ASPECT
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aspect::MaterialModel::Viscoelastic< dim > Class Template Reference
Inheritance diagram for aspect::MaterialModel::Viscoelastic< dim >:
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Public Member Functions

virtual void evaluate (const MaterialModel::MaterialModelInputs< dim > &in, MaterialModel::MaterialModelOutputs< dim > &out) const
 
virtual void create_additional_named_outputs (MaterialModel::MaterialModelOutputs< dim > &out) const
 
Qualitative properties one can ask a material model
virtual bool is_compressible () const
 
Reference quantities
virtual double reference_viscosity () const
 
- Public Member Functions inherited from aspect::MaterialModel::Interface< dim >
virtual ~Interface ()
 
virtual void initialize ()
 
virtual void update ()
 
virtual void fill_additional_material_model_inputs (MaterialModel::MaterialModelInputs< dim > &input, const LinearAlgebra::BlockVector &solution, const FEValuesBase< dim > &fe_values, const Introspection< dim > &introspection) const
 
const NonlinearDependence::ModelDependenceget_model_dependence () const
 
- Public Member Functions inherited from aspect::SimulatorAccess< dim >
 SimulatorAccess ()
 
 SimulatorAccess (const Simulator< dim > &simulator_object)
 
virtual ~SimulatorAccess ()
 
virtual void initialize_simulator (const Simulator< dim > &simulator_object)
 
template<typename PostprocessorType >
PostprocessorType * find_postprocessor () const
 
const Introspection< dim > & introspection () const
 
const Simulator< dim > & get_simulator () const
 
const Parameters< dim > & get_parameters () const
 
SimulatorSignals< dim > & get_signals () const
 
MPI_Comm get_mpi_communicator () const
 
TimerOutputget_computing_timer () const
 
const ConditionalOStreamget_pcout () const
 
double get_time () const
 
double get_timestep () const
 
double get_old_timestep () const
 
unsigned int get_timestep_number () const
 
unsigned int get_nonlinear_iteration () const
 
const parallel::distributed::Triangulation< dim > & get_triangulation () const
 
double get_volume () const
 
const Mapping< dim > & get_mapping () const
 
std::string get_output_directory () const
 
bool include_adiabatic_heating () const
 
bool include_latent_heat () const
 
bool include_melt_transport () const
 
int get_stokes_velocity_degree () const
 
double get_adiabatic_surface_temperature () const
 
double get_surface_pressure () const
 
bool convert_output_to_years () const
 
unsigned int get_pre_refinement_step () const
 
unsigned int n_compositional_fields () const
 
void get_refinement_criteria (Vector< float > &estimated_error_per_cell) const
 
void get_artificial_viscosity (Vector< float > &viscosity_per_cell, const bool skip_interior_cells=false) const
 
void get_artificial_viscosity_composition (Vector< float > &viscosity_per_cell, const unsigned int compositional_variable) const
 
const LinearAlgebra::BlockVectorget_current_linearization_point () const
 
const LinearAlgebra::BlockVectorget_solution () const
 
const LinearAlgebra::BlockVectorget_old_solution () const
 
const LinearAlgebra::BlockVectorget_old_old_solution () const
 
const LinearAlgebra::BlockVectorget_reaction_vector () const
 
const LinearAlgebra::BlockVectorget_mesh_velocity () const
 
const DoFHandler< dim > & get_dof_handler () const
 
const FiniteElement< dim > & get_fe () const
 
const LinearAlgebra::BlockSparseMatrixget_system_matrix () const
 
const LinearAlgebra::BlockSparseMatrixget_system_preconditioner_matrix () const
 
const MaterialModel::Interface< dim > & get_material_model () const
 
void compute_material_model_input_values (const LinearAlgebra::BlockVector &input_solution, const FEValuesBase< dim, dim > &input_finite_element_values, const typename DoFHandler< dim >::active_cell_iterator &cell, const bool compute_strainrate, MaterialModel::MaterialModelInputs< dim > &material_model_inputs) const
 
const GravityModel::Interface< dim > & get_gravity_model () const
 
const InitialTopographyModel::Interface< dim > & get_initial_topography_model () const
 
const GeometryModel::Interface< dim > & get_geometry_model () const
 
const AdiabaticConditions::Interface< dim > & get_adiabatic_conditions () const
 
bool has_boundary_temperature () const
 
DEAL_II_DEPRECATED const BoundaryTemperature::Interface< dim > & get_boundary_temperature () const
 
const BoundaryTemperature::Manager< dim > & get_boundary_temperature_manager () const
 
const BoundaryHeatFlux::Interface< dim > & get_boundary_heat_flux () const
 
bool has_boundary_composition () const
 
DEAL_II_DEPRECATED const BoundaryComposition::Interface< dim > & get_boundary_composition () const
 
const BoundaryComposition::Manager< dim > & get_boundary_composition_manager () const
 
const std::map< types::boundary_id, std::unique_ptr< BoundaryTraction::Interface< dim > > > & get_boundary_traction () const
 
DEAL_II_DEPRECATED const InitialTemperature::Interface< dim > & get_initial_temperature () const
 
const InitialTemperature::Manager< dim > & get_initial_temperature_manager () const
 
DEAL_II_DEPRECATED const InitialComposition::Interface< dim > & get_initial_composition () const
 
const InitialComposition::Manager< dim > & get_initial_composition_manager () const
 
const std::set< types::boundary_id > & get_fixed_temperature_boundary_indicators () const
 
const std::set< types::boundary_id > & get_fixed_heat_flux_boundary_indicators () const
 
const std::set< types::boundary_id > & get_fixed_composition_boundary_indicators () const
 
const std::set< types::boundary_id > & get_free_surface_boundary_indicators () const
 
DEAL_II_DEPRECATED const std::map< types::boundary_id, std::shared_ptr< BoundaryVelocity::Interface< dim > > > get_prescribed_boundary_velocity () const
 
const BoundaryVelocity::Manager< dim > & get_boundary_velocity_manager () const
 
const HeatingModel::Manager< dim > & get_heating_model_manager () const
 
const MeshRefinement::Manager< dim > & get_mesh_refinement_manager () const
 
const MeltHandler< dim > & get_melt_handler () const
 
const VolumeOfFluidHandler< dim > & get_volume_of_fluid_handler () const
 
const NewtonHandler< dim > & get_newton_handler () const
 
const WorldBuilder::World & get_world_builder () const
 
const FreeSurfaceHandler< dim > & get_free_surface_handler () const
 
const LateralAveraging< dim > & get_lateral_averaging () const
 
const ConstraintMatrix & get_current_constraints () const
 
bool simulator_is_initialized () const
 
double get_pressure_scaling () const
 
bool pressure_rhs_needs_compatibility_modification () const
 
bool model_has_prescribed_stokes_solution () const
 
TableHandlerget_statistics_object () const
 
template<typename PostprocessorType >
DEAL_II_DEPRECATED PostprocessorType * find_postprocessor () const
 
const Postprocess::Manager< dim > & get_postprocess_manager () const
 

Private Member Functions

double calculate_average_vector (const std::vector< double > &composition, const std::vector< double > &parameter_values, const MaterialUtilities::CompositionalAveragingOperation &average_type) const
 
double calculate_average_viscoelastic_viscosity (const double average_viscosity, const double average_elastic_shear_modulus, const double dte) const
 

Private Attributes

double reference_T
 
MaterialUtilities::CompositionalAveragingOperation viscosity_averaging
 
std::vector< double > densities
 
std::vector< double > viscosities
 
std::vector< double > thermal_expansivities
 
std::vector< double > thermal_conductivities
 
std::vector< double > specific_heats
 
std::vector< double > elastic_shear_moduli
 
bool use_fixed_elastic_time_step
 
bool use_stress_averaging
 
double fixed_elastic_time_step
 

Functions used in dealing with run-time parameters

virtual void parse_parameters (ParameterHandler &prm)
 
static void declare_parameters (ParameterHandler &prm)
 

Additional Inherited Members

- Public Types inherited from aspect::MaterialModel::Interface< dim >
typedef MaterialModel::MaterialModelInputs< dim > MaterialModelInputs
 
typedef MaterialModel::MaterialModelOutputs< dim > MaterialModelOutputs
 
- Static Public Member Functions inherited from aspect::MaterialModel::Interface< dim >
static void declare_parameters (ParameterHandler &prm)
 
- Static Public Member Functions inherited from aspect::SimulatorAccess< dim >
static void get_composition_values_at_q_point (const std::vector< std::vector< double > > &composition_values, const unsigned int q, std::vector< double > &composition_values_at_q_point)
 
- Protected Attributes inherited from aspect::MaterialModel::Interface< dim >
NonlinearDependence::ModelDependence model_dependence
 

Detailed Description

template<int dim>
class aspect::MaterialModel::Viscoelastic< dim >

An implementation of a simple linear viscoelastic rheology that only includes the deviatoric components of elasticity. Specifically, the viscoelastic rheology only takes into account the elastic shear strength (e.g., shear modulus), while the tensile and volumetric strength (e.g., Young's and bulk modulus) are not considered. The model is incompressible and allows specifying an arbitrary number of compositional fields, where each field represents a different rock type or component of the viscoelastic stress tensor. The stress tensor in 2D and 3D, respectively, contains 3 or 6 components. The compositional fields representing these components must be named and listed in a very specific format, which is designed to minimize mislabeling stress tensor components as distinct 'compositional rock types' (or vice versa). For 2D models, the first three compositional fields must be labeled stress_xx, stress_yy and stress_xy. In 3D, the first six compositional fields must be labeled stress_xx, stress_yy, stress_zz, stress_xy, stress_xz, stress_yz.

Expanding the model to include non-linear viscous flow (e.g., diffusion/dislocation creep) and plasticity would produce a constitutive relationship commonly referred to as partial elastoviscoplastic (e.g., pEVP) in the geodynamics community. While extensively discussed and applied within the geodynamics literature, notable references include: Moresi et al. (2003), J. Comp. Phys., v. 184, p. 476-497. Gerya and Yuen (2007), Phys. Earth. Planet. Inter., v. 163, p. 83-105. Gerya (2010), Introduction to Numerical Geodynamic Modeling. Kaus (2010), Tectonophysics, v. 484, p. 36-47. Choi et al. (2013), J. Geophys. Res., v. 118, p. 2429-2444. Keller et al. (2013), Geophys. J. Int., v. 195, p. 1406-1442.

The overview below directly follows Moresi et al. (2003) eqns. 23-32. However, an important distinction between this material model and the studies above is the use of compositional fields, rather than tracers, to track individual components of the viscoelastic stress tensor. The material model will be udpated when an option to track and calculate viscoelastic stresses with tracers is implemented.

Moresi et al. (2003) begins (eqn. 23) by writing the deviatoric rate of deformation ( $\hat{D}$) as the sum of elastic ( $\hat{D_{e}}$) and viscous ( $\hat{D_{v}}$) components: $\hat{D} = \hat{D_{e}} + \hat{D_{v}}$. These terms further decompose into $\hat{D_{v}} = \frac{\tau}{2\eta}$ and $\hat{D_{e}} = \frac{\overset{\nabla}{\tau}}{2\mu}$, where $\tau$ is the viscous deviatoric stress, $\eta$ is the shear viscosity, $\mu$ is the shear modulus and $\overset{\nabla}{\tau}$ is the Jaumann corotational stress rate. This later term (eqn. 24) contains the time derivative of the deviatoric stress ( $\dot{\tau}$) and terms that account for material spin (e.g., rotation) due to advection: $\overset{\nabla}{\tau} = \dot{\tau} + {\tau}W -W\tau$. Above, $W$ is the material spin tensor (eqn. 25): $W_{ij} = \frac{1}{2} \left (\frac{\partial V_{i}}{\partial x_{j}} - \frac{\partial V_{j}}{\partial x_{i}} \right )$.

The Jaumann stress-rate can also be approximated using terms from the time at the previous time step ( $t$) and current time step ( $t + \Delta t^{e}$): $\smash[t]{\overset{\nabla}{\tau}}^{t + \Delta t^{e}} \approx \frac{\tau^{t + \Delta t^{e} - \tau^{t}}}{\Delta t^{e}} - W^{t}\tau^{t} + \tau^{t}W^{t}$. In this material model, the size of the time step above ( $\\Delta t^{e}$) can be specified as the numerical time step size or an independent fixed time step. If the latter case is a selected, the user has an option to apply a stress averaging scheme to account for the differences between the numerical and fixed elastic time step (eqn. 32). If one selects to use a fixed elastic time step throughout the model run, this can still be achieved by using CFL and maximum time step values that restrict the numerical time step to a specific time.

The formulation above allows rewriting the total rate of deformation (eqn. 29) as $\tau^{t + \Delta t^{e}} = \eta_{eff} \left ( 2\\hat{D}^{t + \\triangle t^{e}} + \\frac{\\tau^{t}}{\\mu \\Delta t^{e}} + \\frac{W^{t}\\tau^{t} - \\tau^{t}W^{t}}{\\mu} \\right )$.

The effective viscosity (eqn. 28) is a function of the viscosity ( $\eta$), elastic time step size ( $\Delta t^{e}$) and shear relaxation time ( $ \alpha = \frac{\eta}{\mu} $): $\eta_{eff} = \eta \frac{\Delta t^{e}}{\Delta t^{e} + \alpha}$ The magnitude of the shear modulus thus controls how much the effective viscosity is reduced relative to the initial viscosity.

Elastic effects are introduced into the governing stokes equations through an elastic force term (eqn. 30) using stresses from the previous time step: $F^{e,t} = -\frac{\eta_{eff}}{\mu \Delta t^{e}} \tau^{t}$. This force term is added onto the right-hand side force vector in the system of equations.

The value of each compositional field representing distinct rock types at a point is interpreted to be a volume fraction of that rock type. If the sum of the compositional field volume fractions is less than one, then the remainder of the volume is assumed to be 'background material'.

Several model parameters (densities, elastic shear moduli, thermal expansivities, thermal conductivies, specific heats) can be defined per-compositional field. For each material parameter the user supplies a comma delimited list of length N+1, where N is the number of compositional fields. The additional field corresponds to the value for background material. They should be ordered ``background, composition1, composition2...''. However, the first 3 (2D) or 6 (3D) composition fields correspond to components of the elastic stress tensor and their material values will not contribute to the volume fractions. If a single value is given, then all the compositional fields are given that value. Other lengths of lists are not allowed. For a given compositional field the material parameters are treated as constant, except density, which varies linearly with temperature according to the thermal expansivity.

When more than one compositional field is present at a point, they are averaged arithmetically. An exception is viscosity, which may be averaged arithmetically, harmonically, geometrically, or by selecting the viscosity of the composition with the greatest volume fraction.

Definition at line 167 of file viscoelastic.h.

Member Function Documentation

§ evaluate()

template<int dim>
virtual void aspect::MaterialModel::Viscoelastic< dim >::evaluate ( const MaterialModel::MaterialModelInputs< dim > &  in,
MaterialModel::MaterialModelOutputs< dim > &  out 
) const
virtual

Function to compute the material properties in out given the inputs in in. If MaterialModelInputs.strain_rate has the length 0, then the viscosity does not need to be computed.

Implements aspect::MaterialModel::Interface< dim >.

§ is_compressible()

template<int dim>
virtual bool aspect::MaterialModel::Viscoelastic< dim >::is_compressible ( ) const
virtual

This model is not compressible, so this returns false.

Implements aspect::MaterialModel::Interface< dim >.

§ reference_viscosity()

template<int dim>
virtual double aspect::MaterialModel::Viscoelastic< dim >::reference_viscosity ( ) const
virtual

Return a reference value typical of the viscosities that appear in this model. This value is not actually used in the material description itself, but is used in scaling variables to the same numerical order of magnitude when solving linear systems. Specifically, the reference viscosity appears in the factor scaling the pressure against the velocity. It is also used in computing dimension-less quantities. You may want to take a look at the Kronbichler, Heister, Bangerth 2012 paper that describes the design of ASPECT for a description of this pressure scaling.

Note
The reference viscosity should take into account the complete constitutive relationship, defined as the scalar viscosity times the constitutive tensor. In most cases, the constitutive tensor will simply be the identity tensor (this is the default case), but this may become important for material models with anisotropic viscosities, if the constitutive tensor is not normalized.

Implements aspect::MaterialModel::Interface< dim >.

§ declare_parameters()

template<int dim>
static void aspect::MaterialModel::Viscoelastic< dim >::declare_parameters ( ParameterHandler prm)
static

Declare the parameters this class takes through input files.

§ parse_parameters()

template<int dim>
virtual void aspect::MaterialModel::Viscoelastic< dim >::parse_parameters ( ParameterHandler prm)
virtual

Read the parameters this class declares from the parameter file.

Reimplemented from aspect::MaterialModel::Interface< dim >.

§ create_additional_named_outputs()

template<int dim>
virtual void aspect::MaterialModel::Viscoelastic< dim >::create_additional_named_outputs ( MaterialModel::MaterialModelOutputs< dim > &  outputs) const
virtual

If this material model can produce additional named outputs that are derived from NamedAdditionalOutputs, create them in here. By default, this does nothing.

Reimplemented from aspect::MaterialModel::Interface< dim >.

§ calculate_average_vector()

template<int dim>
double aspect::MaterialModel::Viscoelastic< dim >::calculate_average_vector ( const std::vector< double > &  composition,
const std::vector< double > &  parameter_values,
const MaterialUtilities::CompositionalAveragingOperation average_type 
) const
private

Used for calculating average elastic shear modulus and viscosity

§ calculate_average_viscoelastic_viscosity()

template<int dim>
double aspect::MaterialModel::Viscoelastic< dim >::calculate_average_viscoelastic_viscosity ( const double  average_viscosity,
const double  average_elastic_shear_modulus,
const double  dte 
) const
private

Member Data Documentation

§ reference_T

template<int dim>
double aspect::MaterialModel::Viscoelastic< dim >::reference_T
private

Reference temperature for thermal expansion. All components use the same reference_T.

Definition at line 232 of file viscoelastic.h.

§ viscosity_averaging

template<int dim>
MaterialUtilities::CompositionalAveragingOperation aspect::MaterialModel::Viscoelastic< dim >::viscosity_averaging
private

Enumeration for selecting which viscosity averaging scheme to use.

Definition at line 237 of file viscoelastic.h.

§ densities

template<int dim>
std::vector<double> aspect::MaterialModel::Viscoelastic< dim >::densities
private

Vector for field densities, read from parameter file.

Definition at line 255 of file viscoelastic.h.

§ viscosities

template<int dim>
std::vector<double> aspect::MaterialModel::Viscoelastic< dim >::viscosities
private

Vector for field viscosities, read from parameter file.

Definition at line 260 of file viscoelastic.h.

§ thermal_expansivities

template<int dim>
std::vector<double> aspect::MaterialModel::Viscoelastic< dim >::thermal_expansivities
private

Vector for field thermal expnsivities, read from parameter file.

Definition at line 265 of file viscoelastic.h.

§ thermal_conductivities

template<int dim>
std::vector<double> aspect::MaterialModel::Viscoelastic< dim >::thermal_conductivities
private

Vector for field thermal conductivities, read from parameter file.

Definition at line 270 of file viscoelastic.h.

§ specific_heats

template<int dim>
std::vector<double> aspect::MaterialModel::Viscoelastic< dim >::specific_heats
private

Vector for field specific heats, read from parameter file.

Definition at line 275 of file viscoelastic.h.

§ elastic_shear_moduli

template<int dim>
std::vector<double> aspect::MaterialModel::Viscoelastic< dim >::elastic_shear_moduli
private

Vector for field elastic shear moduli, read from parameter file.

Definition at line 280 of file viscoelastic.h.

§ use_fixed_elastic_time_step

template<int dim>
bool aspect::MaterialModel::Viscoelastic< dim >::use_fixed_elastic_time_step
private

Bool indicating whether to use a fixed material time scale in the viscoelastic rheology for all time steps (if true) or to use the actual (variable) advection time step of the model (if false). Read from parameter file.

Definition at line 288 of file viscoelastic.h.

§ use_stress_averaging

template<int dim>
bool aspect::MaterialModel::Viscoelastic< dim >::use_stress_averaging
private

Bool indicating whether to use a stress averaging scheme to account for differences between the numerical and fixed elastic time step (if true). When set to false, the viscoelastic stresses are not modified to account for differences between the viscoelastic time step and the numerical time step. Read from parameter file.

Definition at line 297 of file viscoelastic.h.

§ fixed_elastic_time_step

template<int dim>
double aspect::MaterialModel::Viscoelastic< dim >::fixed_elastic_time_step
private

Double for fixed elastic time step value, read from parameter file

Definition at line 302 of file viscoelastic.h.


The documentation for this class was generated from the following file: