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

Public Member Functions

void evaluate (const MaterialModel::MaterialModelInputs< dim > &in, MaterialModel::MaterialModelOutputs< dim > &out) const override
bool is_compressible () const override
void parse_parameters (ParameterHandler &prm) override
void create_additional_named_outputs (MaterialModel::MaterialModelOutputs< dim > &out) const override
double get_min_strain_rate () const
DEAL_II_DEPRECATED bool is_yielding (const double pressure, const double temperature, const std::vector< double > &composition, const SymmetricTensor< 2, dim > &strain_rate) const
bool is_yielding (const MaterialModelInputs< dim > &in) const
- Public Member Functions inherited from aspect::MaterialModel::Interface< dim >
virtual ~Interface ()=default
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 ()=default
virtual void initialize_simulator (const Simulator< dim > &simulator_object)
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
TimerOutput & get_computing_timer () const
const ConditionalOStream & get_pcout () const
double get_time () const
double get_timestep () const
double get_old_timestep () const
unsigned int get_timestep_number () const
const TimeStepping::Manager< dim > & get_timestepping_manager () 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
double get_end_time () 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
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
const BoundaryTemperature::Manager< dim > & get_boundary_temperature_manager () const
const BoundaryHeatFlux::Interface< dim > & get_boundary_heat_flux () const
bool has_boundary_composition () const
const BoundaryComposition::Manager< dim > & get_boundary_composition_manager () const
const BoundaryTraction::Manager< dim > & get_boundary_traction_manager () const
std::shared_ptr< const InitialTemperature::Manager< dim > > get_initial_temperature_manager_pointer () const
const InitialTemperature::Manager< dim > & get_initial_temperature_manager () const
std::shared_ptr< const InitialComposition::Manager< dim > > get_initial_composition_manager_pointer () 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
TableHandler & get_statistics_object () 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

Static Public Member Functions

static void declare_parameters (ParameterHandler &prm)
- 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)

Private Attributes

std::unique_ptr< Rheology::ViscoPlastic< dim > > rheology
std::vector< double > thermal_diffusivities
bool define_conductivities
std::vector< double > thermal_conductivities
std::vector< unsigned int > n_phase_transitions_for_each_chemical_composition
unsigned int n_phases
EquationOfState::MulticomponentIncompressible< dim > equation_of_state
MaterialUtilities::PhaseFunction< dim > phase_function

Additional Inherited Members

- Public Types inherited from aspect::MaterialModel::Interface< dim >
using MaterialModelInputs = MaterialModel::MaterialModelInputs< dim >
using MaterialModelOutputs = MaterialModel::MaterialModelOutputs< dim >
- Protected Attributes inherited from aspect::MaterialModel::Interface< dim >
NonlinearDependence::ModelDependence model_dependence

Detailed Description

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

A material model combining viscous and plastic deformation, with the option to also include viscoelastic deformation.

Viscous deformation is defined by a viscous flow law describing dislocation and diffusion creep: \( v = \frac{1}{2} A^{-\frac{1}{n}} d^{\frac{m}{n}} \dot{\varepsilon}_{ii}^{\frac{1-n}{n}} \exp\left(\frac{E + PV}{nRT}\right) \) where where \(A\) is the prefactor, \(n\) is the stress exponent, \(\dot{\varepsilon}_{ii}\) is the square root of the deviatoric strain rate tensor second invariant, \(d\) is grain size, \(m\) is the grain size exponent, \(E\) is activation energy, \(V\) is activation volume, \(P\) is pressure, \(R\) is the gas exponent and \(T\) is temperature.

One may select to use the diffusion ( \(v_{diff}\); \(n=1\), \(m!=0\)), dislocation ( \(v_{disl}\), \(n>1\), \(m=0\)) or composite \(\frac{v_{diff}v_{disl}}{v_{diff}+v_{disl}}\) equation form.

Viscous stress is limited by plastic deformation, which follows a Drucker Prager yield criterion: \(\sigma_y = C\cos(\phi) + P\sin(\phi)\) (2D) or in 3D \(\sigma_y = \frac{6C\cos(\phi) + 2P\sin(\phi)}{\sqrt{3}(3+\sin(\phi))}\) where \(\sigma_y\) is the yield stress, \(C\) is cohesion, \(phi\) is the angle of internal friction and \(P\) is pressure. If the viscous stress ( \(2v{\varepsilon}_{ii})\)) exceeds the yield stress ( \(\sigma_{y}\)), the viscosity is rescaled back to the yield surface: \(v_{y}=\sigma_{y}/(2{\varepsilon}_{ii})\)

When included, the viscoelastic rheology 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 symmetric 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.

Combining this viscoelasticity implementation with non-linear viscous flow and plasticity produces 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 \(\hat{D_{e}} = \frac{\overset{\triangledown}{\tau}}{2\mu}\), where \(\tau\) is the viscous deviatoric stress, \(\eta\) is the shear viscosity, \(\mu\) is the shear modulus and \(\overset{\triangledown}{\tau}\) is the Jaumann corotational stress rate. If plasticity is included the deviatoric rate of deformation may be written as: \(\hat{D} = \hat{D_{e}} + \hat{D_{v}} + \hat{D_{p}}\), where \(\hat{D_{p}}\) is the plastic component. As defined in the second paragraph, \(\hat{D_{p}}\) decomposes to \(\frac{\tau_{y}}{2\eta_{y}}\), where \(\tau_{y}\) is the yield stress and \(\eta_{y}\) is the viscosity rescaled to the yield surface.

Above, the Jaumann corotational stress rate (eqn. 24) from the elastic component contains the time derivative of the deviatoric stress ( \(\dot{\tau}\)) and terms that account for material spin (e.g., rotation) due to advection: \(\overset{\triangledown}{\tau} = \dot{\tau} + {\tau}W -W\tau\). 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 ( \(t + \Delta t^{e}\)): \(\smash[t]{\overset{\triangledown}{\tau}}^{t + \Delta t^{e}} \approx \frac{\tau^{t + \Delta t^{e} - \tau^{t}}}{\Delta t^{e}} - W^{t}\tau^{t} + \tau^{t}W^{t}\). 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 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, an equal numerical and elastic time step can be achieved by using CFL and maximum time step values that restrict the numerical time step to the fixed elastic time step.

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.

Several model parameters (reference densities, thermal expansivities thermal diffusivities, heat capacities and rheology parameters) 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...''

If a list of values is given for the density, thermal expansivity, thermal diffusivity and heat capacity, the volume weighted sum of the values of each of the compositional fields is used in their place, for example \(\rho = \sum \left( \rho_i V_i \right)\)

The individual output viscosities for each compositional field are also averaged. The user can choose from a range of options for this viscosity averaging. If only one value is given for any of these parameters, all compositions are assigned the same value. The first value in the list is the value assigned to "background material" (regions where the sum of the compositional fields is < 1.0).

Definition at line 181 of file visco_plastic.h.

Member Function Documentation

§ evaluate()

template<int dim>
void aspect::MaterialModel::ViscoPlastic< 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.

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

§ is_compressible()

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

Return whether the model is compressible or not. Incompressibility does not necessarily imply that the density is constant; rather, it may still depend on temperature or pressure. In the current context, compressibility means whether we should solve the continuity equation as \(\nabla \cdot (\rho \mathbf u)=0\) (compressible Stokes) or as \(\nabla \cdot \mathbf{u}=0\) (incompressible Stokes).

This material model is incompressible.

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

§ declare_parameters()

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

§ parse_parameters()

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

Read the parameters this class declares from the parameter file. The default implementation of this function does not read any parameters. Consequently, derived classes do not have to overload this function if they do not take any runtime parameters.

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

§ create_additional_named_outputs()

template<int dim>
void aspect::MaterialModel::ViscoPlastic< 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 >.

§ get_min_strain_rate()

template<int dim>
double aspect::MaterialModel::ViscoPlastic< dim >::get_min_strain_rate ( ) const

§ is_yielding() [1/2]

template<int dim>
DEAL_II_DEPRECATED bool aspect::MaterialModel::ViscoPlastic< dim >::is_yielding ( const double  pressure,
const double  temperature,
const std::vector< double > &  composition,
const SymmetricTensor< 2, dim > &  strain_rate 
) const

A function that returns whether the material is plastically yielding at the given pressure, temperature, composition, and strain rate.

: Use the other function with this name instead, which allows to pass in more general input variables.

§ is_yielding() [2/2]

template<int dim>
bool aspect::MaterialModel::ViscoPlastic< dim >::is_yielding ( const MaterialModelInputs< dim > &  in) const

A function that returns whether the material is plastically yielding at the given input variables (pressure, temperature, composition, strain rate, and so on).

Member Data Documentation

§ rheology

template<int dim>
std::unique_ptr<Rheology::ViscoPlastic<dim> > aspect::MaterialModel::ViscoPlastic< dim >::rheology

Pointer to the object used to compute the rheological properties. In this case, the rheology in question is visco(elasto)plastic. The object contains functions for parameter declaration and parsing, and further functions that calculate viscosity and viscosity derivatives. It also contains functions that create and fill additional material model outputs, specifically plastic outputs. The rheology itself is a composite rheology, and so the object contains further objects and/or pointers to objects that provide functions and parameters for all subordinate rheologies.

Definition at line 247 of file visco_plastic.h.

§ thermal_diffusivities

template<int dim>
std::vector<double> aspect::MaterialModel::ViscoPlastic< dim >::thermal_diffusivities

Definition at line 249 of file visco_plastic.h.

§ define_conductivities

template<int dim>
bool aspect::MaterialModel::ViscoPlastic< dim >::define_conductivities

Whether to use user-defined thermal conductivities instead of thermal diffusivities.

Definition at line 254 of file visco_plastic.h.

§ thermal_conductivities

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

Definition at line 256 of file visco_plastic.h.

§ n_phase_transitions_for_each_chemical_composition

template<int dim>
std::vector<unsigned int> aspect::MaterialModel::ViscoPlastic< dim >::n_phase_transitions_for_each_chemical_composition

Number of phase transitions for each chemical composition (including the background field).

Definition at line 261 of file visco_plastic.h.

§ n_phases

template<int dim>
unsigned int aspect::MaterialModel::ViscoPlastic< dim >::n_phases

Total number of phases.

Definition at line 266 of file visco_plastic.h.

§ equation_of_state

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

Object for computing the equation of state.

Definition at line 271 of file visco_plastic.h.

§ phase_function

template<int dim>
MaterialUtilities::PhaseFunction<dim> aspect::MaterialModel::ViscoPlastic< dim >::phase_function

Object that handles phase transitions.

Definition at line 276 of file visco_plastic.h.

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