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| void | evaluate (const MaterialModel::MaterialModelInputs< dim > &in, MaterialModel::MaterialModelOutputs< dim > &out) const override |
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| bool | is_compressible () const override |
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| virtual void | create_additional_named_outputs (MaterialModelOutputs &outputs) const |
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| 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 |
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| const NonlinearDependence::ModelDependence & | get_model_dependence () const |
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| virtual | ~InterfaceBase ()=default |
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| virtual void | initialize () |
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| virtual void | update () |
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| | SimulatorAccess () |
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| | SimulatorAccess (const Simulator< dim > &simulator_object) |
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| virtual | ~SimulatorAccess ()=default |
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| virtual void | initialize_simulator (const Simulator< dim > &simulator_object) |
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| const Introspection< dim > & | introspection () const |
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| const Simulator< dim > & | get_simulator () const |
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| const Parameters< dim > & | get_parameters () const |
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| SimulatorSignals< dim > & | get_signals () const |
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| MPI_Comm | get_mpi_communicator () const |
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| TimerOutput & | get_computing_timer () const |
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| const ConditionalOStream & | get_pcout () const |
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| double | get_time () const |
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| double | get_timestep () const |
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| double | get_old_timestep () const |
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| unsigned int | get_timestep_number () const |
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| const TimeStepping::Manager< dim > & | get_timestepping_manager () const |
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| unsigned int | get_nonlinear_iteration () const |
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| const parallel::distributed::Triangulation< dim > & | get_triangulation () const |
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| double | get_volume () const |
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| const Mapping< dim > & | get_mapping () const |
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| std::string | get_output_directory () const |
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| bool | include_adiabatic_heating () const |
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| bool | include_latent_heat () const |
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| bool | include_melt_transport () const |
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| int | get_stokes_velocity_degree () const |
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| double | get_adiabatic_surface_temperature () const |
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| double | get_surface_pressure () const |
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| bool | convert_output_to_years () const |
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| unsigned int | get_pre_refinement_step () const |
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| unsigned int | n_compositional_fields () const |
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| double | get_end_time () const |
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| void | get_refinement_criteria (Vector< float > &estimated_error_per_cell) const |
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| void | get_artificial_viscosity (Vector< float > &viscosity_per_cell, const bool skip_interior_cells=false) const |
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| void | get_artificial_viscosity_composition (Vector< float > &viscosity_per_cell, const unsigned int compositional_variable) const |
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| const LinearAlgebra::BlockVector & | get_current_linearization_point () const |
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| const LinearAlgebra::BlockVector & | get_solution () const |
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| const LinearAlgebra::BlockVector & | get_old_solution () const |
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| const LinearAlgebra::BlockVector & | get_old_old_solution () const |
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| const LinearAlgebra::BlockVector & | get_reaction_vector () const |
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| const LinearAlgebra::BlockVector & | get_mesh_velocity () const |
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| const DoFHandler< dim > & | get_dof_handler () const |
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| const FiniteElement< dim > & | get_fe () const |
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| const LinearAlgebra::BlockSparseMatrix & | get_system_matrix () const |
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| const LinearAlgebra::BlockSparseMatrix & | get_system_preconditioner_matrix () const |
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| const MaterialModel::Interface< dim > & | get_material_model () const |
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| const GravityModel::Interface< dim > & | get_gravity_model () const |
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| const InitialTopographyModel::Interface< dim > & | get_initial_topography_model () const |
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| const GeometryModel::Interface< dim > & | get_geometry_model () const |
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| const AdiabaticConditions::Interface< dim > & | get_adiabatic_conditions () const |
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| bool | has_boundary_temperature () const |
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| const BoundaryTemperature::Manager< dim > & | get_boundary_temperature_manager () const |
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| const BoundaryHeatFlux::Interface< dim > & | get_boundary_heat_flux () const |
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| bool | has_boundary_composition () const |
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| const BoundaryComposition::Manager< dim > & | get_boundary_composition_manager () const |
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| const BoundaryTraction::Manager< dim > & | get_boundary_traction_manager () const |
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| std::shared_ptr< const InitialTemperature::Manager< dim > > | get_initial_temperature_manager_pointer () const |
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| const InitialTemperature::Manager< dim > & | get_initial_temperature_manager () const |
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| std::shared_ptr< const InitialComposition::Manager< dim > > | get_initial_composition_manager_pointer () const |
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| const InitialComposition::Manager< dim > & | get_initial_composition_manager () const |
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| const std::set< types::boundary_id > & | get_fixed_temperature_boundary_indicators () const |
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| const std::set< types::boundary_id > & | get_fixed_heat_flux_boundary_indicators () const |
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| const std::set< types::boundary_id > & | get_fixed_composition_boundary_indicators () const |
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| const std::set< types::boundary_id > & | get_mesh_deformation_boundary_indicators () const |
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| const BoundaryVelocity::Manager< dim > & | get_boundary_velocity_manager () const |
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| const HeatingModel::Manager< dim > & | get_heating_model_manager () const |
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| const MeshRefinement::Manager< dim > & | get_mesh_refinement_manager () const |
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| const MeltHandler< dim > & | get_melt_handler () const |
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| const VolumeOfFluidHandler< dim > & | get_volume_of_fluid_handler () const |
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| const NewtonHandler< dim > & | get_newton_handler () const |
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| const MeshDeformation::MeshDeformationHandler< dim > & | get_mesh_deformation_handler () const |
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| const LateralAveraging< dim > & | get_lateral_averaging () const |
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| const AffineConstraints< double > & | get_current_constraints () const |
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| bool | simulator_is_past_initialization () const |
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| double | get_pressure_scaling () const |
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| bool | pressure_rhs_needs_compatibility_modification () const |
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| bool | model_has_prescribed_stokes_solution () const |
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| TableHandler & | get_statistics_object () const |
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| const Postprocess::Manager< dim > & | get_postprocess_manager () const |
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| unsigned int | n_particle_managers () const |
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| const Particle::Manager< dim > & | get_particle_manager (const unsigned int particle_manager_index) const |
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| Particle::Manager< dim > & | get_particle_manager (const unsigned int particle_manager_index) |
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| bool | is_stokes_matrix_free () |
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| const StokesMatrixFreeHandler< dim > & | get_stokes_matrix_free () const |
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| RotationProperties< dim > | compute_net_angular_momentum (const bool use_constant_density, const LinearAlgebra::BlockVector &solution, const bool limit_to_top_faces=false) const |
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| void | remove_nullspace (LinearAlgebra::BlockVector &solution, LinearAlgebra::BlockVector &distributed_stokes_solution) const |
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| double | normalize_pressure (LinearAlgebra::BlockVector &vector) const |
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| void | denormalize_pressure (const double pressure_adjustment, LinearAlgebra::BlockVector &vector) const |
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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: \(\sigma_y = \frac{6 C \cos(\phi)}{\sqrt{3} (3+\sin(\phi))} + \frac{6 P \sin(\phi)}{\sqrt{3} (3+\sin(\phi))}\), 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.
Public Types inherited from aspect::MaterialModel::Interface< dim >