BCs]
[x_front]
type = ExplicitDirichletBC
variable = disp_x
boundary = 'ball_front'
value = 0.0
[]
[y_front]
type = ExplicitDirichletBC
variable = disp_y
boundary = 'ball_front'
value = 0.0
[]
[x_fixed]
type = ExplicitDirichletBC
variable = disp_x
boundary = 'base_back'
value = 0.0
[]
[y_fixed]
type = ExplicitDirichletBC
variable = disp_y
boundary = 'base_back'
value = 0.0
[]
[z_fixed]
type = ExplicitDirichletBC
variable = disp_z
boundary = 'base_back'
value = 0.0
[]
[z_fixed_front]
type = ExplicitDirichletBC
variable = disp_z
boundary = 'base_front'
value = 0.0
[]
[]
[ExplicitDynamicsContact]
[my_contact]
model = frictionless_balance
primary = base_front
secondary = ball_back
vel_x = 'vel_x'
vel_y = 'vel_y'
vel_z = 'vel_z'
verbose = true
[]
[]
[Materials]
[elasticity_tensor_block_one]
type = ComputeIsotropicElasticityTensor
youngs_modulus = 1e6
poissons_ratio = 0.0
block = 1
outputs = 'exodus'
output_properties = __all__
[]
[elasticity_tensor_block_two]
type = ComputeIsotropicElasticityTensor
youngs_modulus = 1e10
poissons_ratio = 0.0
block = 2
outputs = 'exodus'
output_properties = __all__
[]
[strain_block]
type = ComputeFiniteStrain # ComputeIncrementalStrain
displacements = 'disp_x disp_y disp_z'
implicit = false
[]
[stress_block]
type = ComputeFiniteStrainElasticStress
[]
[density_one]
type = GenericConstantMaterial
prop_names = density
prop_values = 1e1
outputs = 'exodus'
output_properties = 'density'
block = '1'
[]
[density_two]
type = GenericConstantMaterial
prop_names = density
prop_values = 1e6
outputs = 'exodus'
output_properties = 'density'
block = '2'
[]
[wave_speed]
type = WaveSpeed
outputs = 'exodus'
output_properties = 'wave_speed'
[]
[]
[Executioner]
type = Transient
start_time = 0
end_time = 0.05
dt = 1.0e-4
timestep_tolerance = 1e-6
[TimeIntegrator]
type = ExplicitMixedOrder
mass_matrix_tag = 'mass'
second_order_vars = 'disp_x disp_y disp_z'
[]
[]
[Outputs]
interval = 1
exodus = true
csv = true
execute_on = 'TIMESTEP_END'
[]
[Postprocessors]
[accel_58z]
type = NodalVariableValue
nodeid = 1
variable = accel_z
[]
[vel_58z]
type = NodalVariableValue
nodeid = 1
variable = vel_z
[]
[critical_time_step]
type = CriticalTimeStep
[]
[contact_pressure_max]
type = NodalExtremeValue
variable = contact_pressure
block = '1 2'
value_type = max
[]
[penetration_max]
type = NodalExtremeValue
variable = penetration
block = '1 2'
value_type = max
[]
[total_kinetic_energy_one]
type = ElementIntegralVariablePostprocessor
variable = kinetic_energy_one
block = '1'
[]
[total_elastic_energy_one]
type = ElementIntegralVariablePostprocessor
variable = elastic_energy_one
block = '1'
[]
[total_kinetic_energy_two]
type = ElementIntegralVariablePostprocessor
variable = kinetic_energy_two
block = '2'
[]
[total_elastic_energy_two]
type = ElementIntegralVariablePostprocessor
variable = elastic_energy_two
block = '2'
[]
[]
(modules/solid_mechanics/test/tests/dynamics/time_integration/direct_central_difference_multiVarBC.i)
###########################################################
# This is a simple test with a time-dependent problem
# demonstrating the use of a central difference with a
# direct calculation of acceleration.
#
# Testing that the first and second time derivatives
# are calculated correctly using the Central Difference Direct
# method
###########################################################
[GlobalParams]
displacements = 'disp_x disp_y'
[]
[Problem]
extra_tag_matrices = 'mass'
[]
[Mesh]
type = GeneratedMesh
dim = 2
xmin = -1
xmax = 1
ymin = -1
ymax = 1
nx = 4
ny = 4
[]
[Variables]
[disp_x]
[]
[disp_y]
[]
[]
[Functions]
[forcing_fn]
type = ParsedFunction
expression = 't'
[]
[]
[Kernels]
[DynamicSolidMechanics]
displacements = 'disp_x disp_y'
[]
[massmatrix]
type = MassMatrix
density = density
matrix_tags = 'mass'
variable = disp_x
[]
[massmatrix_y]
type = MassMatrix
density = density
matrix_tags = 'mass'
variable = disp_y
[]
[]
[Materials]
[elasticity_tensor_block_one]
type = ComputeIsotropicElasticityTensor
youngs_modulus = 1e1
poissons_ratio = 0.33
[]
[strain_block]
type = ComputeFiniteStrain
displacements = 'disp_x disp_y'
implicit = false
[]
[stress_block]
type = ComputeFiniteStrainElasticStress
implicit = false
[]
[density]
type = GenericConstantMaterial
prop_names = 'density'
prop_values = 1
[]
[]
[BCs]
[left_x]
type = ExplicitDirichletBC
variable = disp_x
boundary = 'left'
value = 0
[]
[left_y]
type = ExplicitDirichletBC
variable = disp_y
boundary = 'left'
value = 0
[]
[right_x]
type = ExplicitFunctionDirichletBC
variable = disp_x
boundary = 'right'
function = forcing_fn
[]
[]
[Executioner]
type = Transient
[TimeIntegrator]
type = ExplicitMixedOrder
mass_matrix_tag = 'mass'
second_order_vars = 'disp_x disp_y'
[]
start_time = 0.0
num_steps = 6
dt = 0.1
[]
[Postprocessors]
[left_x]
type = AverageNodalVariableValue
variable = disp_x
boundary = left
[]
[right_y]
type = AverageNodalVariableValue
variable = disp_x
boundary = left
[]
[]
[Outputs]
exodus = true
[]
(modules/solid_mechanics/test/tests/dynamics/explicit_mms/mms_direct_combined.i)
[Mesh]
type = GeneratedMesh
dim = 2
xmin = -1
xmax = 1
ymin = -1
ymax = 1
nx = 10
ny = 10
elem_type = QUAD4
[]
[Problem]
extra_tag_matrices = 'mass'
[]
[Variables]
[u_first]
[]
[u_second]
[]
[]
[AuxVariables]
[dot_u_second]
[]
[]
[AuxKernels]
[dot_u_second]
type = TestNewmarkTI
variable = dot_u_second
displacement = u_second
first = true
execute_on = 'TIMESTEP_END'
[]
[]
[Functions]
[ic]
type = ParsedFunction
expression = 0
[]
[forcing_fn_first]
type = ParsedFunction
expression = (x+y)
[]
[exact_fn_first]
type = ParsedFunction
expression = t*(x+y)
[]
[exact_fn_second]
type = ParsedFunction
expression = '0.5*t^2'
[]
[exact_dot_fn_second]
type = ParsedFunction
expression = 't'
[]
[]
[Kernels]
[Mass_x_second]
type = MassMatrix
variable = u_second
density = 1
matrix_tags = 'mass'
[]
[ffn_second]
type = BodyForce
variable = u_second
function = 1
[]
[Mass_x_first]
type = MassMatrix
variable = u_first
density = 1
matrix_tags = 'mass'
[]
[diff]
type = Diffusion
variable = u_first
[]
[ffn]
type = BodyForce
variable = u_first
function = forcing_fn_first
[]
[]
[BCs]
[all]
type = ExplicitFunctionDirichletBC
variable = u_first
boundary = '0 1 2 3'
function = exact_fn_first
[]
[]
[Postprocessors]
[l2_err_second]
type = ElementL2Error
variable = u_second
function = exact_fn_second
[]
[l2_dot_err_second]
type = ElementL2Error
variable = dot_u_second
function = exact_dot_fn_second
[]
[l2_err_first]
type = ElementL2Error
variable = u_first
function = exact_fn_first
[]
[]
[Executioner]
type = Transient
start_time = 0.0
num_steps = 20
dt = 0.00005
l_tol = 1e-12
[TimeIntegrator]
type = ExplicitMixedOrder
mass_matrix_tag = 'mass'
use_constant_mass = true
second_order_vars = 'u_second'
first_order_vars = 'u_first'
[]
[]
[Outputs]
exodus = true
[console]
type = Console
max_rows = 10
[]
[]
# Tests stateful material properties below
[Materials]
[u_sqrd]
type = ParsedMaterial
expression = 'u_first^2'
property_name = u_sqrd
coupled_variables = 'u_first'
[]
[]
[AuxVariables]
[diff_t_begin]
family = MONOMIAL
order = CONSTANT
[]
[diff_t_end]
family = MONOMIAL
order = CONSTANT
[]
[]
[AuxKernels]
[diff_t_begin]
type = MaterialRateRealAux
property = u_sqrd
variable = diff_t_begin
execute_on = LINEAR
[]
[diff_t_end]
type = MaterialRateRealAux
property = u_sqrd
variable = diff_t_end
execute_on = TIMESTEP_END
[]
[]
[Postprocessors]
[l2_norm_begin]
type = ElementL2Norm
variable = diff_t_begin
[]
[l2_norm_end]
type = ElementL2Norm
variable = diff_t_end
[]
[]
(modules/contact/test/tests/explicit_dynamics/test_balance.i)
# One element test to test the central difference time integrator in 3D.
[GlobalParams]
displacements = 'disp_x disp_y disp_z'
volumetric_locking_correction = true
[]
[Problem]
extra_tag_matrices = 'mass'
[]
[Mesh]
[block_one]
type = GeneratedMeshGenerator
dim = 3
nx = 3
ny = 3
nz = 3
xmin = 4.5
xmax = 5.5
ymin = 4.5
ymax = 5.5
zmin = 0.0001
zmax = 1.0001
boundary_name_prefix = 'ball'
[]
[block_two]
type = GeneratedMeshGenerator
dim = 3
nx = 2
ny = 2
nz = 2
xmin = 0.0
xmax = 10
ymin = 0.0
ymax = 10
zmin = -2
zmax = 0
boundary_name_prefix = 'base'
boundary_id_offset = 10
[]
[block_one_id]
type = SubdomainIDGenerator
input = block_one
subdomain_id = 1
[]
[block_two_id]
type = SubdomainIDGenerator
input = block_two
subdomain_id = 2
[]
[combine]
type = MeshCollectionGenerator
inputs = ' block_one_id block_two_id'
[]
allow_renumbering = false
[]
[Variables]
[disp_x]
[]
[disp_y]
[]
[disp_z]
[]
[]
[AuxVariables]
[gap_rate]
[]
[vel_x]
[]
[accel_x]
[]
[vel_y]
[]
[accel_y]
[]
[vel_z]
[]
[accel_z]
[]
[stress_zz]
family = MONOMIAL
order = CONSTANT
[]
[strain_zz]
family = MONOMIAL
order = CONSTANT
[]
[]
[AuxKernels]
[stress_zz]
type = RankTwoAux
rank_two_tensor = stress
index_i = 2
index_j = 2
variable = stress_zz
execute_on = 'TIMESTEP_END'
[]
[strain_zz]
type = RankTwoAux
rank_two_tensor = mechanical_strain
index_i = 2
index_j = 2
variable = strain_zz
[]
[accel_x]
type = TestNewmarkTI
variable = accel_x
displacement = disp_x
first = false
execute_on = 'LINEAR TIMESTEP_BEGIN TIMESTEP_END'
[]
[vel_x]
type = TestNewmarkTI
variable = vel_x
displacement = disp_x
execute_on = 'LINEAR TIMESTEP_BEGIN TIMESTEP_END'
[]
[accel_y]
type = TestNewmarkTI
variable = accel_y
displacement = disp_y
first = false
execute_on = 'LINEAR TIMESTEP_BEGIN TIMESTEP_END'
[]
[vel_y]
type = TestNewmarkTI
variable = vel_y
displacement = disp_x
execute_on = 'LINEAR TIMESTEP_BEGIN TIMESTEP_END'
[]
[accel_z]
type = TestNewmarkTI
variable = accel_z
displacement = disp_z
first = false
execute_on = 'LINEAR TIMESTEP_BEGIN TIMESTEP_END'
[]
[vel_z]
type = TestNewmarkTI
variable = vel_z
displacement = disp_z
execute_on = 'LINEAR TIMESTEP_BEGIN TIMESTEP_END'
[]
[]
[AuxVariables]
[penetration]
[]
[]
[AuxKernels]
[penetration]
type = PenetrationAux
variable = penetration
boundary = ball_back
paired_boundary = base_front
quantity = distance
[]
[]
[Kernels]
[DynamicTensorMechanics]
displacements = 'disp_x disp_y disp_z'
volumetric_locking_correction = true
stiffness_damping_coefficient = 0.001
generate_output = 'stress_zz strain_zz'
[]
[Mass_x]
type = MassMatrix
variable = disp_x
density = density
matrix_tags = 'mass'
[]
[Mass_y]
type = MassMatrix
variable = disp_y
density = density
matrix_tags = 'mass'
[]
[Mass_z]
type = MassMatrix
variable = disp_z
density = density
matrix_tags = 'mass'
[]
[]
[Kernels]
[gravity]
type = Gravity
variable = disp_z
value = -981.0
[]
[]
[BCs]
[x_front]
type = ExplicitDirichletBC
variable = disp_x
boundary = 'ball_front'
value = 0.0
[]
[y_front]
type = ExplicitDirichletBC
variable = disp_y
boundary = 'ball_front'
value = 0.0
[]
[x_fixed]
type = ExplicitDirichletBC
variable = disp_x
boundary = 'base_back'
value = 0.0
[]
[y_fixed]
type = ExplicitDirichletBC
variable = disp_y
boundary = 'base_back'
value = 0.0
[]
[z_fixed]
type = ExplicitDirichletBC
variable = disp_z
boundary = 'base_back'
value = 0.0
[]
[z_fixed_front]
type = ExplicitDirichletBC
variable = disp_z
boundary = 'base_front'
value = 0.0
[]
[]
[ExplicitDynamicsContact]
[my_contact]
model = frictionless_balance
primary = base_front
secondary = ball_back
vel_x = 'vel_x'
vel_y = 'vel_y'
vel_z = 'vel_z'
verbose = true
[]
[]
[Materials]
[elasticity_tensor_block_one]
type = ComputeIsotropicElasticityTensor
youngs_modulus = 1e6
poissons_ratio = 0.0
block = 1
outputs = 'exodus'
output_properties = __all__
[]
[elasticity_tensor_block_two]
type = ComputeIsotropicElasticityTensor
youngs_modulus = 1e10
poissons_ratio = 0.0
block = 2
outputs = 'exodus'
output_properties = __all__
[]
[strain_block]
type = ComputeFiniteStrain
displacements = 'disp_x disp_y disp_z'
implicit = false
[]
[stress_block]
type = ComputeFiniteStrainElasticStress
[]
[density_one]
type = GenericConstantMaterial
prop_names = density
prop_values = 1e1
outputs = 'exodus'
output_properties = 'density'
block = '1'
[]
[density_two]
type = GenericConstantMaterial
prop_names = density
prop_values = 1e6
outputs = 'exodus'
output_properties = 'density'
block = '2'
[]
[wave_speed]
type = WaveSpeed
outputs = 'exodus'
output_properties = 'wave_speed'
[]
[]
[Executioner]
type = Transient
start_time = 0
end_time = 0.0025
dt = 0.00001
timestep_tolerance = 1e-6
[TimeIntegrator]
type = ExplicitMixedOrder
mass_matrix_tag = 'mass'
second_order_vars = 'disp_x disp_y disp_z'
[]
[]
[Outputs]
interval = 10
exodus = true
csv = true
[]
[Postprocessors]
[accel_58z]
type = NodalVariableValue
nodeid = 1
variable = accel_z
[]
[vel_58z]
type = NodalVariableValue
nodeid = 1
variable = vel_z
[]
[disp_58z]
type = NodalVariableValue
nodeid = 1
variable = disp_z
[]
[critical_time_step]
type = CriticalTimeStep
[]
[contact_pressure_max]
type = NodalExtremeValue
variable = contact_pressure
block = '1 2'
value_type = max
[]
[]
(modules/solid_mechanics/test/tests/dynamics/explicit_mms/mms_direct_second_order_with_ic.i)
[Mesh]
type = GeneratedMesh
dim = 2
xmin = -1
xmax = 1
ymin = -1
ymax = 1
nx = 10
ny = 10
elem_type = QUAD4
[]
dt_and_v0 = 0.00005
[Problem]
extra_tag_matrices = 'mass'
[]
[Variables]
[u]
[]
[]
[AuxVariables]
[dot_u]
[]
[]
[ICs]
[u_old]
type = ConstantIC
variable = u
state = OLD
# set's v_0 to 1
value = -${dt_and_v0}
[]
[]
[AuxKernels]
[dot_u]
type = TestNewmarkTI
variable = dot_u
displacement = u
first = true
execute_on = 'TIMESTEP_END'
[]
[]
[Functions]
[exact_fn]
type = ParsedFunction
expression = 't + 0.5*t^2'
[]
[exact_dot_fn]
type = ParsedFunction
expression = '1 + t'
[]
[]
[Kernels]
[Mass_x]
type = MassMatrix
variable = u
density = 1
matrix_tags = 'mass'
[]
[ffn]
type = BodyForce
variable = u
function = 1
[]
[]
[Postprocessors]
[l2_err]
type = ElementL2Error
variable = u
function = exact_fn
[]
[l2_dot_err]
type = ElementL2Error
variable = dot_u
function = exact_dot_fn
[]
[]
[Executioner]
type = Transient
start_time = 0.0
num_steps = 20
dt = ${dt_and_v0}
l_tol = 1e-12
[TimeIntegrator]
type = ExplicitMixedOrder
mass_matrix_tag = 'mass'
use_constant_mass = true
second_order_vars = 'u'
[]
[]
[Outputs]
exodus = true
[console]
type = Console
max_rows = 10
[]
[]
(modules/solid_mechanics/test/tests/dynamics/time_integration/direct_central_difference_varied_dt.i)
###########################################################
# This is a simple test with a time-dependent problem
# demonstrating the use of a central difference with a
# direct calculation of acceleration.
#
# Testing that the first and second time derivatives
# are calculated correctly using the Direct Central Difference
# method
# Testing the accuracy of the timestep averaging method within
# the Direct Central Difference method
###########################################################
[GlobalParams]
displacements = 'disp_x disp_y'
[]
[Problem]
extra_tag_matrices = 'mass'
[]
[Mesh]
type = GeneratedMesh
dim = 2
xmin = -1
xmax = 1
ymin = -1
ymax = 1
nx = 1
ny = 1
[]
[Variables]
[disp_x]
[]
[disp_y]
[]
[]
[Functions]
#Mid-step velocities
#0 0.00625 0.015 0.0075 0.25 0
#Accelerations
#0.025 0.01944 -0.01 0.48 -2.17
[forcing_fn]
type = PiecewiseLinear
x = '0.0 0.1 0.5 1.0 2.0 2.01 2.23'
y = '0.0 0.0 0.0025 0.01 0.0175 0.02 0.02'
[]
[]
[Kernels]
[DynamicSolidMechanics]
displacements = 'disp_x disp_y'
[]
[massmatrix]
type = MassMatrix
density = density
matrix_tags = 'mass'
variable = disp_x
[]
[massmatrix_y]
type = MassMatrix
density = density
matrix_tags = 'mass'
variable = disp_y
[]
[]
[Materials]
[elasticity_tensor_block_one]
type = ComputeIsotropicElasticityTensor
youngs_modulus = 1e1
poissons_ratio = 0.0
[]
[strain_block]
type = ComputeFiniteStrain
displacements = 'disp_x disp_y'
implicit = false
[]
[stress_block]
type = ComputeFiniteStrainElasticStress
implicit = false
[]
[density]
type = GenericConstantMaterial
prop_names = 'density'
prop_values = 5
[]
[]
[BCs]
[left_x]
type = ExplicitFunctionDirichletBC
variable = disp_x
boundary = 'left'
function = forcing_fn
[]
[right_x]
type = ExplicitFunctionDirichletBC
variable = disp_x
boundary = 'right'
function = forcing_fn
[]
[]
[Executioner]
type = Transient
[TimeIntegrator]
type = ExplicitMixedOrder
mass_matrix_tag = 'mass'
second_order_vars = 'disp_x disp_y'
[]
[TimeStepper]
type = TimeSequenceStepper
time_sequence = '0.0 0.1 0.5 1.0 2.0 2.01 2.23'
[]
start_time = 0.0
num_steps = 6
dt = 0.1
[]
[Postprocessors]
[udot]
type = ElementAverageTimeDerivative
variable = disp_x
[]
[udotdot]
type = ElementAverageSecondTimeDerivative
variable = disp_x
[]
[u]
type = ElementAverageValue
variable = disp_x
[]
[]
[Outputs]
exodus = true
[]
(modules/solid_mechanics/test/tests/dynamics/time_integration/direct_central_difference.i)
###########################################################
# This is a simple test with a time-dependent problem
# demonstrating the use of a central difference with a
# direct calculation of acceleration.
#
# Testing that the first and second time derivatives
# are calculated correctly using the Central Difference Direct
# method
###########################################################
[GlobalParams]
displacements = 'disp_x disp_y'
[]
[Problem]
extra_tag_matrices = 'mass'
[]
[Mesh]
type = GeneratedMesh
dim = 2
xmin = -1
xmax = 1
ymin = -1
ymax = 1
nx = 1
ny = 1
[]
[Variables]
[disp_x]
[]
[disp_y]
[]
[]
[Functions]
[forcing_fn]
type = PiecewiseLinear
x = '0.0 0.1 0.2 0.3 0.4 0.5 0.6'
y = '0.0 0.0 0.0025 0.01 0.0175 0.02 0.02'
[]
[]
[Kernels]
[DynamicSolidMechanics]
displacements = 'disp_x disp_y'
[]
[massmatrix]
type = MassMatrix
density = density
matrix_tags = 'mass'
variable = disp_x
[]
[massmatrix_y]
type = MassMatrix
density = density
matrix_tags = 'mass'
variable = disp_y
[]
[]
[Materials]
[elasticity_tensor_block_one]
type = ComputeIsotropicElasticityTensor
youngs_modulus = 1e1
poissons_ratio = 0.0
[]
[strain_block]
type = ComputeFiniteStrain
displacements = 'disp_x disp_y'
implicit = false
[]
[stress_block]
type = ComputeFiniteStrainElasticStress
implicit = false
[]
[density]
type = GenericConstantMaterial
prop_names = 'density'
prop_values = 1
[]
[]
[BCs]
[left_x]
type = ExplicitFunctionDirichletBC
variable = disp_x
boundary = 'left'
function = forcing_fn
[]
[right_x]
type = ExplicitFunctionDirichletBC
variable = disp_x
boundary = 'right'
function = forcing_fn
[]
[]
[Executioner]
type = Transient
[TimeIntegrator]
type = ExplicitMixedOrder
mass_matrix_tag = 'mass'
second_order_vars = 'disp_x disp_y'
[]
start_time = 0.0
num_steps = 6
dt = 0.1
[]
[Postprocessors]
[udot]
type = ElementAverageTimeDerivative
variable = disp_x
[]
[udotdot]
type = ElementAverageSecondTimeDerivative
variable = disp_x
[]
[u]
type = ElementAverageValue
variable = disp_x
[]
[]
[Outputs]
exodus = true
[]