Generalized Kelvin-Voigt Model

Generalized Kelvin-Voigt model composed of a serial assembly of unit Kelvin-Voigt modules

Description

The GeneralizedKelvinVoigtModel material represents a generalized Kelvin-Voigt model, that is, a material composed of Kelvin-Voigt units assembled in series. The material obeys to the following constitutive equation:

The are the internal strains associated to each Kelvin-Voigt unit and obey the following time-dependent differential equation: is the stiffness of the spring in the chain (a fourth-order tensor, identical in symmetry and dimensions to a standard elasticity tensor), while is the viscosity of the associated dashpot (a scalar with the dimension of time).

Internal Time-Stepping Scheme

The constitutive equations are solved using a semi-implicit single-step first-order finite difference scheme. The internal strains at time step are computed from their values at the previous time step : is a scalar between 0 (fully explicit) and 1 (fully implicit) that controls the time-stepping scheme (default value: 1). The value is determined by the "integration_rule" input parameter, which can take one of the forms shown in Table 1.

Table 1: Integration Rule and Time-Stepping Scheme

Integration RuleValue of Unconditional Convergence
BackwardEuler1yes
MidPoint0.5yes
Newmarkuser-defined
Zienkiewiczyes
warningwarning:Convergence

The scheme is not valid for , so this value is forbidden.

Using this formalism, the stress-strain constitutive equation, which depends on the (unknown) can be rewritten so that it only depends on the and (both being known).

For efficiency reasons, the and are not stored separately, but as a single variable .

commentnote:Update the Scheme with a Linear Viscoelastic Manager Material

For the time-stepping scheme to be properly updated, a LinearViscoelasticityManager object must be included in the input file, and linked to the material

Stress-Strain Computation

The material is compatible with either the total small strain approximation, or either of the incremental strain approximation (incremental small strains or finite strains). The model requires the stress calculators listed in Table 2.

Table 2: Consistent Strain and Stress Calculators

StrainStressAdditional Materials
ComputeSmallStrainComputeLinearViscoelasticStressnone
ComputeIncrementalStrainComputeMultipleInelasticStressLinearViscoelasticStressUpdate
ComputeFiniteStrainComputeMultipleInelasticStressLinearViscoelasticStressUpdate

The stress calculators use the actual elasticity tensor of the material , which is provided by the material itself.

Driving Eigenstrain (Optional)

If the user defines a driving eigenstrain, then the stress induced by this eigenstrain is added to the creep calculation. Essentially, this replaces the differential relation in each material module with:

Example Input File Syntax

[./kelvin_voigt]
  type = GeneralizedKelvinVoigtModel
  creep_modulus = '10e9 10e9'
  creep_viscosity = '1 10'
  poisson_ratio = 0.2
  young_modulus = 10e9
[../]
(moose/modules/solid_mechanics/test/tests/visco/visco_finite_strain.i)

with the required strain calculator

[./strain]
  type = ComputeFiniteStrain
  displacements = 'disp_x disp_y disp_z'
[../]
(moose/modules/solid_mechanics/test/tests/visco/visco_finite_strain.i)

the required stress calculator

[./stress]
  type = ComputeMultipleInelasticStress
  inelastic_models = 'creep'
[../]
(moose/modules/solid_mechanics/test/tests/visco/visco_finite_strain.i)

and the additional material to define the viscoelastic behavior

[./creep]
  type = LinearViscoelasticStressUpdate
[../]
(moose/modules/solid_mechanics/test/tests/visco/visco_finite_strain.i)

and the required Linear Viscoelasticity Manager User Object:

[UserObjects]
  [./update]
    type = LinearViscoelasticityManager
    viscoelastic_model = kelvin_voigt
  [../]
[]
(moose/modules/solid_mechanics/test/tests/visco/visco_finite_strain.i)

Input Parameters

  • creep_moduluslist of the elastic moduli of the different springs in the material

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

    Unit:(no unit assumed)

    Controllable:No

    Description:list of the elastic moduli of the different springs in the material

  • creep_viscositylist of the characteristic times of the different dashpots in the material

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

    Unit:(no unit assumed)

    Controllable:No

    Description:list of the characteristic times of the different dashpots in the material

  • poisson_ratioinitial poisson ratio of the material

    C++ Type:double

    Unit:(no unit assumed)

    Controllable:No

    Description:initial poisson ratio of the material

  • young_modulusinitial elastic modulus of the material

    C++ Type:double

    Unit:(no unit assumed)

    Controllable:No

    Description:initial elastic modulus of the material

Required Parameters

  • base_nameOptional parameter that allows the user to define multiple mechanics material systems on the same block, i.e. for multiple phases

    C++ Type:std::string

    Unit:(no unit assumed)

    Controllable:No

    Description:Optional parameter that allows the user to define multiple mechanics material systems on the same block, i.e. for multiple phases

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

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

    Unit:(no unit assumed)

    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>

    Unit:(no unit assumed)

    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

    Unit:(no unit assumed)

    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

    Unit:(no unit assumed)

    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

  • creep_ratiolist of the poisson ratios of the different springs in the material

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

    Unit:(no unit assumed)

    Controllable:No

    Description:list of the poisson ratios of the different springs in the material

  • creep_strain_namecreep_strainname of the true creep strain of the material(computed by LinearViscoelasticStressUpdate orComputeLinearViscoelasticStress)

    Default:creep_strain

    C++ Type:std::string

    Unit:(no unit assumed)

    Controllable:No

    Description:name of the true creep strain of the material(computed by LinearViscoelasticStressUpdate orComputeLinearViscoelasticStress)

  • 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.

  • driving_eigenstrainname of the eigenstrain that increases the creep strains

    C++ Type:std::string

    Unit:(no unit assumed)

    Controllable:No

    Description:name of the eigenstrain that increases the creep strains

  • elastic_strain_nameelastic_strainname of the true elastic strain of the material

    Default:elastic_strain

    C++ Type:std::string

    Unit:(no unit assumed)

    Controllable:No

    Description:name of the true elastic strain of the material

  • integration_rulebackward-eulerdescribes how the viscoelastic behavior is integrated through time

    Default:backward-euler

    C++ Type:MooseEnum

    Unit:(no unit assumed)

    Options:backward-euler, mid-point, newmark, zienkiewicz

    Controllable:No

    Description:describes how the viscoelastic behavior is integrated through time

  • 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.

  • theta1coefficient for Newmark integration rule (between 0 and 1)

    Default:1

    C++ Type:double

    Unit:(no unit assumed)

    Controllable:No

    Description:coefficient for Newmark integration rule (between 0 and 1)

  • 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

    Unit:(no unit assumed)

    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.

Optional Parameters

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

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

    Unit:(no unit assumed)

    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

    Unit:(no unit assumed)

    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

    Unit:(no unit assumed)

    Controllable:No

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

  • seed0The seed for the master random number generator

    Default:0

    C++ Type:unsigned int

    Unit:(no unit assumed)

    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

    Unit:(no unit assumed)

    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>

    Unit:(no unit assumed)

    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>

    Unit:(no unit assumed)

    Controllable:No

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

Outputs Parameters