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

Physical parameters used in the basic equations
virtual void evaluate (const MaterialModel::MaterialModelInputs< dim > &in, 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 create_additional_named_outputs (MaterialModelOutputs &outputs) const
 
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 Attributes

double reference_rho
 
double reference_T
 
double reference_eta
 
double thermal_expansivity
 
double reference_specific_heat
 
double thermal_conductivities
 
double angle_of_internal_friction
 
double cohesion
 
double minimum_viscosity
 
double maximum_viscosity
 
double reference_strain_rate
 

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::DruckerPrager< dim >

A material model that consists of globally constant values for all material parameters except density and viscosity.

The model is considered incompressible, following the definition described in Interface::is_compressible.

The viscosity is computed according to the Drucker Prager frictional plasticity criterion based on a user-defined internal angle of friction $\phi$ and cohesion $C$. In 3D: $\sigma_y = \frac{6 C \cos(\phi)}{\sqrt(3) (3+\sin(\phi))} + \frac{2 P \sin(\phi)}{\sqrt(3) (3+\sin(\phi))}$, where $P$ is the pressure. See for example Zienkiewicz, O. C., Humpheson, C. and Lewis, R. W. (1975), Géotechnique 25, No. 4, 671-689. With this formulation we circumscribe instead of inscribe the Mohr Coulomb yield surface. In 2D the Drucker Prager yield surface is the same as the Mohr Coulomb surface: $\sigma_y = P \sin(\phi) + C \cos(\phi)$. Note that in 2D for $\phi=0$, these criteria revert to the von Mises criterion (no pressure dependence). See for example Thieulot, C. (2011), PEPI 188, 47-68.

Note that we enforce the pressure to be positive in the computation of the yield strength by replacing it with a zero value whenever it is negative to prevent negative yield strengths and viscosities. We then use the computed yield strength to scale back the viscosity on to the yield surface using the Viscosity Rescaling Method described in Kachanov, L. M. (2004), Fundamentals of the Theory of Plasticity, Dover Publications, Inc.

To avoid numerically unfavourably large (or even negative) viscosity ranges, we cut off the viscosity with a user-defined minimum and maximum viscosity: $\eta_eff = \frac{1}{\frac{1}{\eta_min + \eta}+\\ \frac{1}{\eta_max}}$.

Note that this model uses the formulation that assumes an incompressible medium despite the fact that the density follows the law $\rho(T)=\rho_0(1-\beta(T-T_{\text{ref}}))$.

Definition at line 79 of file drucker_prager.h.

Member Function Documentation

§ evaluate()

template<int dim>
virtual void aspect::MaterialModel::DruckerPrager< 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::DruckerPrager< dim >::is_compressible ( ) const
virtual

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).

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

§ reference_viscosity()

template<int dim>
virtual double aspect::MaterialModel::DruckerPrager< 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::DruckerPrager< dim >::declare_parameters ( ParameterHandler prm)
static

Declare the parameters this class takes through input files.

§ parse_parameters()

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

Read the parameters this class declares from the parameter file.

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

Member Data Documentation

§ reference_rho

template<int dim>
double aspect::MaterialModel::DruckerPrager< dim >::reference_rho
private

Definition at line 143 of file drucker_prager.h.

§ reference_T

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

Definition at line 144 of file drucker_prager.h.

§ reference_eta

template<int dim>
double aspect::MaterialModel::DruckerPrager< dim >::reference_eta
private

Definition at line 145 of file drucker_prager.h.

§ thermal_expansivity

template<int dim>
double aspect::MaterialModel::DruckerPrager< dim >::thermal_expansivity
private

Definition at line 146 of file drucker_prager.h.

§ reference_specific_heat

template<int dim>
double aspect::MaterialModel::DruckerPrager< dim >::reference_specific_heat
private

Definition at line 147 of file drucker_prager.h.

§ thermal_conductivities

template<int dim>
double aspect::MaterialModel::DruckerPrager< dim >::thermal_conductivities
private

Definition at line 148 of file drucker_prager.h.

§ angle_of_internal_friction

template<int dim>
double aspect::MaterialModel::DruckerPrager< dim >::angle_of_internal_friction
private

The angle of internal friction

Definition at line 153 of file drucker_prager.h.

§ cohesion

template<int dim>
double aspect::MaterialModel::DruckerPrager< dim >::cohesion
private

The cohesion

Definition at line 158 of file drucker_prager.h.

§ minimum_viscosity

template<int dim>
double aspect::MaterialModel::DruckerPrager< dim >::minimum_viscosity
private

The applied viscosity bounds

Definition at line 163 of file drucker_prager.h.

§ maximum_viscosity

template<int dim>
double aspect::MaterialModel::DruckerPrager< dim >::maximum_viscosity
private

Definition at line 164 of file drucker_prager.h.

§ reference_strain_rate

template<int dim>
double aspect::MaterialModel::DruckerPrager< dim >::reference_strain_rate
private

The reference strain rate used as a first estimate

Definition at line 169 of file drucker_prager.h.


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