Public Member Functions | Private Attributes | List of all members
aspect::MaterialModel::Viscoelastic< dim > Class Template Reference
Inheritance diagram for aspect::MaterialModel::Viscoelastic< dim >:
Inheritance graph

Public Member Functions

void evaluate (const MaterialModel::MaterialModelInputs< dim > &in, MaterialModel::MaterialModelOutputs< dim > &out) const override
void create_additional_named_outputs (MaterialModel::MaterialModelOutputs< dim > &out) const override
Qualitative properties one can ask a material model
bool is_compressible () const override
Reference quantities
double reference_viscosity () const override
- 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_mesh_deformation_boundary_indicators () 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 MeshDeformation::MeshDeformationHandler< dim > & get_mesh_deformation_handler () const
const LateralAveraging< dim > & get_lateral_averaging () const
const AffineConstraints< double > & get_current_constraints () const
bool simulator_is_past_initialization () 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
const Particle::World< dim > & get_particle_world () const
Particle::World< dim > & get_particle_world ()
bool is_stokes_matrix_free ()
const StokesMatrixFreeHandler< dim > & get_stokes_matrix_free () const
RotationProperties< dim > compute_net_angular_momentum (const bool use_constant_density, const LinearAlgebra::BlockVector &solution, const bool limit_to_top_faces=false) const

Private Attributes

MaterialUtilities::CompositionalAveragingOperation viscosity_averaging
EquationOfState::MulticomponentIncompressible< dim > equation_of_state
std::vector< double > viscosities
std::vector< double > thermal_conductivities
Rheology::Elasticity< dim > elastic_rheology

Functions used in dealing with run-time parameters

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

Additional Inherited Members

- Public Types inherited from aspect::MaterialModel::Interface< dim >
using MaterialModelInputs = MaterialModel::MaterialModelInputs< dim >
using MaterialModelOutputs = MaterialModel::MaterialModelOutputs< dim >
- 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 ve_stress_xx, ve_stress_yy and ve_stress_xy. In 3D, the first six compositional fields must be labeled ve_stress_xx, ve_stress_yy, ve_stress_zz, ve_stress_xy, ve_stress_xz, ve_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 particles, to track individual components of the viscoelastic stress tensor. The material model will be updated when an option to track and calculate viscoelastic stresses with particles 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 148 of file viscoelastic.h.

Member Function Documentation

§ evaluate()

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

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

This model is not compressible, so this returns false.

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

§ reference_viscosity()

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

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.

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)

Declare the parameters this class takes through input files.

§ parse_parameters()

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

Read the parameters this class declares from the parameter file.

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

§ create_additional_named_outputs()

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

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 >.

Member Data Documentation

§ viscosity_averaging

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

Enumeration for selecting which viscosity averaging scheme to use.

Definition at line 210 of file viscoelastic.h.

§ equation_of_state

template<int dim>
EquationOfState::MulticomponentIncompressible<dim> aspect::MaterialModel::Viscoelastic< dim >::equation_of_state

Definition at line 212 of file viscoelastic.h.

§ viscosities

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

Vector for field viscosities, read from parameter file.

Definition at line 217 of file viscoelastic.h.

§ thermal_conductivities

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

Vector for field thermal conductivities, read from parameter file.

Definition at line 222 of file viscoelastic.h.

§ elastic_rheology

template<int dim>
Rheology::Elasticity<dim> aspect::MaterialModel::Viscoelastic< dim >::elastic_rheology

Definition at line 224 of file viscoelastic.h.

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