Density Scaling

Computes the scaled inertial density needed to enable stable explicit time-stepping using the desired_time_step in solid-mechanics problems. Note that if this inertial density is used in input files (for instance, in the mass matrix) it will impact the dynamics of the system, largely eliminating high-frequency oscillations, and impacting low-frequency dynamics. Hence, use with caution.

Description

This material computes the density required to achieve stable explicit time stepping with a user-defined time step (see CriticalTimeStep for the stability condition). This Material computes:

  • the density needed to enable time-stepping with given desired_time_step;

  • scaled_density minus the true density.

The names of these are defined by the scaled_density and additional_density input parameters.

Note that the density computed acts as your model's inertial density (see example below) and you should not use it as your gravitational density.

When used in the MassMatrix, time-steps of size desired_time_step will be stable. However, note that the addition of mass will alter the dynamics of the system. In particular, high-frequency oscillations will largely be eliminated in elements that are small and/or stiff and/or light. Hence, using mass scaling is particularly recommended when the finite element mesh contains a handful of small/stiff/light elements, or when high-frequency dynamics are unimportant. Mass scaling has a smaller, yet noticeable, impact on low-frequency dynamics.

Example

To use DensityScaling effectively, two steps are needed. The following is a worked example.

Step 1

To ensure that a user-defined time step ( in this case) is stable, use a DensityScaling Material to compute the required density in each element:

  [density_true]
    type = GenericConstantMaterial
    prop_names = density_true
    prop_values = ${density_true}
    implicit = false
  []
  [density_scaled]
    type = DensityScaling
    true_density = density_true
    scaled_density = density_scaled
    desired_time_step = 4
    safety_factor = 0.8
    output_properties = 'density_scaled additional_density'
    outputs = exodus
    implicit = false
  []
(moose/modules/solid_mechanics/test/tests/dynamics/time_integration/mass_scaling.i)

The important features here are:

  • A Material Property called density_true is calculated by some Material (in this case, the density_true Material) and fed into the DensityScaling Material

  • The desired_time_step is defined in the DensityScaling Material

  • The DensityScaling Material computes the density required for stable time-stepping, then increases it by multiplying it by 1/safety_factor. For example, in this case, is theoretically stable, but for safety, the input file only uses .

  • The DensityScaling Material stores the computed density in density_scaled (or whatever is specified by the scaled_density parameter).

The other specified parameters, such as implicit = false, output_properties, outputs, are unimportant for this example (eg, the outputs are just so the result is stored in the exodus file).

Step 2

Ensure your MassMatrix uses the scaled density. For instance:

  [massmatrix_x]
    type = MassMatrix
    density = density_scaled
    matrix_tags = mass
    variable = disp_x
  []
(moose/modules/solid_mechanics/test/tests/dynamics/time_integration/mass_scaling.i)

Input Parameters

  • desired_time_stepThe desired time step.

    C++ Type:double

    Unit:(no unit assumed)

    Controllable:No

    Description:The desired time step.

  • scaled_densityName of the scaled density property that this Material computes.

    C++ Type:MaterialPropertyName

    Unit:(no unit assumed)

    Controllable:No

    Description:Name of the scaled density property that this Material computes.

  • true_densityName of Material Property defining the true inertial density of the material.

    C++ Type:MaterialPropertyName

    Unit:(no unit assumed)

    Controllable:No

    Description:Name of Material Property defining the true inertial density of the material.

Required Parameters

  • additional_densityadditional_densityName of the additional density property that this Material computes

    Default:additional_density

    C++ Type:MaterialPropertyName

    Unit:(no unit assumed)

    Controllable:No

    Description:Name of the additional density property that this Material computes

  • blockThe list of blocks (ids or names) that this object will be applied

    C++ Type:std::vector<SubdomainName>

    Controllable:No

    Description:The list of blocks (ids or names) that this object will be applied

  • boundaryThe list of boundaries (ids or names) from the mesh where this object applies

    C++ Type:std::vector<BoundaryName>

    Controllable:No

    Description:The list of boundaries (ids or names) from the mesh where this object applies

  • computeTrueWhen false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.

    Default:True

    C++ Type:bool

    Controllable:No

    Description:When false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.

  • constant_onNONEWhen ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped

    Default:NONE

    C++ Type:MooseEnum

    Options:NONE, ELEMENT, SUBDOMAIN

    Controllable:No

    Description:When ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped

  • declare_suffixAn optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.

    C++ Type:MaterialPropertyName

    Unit:(no unit assumed)

    Controllable:No

    Description:An optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.

  • safety_factor0.7The scaled density that this Material produces will potentially allow stable time-step sizes of desired_time_step / safety_factor. In practice, however, using such a time step might result in instabilities, because of time-step lagging and the approximate critical time-step formula used by this Material. Hence, safety_factor allows for a safety margin.

    Default:0.7

    C++ Type:double

    Unit:(no unit assumed)

    Range:(safety_factor>0) & (safety_factor<=1)

    Controllable:No

    Description:The scaled density that this Material produces will potentially allow stable time-step sizes of desired_time_step / safety_factor. In practice, however, using such a time step might result in instabilities, because of time-step lagging and the approximate critical time-step formula used by this Material. Hence, safety_factor allows for a safety margin.

Optional Parameters

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

    C++ Type:std::vector<std::string>

    Controllable:No

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

  • enableTrueSet the enabled status of the MooseObject.

    Default:True

    C++ Type:bool

    Controllable:Yes

    Description:Set the enabled status of the MooseObject.

  • implicitTrueDetermines whether this object is calculated using an implicit or explicit form

    Default:True

    C++ Type:bool

    Controllable:No

    Description:Determines whether this object is calculated using an implicit or explicit form

  • 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

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

    C++ Type:std::vector<std::string>

    Controllable:No

    Description:List of material properties, from this material, to output (outputs must also be defined to an output type)

  • outputsnone Vector of output names where you would like to restrict the output of variables(s) associated with this object

    Default:none

    C++ Type:std::vector<OutputName>

    Controllable:No

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

Outputs Parameters

  • 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

References

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