From fd497b05832718e3f5bbfce28548fffe777d1ac3 Mon Sep 17 00:00:00 2001 From: xingyuanmiao <xingyuanmiao@users.noreply.github.com> Date: Tue, 15 Aug 2017 19:35:20 +0200 Subject: [PATCH] Phasefield (#1895) * added phasefield process and test. * apply clang-format. * added missing integralMeasure for axisymmetric problem. * fixed compilation errors after rebasing. * added unconfined compression ctest. * added missing reference. * renamed specialFunction as calculateDegradedStress. * changed order of stress and strain components. * deleted unused file. * changed IntegrationPointData. * added local results to highlight the deviation. * returned DeltaXCheck true. * modified dimension in ProjectData. * removed second order mesh. * moved history_variable to pushBackState. * added absolute error of displacement for beam3d test. * removed eval() calls in calculation of stress components. * added description for the calculateDegradedStress function. * added types available. * rephrased description. * removed unused C variable. * added model description. * modified types of constitutive relation. * removed CreateLinearElasticPhaseField.h. * added a tag for phasefield_parameters. * added missing phasefield_parameters after PHASE_FIELD. * removed eval() calls in calculation of tensile stress component. * moved process description to PhaseFieldProcess.h. * added description to the undocumented function. * created missing file in documentation. * removed two duplicated files in phasefield process. * removed unused file in documentation. * removed the call to material_model.integrateStress. * removed unused variables. * fixed expression of length scale parameter in documentation. --- Applications/ApplicationsLib/ProjectData.cpp | 21 + .../process/PHASE_FIELD/c_PHASE_FIELD.md | 1 + .../i_constitutive_relation.md | 1 + .../constitutive_relation/t_type.md | 2 + .../i_phasefield_parameters.md | 1 + .../t_crack_length_scale.md | 1 + .../t_crack_resistance.md | 1 + .../phasefield_parameters/t_history_field.md | 1 + .../t_kinetic_coefficient.md | 1 + .../t_residual_stiffness.md | 1 + .../process_variables/i_process_variables.md | 1 + .../process_variables/t_displacement.md | 1 + .../process_variables/t_phasefield.md | 1 + .../process/PHASE_FIELD/t_solid_density.md | 1 + .../PHASE_FIELD/t_specific_body_force.md | 1 + .../SolidModels/LinearElasticIsotropic.h | 13 +- .../LinearElasticIsotropicPhaseField.cpp | 21 + .../LinearElasticIsotropicPhaseField.h | 135 ++++ MaterialLib/SolidModels/PhaseFieldExtension.h | 89 +++ ProcessLib/CMakeLists.txt | 2 + .../PhaseField/CreatePhaseFieldProcess.cpp | 208 ++++++ .../PhaseField/CreatePhaseFieldProcess.h | 28 + ProcessLib/PhaseField/PhaseFieldFEM.h | 653 ++++++++++++++++++ ProcessLib/PhaseField/PhaseFieldProcess.cpp | 20 + ProcessLib/PhaseField/PhaseFieldProcess.h | 244 +++++++ ProcessLib/PhaseField/PhaseFieldProcessData.h | 82 +++ ProcessLib/PhaseField/Tests.cmake | 13 + .../benchmarks/phase-field/Miao_Biot2017.pdf | Bin 0 -> 358898 bytes .../docs/benchmarks/phase-field/beam.png | Bin 0 -> 26999 bytes .../docs/benchmarks/phase-field/beam_d.png | Bin 0 -> 22954 bytes .../docs/benchmarks/phase-field/beam_u.png | Bin 0 -> 25056 bytes .../docs/benchmarks/phase-field/error_u.png | Bin 0 -> 104276 bytes .../docs/benchmarks/phase-field/phasefield.md | 50 ++ 33 files changed, 1592 insertions(+), 2 deletions(-) create mode 100644 Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/c_PHASE_FIELD.md create mode 100644 Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/constitutive_relation/i_constitutive_relation.md create mode 100644 Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/constitutive_relation/t_type.md create mode 100644 Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/phasefield_parameters/i_phasefield_parameters.md create mode 100644 Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/phasefield_parameters/t_crack_length_scale.md create mode 100644 Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/phasefield_parameters/t_crack_resistance.md create mode 100644 Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/phasefield_parameters/t_history_field.md create mode 100644 Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/phasefield_parameters/t_kinetic_coefficient.md create mode 100644 Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/phasefield_parameters/t_residual_stiffness.md create mode 100644 Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/process_variables/i_process_variables.md create mode 100644 Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/process_variables/t_displacement.md create mode 100644 Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/process_variables/t_phasefield.md create mode 100644 Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/t_solid_density.md create mode 100644 Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/t_specific_body_force.md create mode 100644 MaterialLib/SolidModels/LinearElasticIsotropicPhaseField.cpp create mode 100644 MaterialLib/SolidModels/LinearElasticIsotropicPhaseField.h create mode 100644 MaterialLib/SolidModels/PhaseFieldExtension.h create mode 100644 ProcessLib/PhaseField/CreatePhaseFieldProcess.cpp create mode 100644 ProcessLib/PhaseField/CreatePhaseFieldProcess.h create mode 100644 ProcessLib/PhaseField/PhaseFieldFEM.h create mode 100644 ProcessLib/PhaseField/PhaseFieldProcess.cpp create mode 100644 ProcessLib/PhaseField/PhaseFieldProcess.h create mode 100644 ProcessLib/PhaseField/PhaseFieldProcessData.h create mode 100644 ProcessLib/PhaseField/Tests.cmake create mode 100755 web/content/docs/benchmarks/phase-field/Miao_Biot2017.pdf create mode 100644 web/content/docs/benchmarks/phase-field/beam.png create mode 100644 web/content/docs/benchmarks/phase-field/beam_d.png create mode 100644 web/content/docs/benchmarks/phase-field/beam_u.png create mode 100644 web/content/docs/benchmarks/phase-field/error_u.png create mode 100644 web/content/docs/benchmarks/phase-field/phasefield.md diff --git a/Applications/ApplicationsLib/ProjectData.cpp b/Applications/ApplicationsLib/ProjectData.cpp index 34f2d5a6588..d494bdec19b 100644 --- a/Applications/ApplicationsLib/ProjectData.cpp +++ b/Applications/ApplicationsLib/ProjectData.cpp @@ -42,6 +42,7 @@ #include "ProcessLib/LIE/HydroMechanics/CreateHydroMechanicsProcess.h" #include "ProcessLib/LIE/SmallDeformation/CreateSmallDeformationProcess.h" #include "ProcessLib/LiquidFlow/CreateLiquidFlowProcess.h" +#include "ProcessLib/PhaseField/CreatePhaseFieldProcess.h" #include "ProcessLib/RichardsFlow/CreateRichardsFlowProcess.h" #include "ProcessLib/SmallDeformation/CreateSmallDeformationProcess.h" #include "ProcessLib/TES/CreateTESProcess.h" @@ -399,6 +400,26 @@ void ProjectData::parseProcesses(BaseLib::ConfigTree const& processes_config, _process_variables, _parameters, integration_order, process_config); } + else if (type == "PHASE_FIELD") + { + switch (_mesh_vec[0]->getDimension()) + { + case 2: + process = + ProcessLib::PhaseField::createPhaseFieldProcess< + 2>(*_mesh_vec[0], std::move(jacobian_assembler), + _process_variables, _parameters, + integration_order, process_config); + break; + case 3: + process = + ProcessLib::PhaseField::createPhaseFieldProcess< + 3>(*_mesh_vec[0], std::move(jacobian_assembler), + _process_variables, _parameters, + integration_order, process_config); + break; + } + } else if (type == "SMALL_DEFORMATION") { switch (_mesh_vec[0]->getDimension()) diff --git a/Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/c_PHASE_FIELD.md b/Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/c_PHASE_FIELD.md new file mode 100644 index 00000000000..47f149e88d3 --- /dev/null +++ b/Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/c_PHASE_FIELD.md @@ -0,0 +1 @@ +Phase-field modelling for brittle fracture. It is implemented monolithically. \ No newline at end of file diff --git a/Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/constitutive_relation/i_constitutive_relation.md b/Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/constitutive_relation/i_constitutive_relation.md new file mode 100644 index 00000000000..4a2457d3f4c --- /dev/null +++ b/Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/constitutive_relation/i_constitutive_relation.md @@ -0,0 +1 @@ +The constitutive relation for the brittle fracture. \ No newline at end of file diff --git a/Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/constitutive_relation/t_type.md b/Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/constitutive_relation/t_type.md new file mode 100644 index 00000000000..c66714fc4af --- /dev/null +++ b/Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/constitutive_relation/t_type.md @@ -0,0 +1,2 @@ +The type of constitutive relation available. +1. Linear elastic \ No newline at end of file diff --git a/Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/phasefield_parameters/i_phasefield_parameters.md b/Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/phasefield_parameters/i_phasefield_parameters.md new file mode 100644 index 00000000000..fa401a8b3df --- /dev/null +++ b/Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/phasefield_parameters/i_phasefield_parameters.md @@ -0,0 +1 @@ +A tag for phase-field parameters. diff --git a/Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/phasefield_parameters/t_crack_length_scale.md b/Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/phasefield_parameters/t_crack_length_scale.md new file mode 100644 index 00000000000..2d624ad71c9 --- /dev/null +++ b/Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/phasefield_parameters/t_crack_length_scale.md @@ -0,0 +1 @@ +A length-scale parameter which controls the regularisation. \ No newline at end of file diff --git a/Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/phasefield_parameters/t_crack_resistance.md b/Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/phasefield_parameters/t_crack_resistance.md new file mode 100644 index 00000000000..29068c95b59 --- /dev/null +++ b/Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/phasefield_parameters/t_crack_resistance.md @@ -0,0 +1 @@ +The critical Griffith-type fracture energy. \ No newline at end of file diff --git a/Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/phasefield_parameters/t_history_field.md b/Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/phasefield_parameters/t_history_field.md new file mode 100644 index 00000000000..f90cb95d6a2 --- /dev/null +++ b/Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/phasefield_parameters/t_history_field.md @@ -0,0 +1 @@ +A damage-driving history field which is associated with the maximum local tensile strain energy. \ No newline at end of file diff --git a/Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/phasefield_parameters/t_kinetic_coefficient.md b/Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/phasefield_parameters/t_kinetic_coefficient.md new file mode 100644 index 00000000000..ad80c785d41 --- /dev/null +++ b/Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/phasefield_parameters/t_kinetic_coefficient.md @@ -0,0 +1 @@ +A kinetic coefficient which is defined to address rate-dependent cases. \ No newline at end of file diff --git a/Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/phasefield_parameters/t_residual_stiffness.md b/Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/phasefield_parameters/t_residual_stiffness.md new file mode 100644 index 00000000000..33a233ac922 --- /dev/null +++ b/Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/phasefield_parameters/t_residual_stiffness.md @@ -0,0 +1 @@ +A residual stiffness which is used in numerical calculations. diff --git a/Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/process_variables/i_process_variables.md b/Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/process_variables/i_process_variables.md new file mode 100644 index 00000000000..949045cf3b3 --- /dev/null +++ b/Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/process_variables/i_process_variables.md @@ -0,0 +1 @@ +The process variables for displacement and phasefield. diff --git a/Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/process_variables/t_displacement.md b/Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/process_variables/t_displacement.md new file mode 100644 index 00000000000..b6e0f53b6b0 --- /dev/null +++ b/Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/process_variables/t_displacement.md @@ -0,0 +1 @@ +Process variable name of displacement. diff --git a/Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/process_variables/t_phasefield.md b/Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/process_variables/t_phasefield.md new file mode 100644 index 00000000000..cc5910921a5 --- /dev/null +++ b/Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/process_variables/t_phasefield.md @@ -0,0 +1 @@ +Process variable name of phasefield. diff --git a/Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/t_solid_density.md b/Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/t_solid_density.md new file mode 100644 index 00000000000..54bbc62fe6c --- /dev/null +++ b/Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/t_solid_density.md @@ -0,0 +1 @@ +Reference solid density. \ No newline at end of file diff --git a/Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/t_specific_body_force.md b/Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/t_specific_body_force.md new file mode 100644 index 00000000000..dd77e37995b --- /dev/null +++ b/Documentation/ProjectFile/prj/processes/process/PHASE_FIELD/t_specific_body_force.md @@ -0,0 +1 @@ +Specific body forces that are used to apply gravitational forces. A vector of displacement dimension's length. diff --git a/MaterialLib/SolidModels/LinearElasticIsotropic.h b/MaterialLib/SolidModels/LinearElasticIsotropic.h index afa40e8a627..23cadbab639 100644 --- a/MaterialLib/SolidModels/LinearElasticIsotropic.h +++ b/MaterialLib/SolidModels/LinearElasticIsotropic.h @@ -17,7 +17,7 @@ namespace MaterialLib namespace Solids { template <int DisplacementDim> -class LinearElasticIsotropic final : public MechanicsBase<DisplacementDim> +class LinearElasticIsotropic : public MechanicsBase<DisplacementDim> { public: /// Variables specific to the material model @@ -47,6 +47,13 @@ public: (2 * (1 + _poissons_ratio(t, x)[0])); } + /// the bulk modulus. + double bulk_modulus(double const t, X const& x) const + { + return _youngs_modulus(t, x)[0] / + (3 * (1 - 2 * _poissons_ratio(t, x)[0])); + } + private: P const& _youngs_modulus; P const& _poissons_ratio; @@ -101,7 +108,9 @@ public: typename MechanicsBase<DisplacementDim>::MaterialStateVariables const& material_state_variables) override; -private: + MaterialProperties getMaterialProperties() {return _mp;} + +protected: MaterialProperties _mp; }; diff --git a/MaterialLib/SolidModels/LinearElasticIsotropicPhaseField.cpp b/MaterialLib/SolidModels/LinearElasticIsotropicPhaseField.cpp new file mode 100644 index 00000000000..e46fa45017a --- /dev/null +++ b/MaterialLib/SolidModels/LinearElasticIsotropicPhaseField.cpp @@ -0,0 +1,21 @@ +/** + * \copyright + * Copyright (c) 2012-2017, OpenGeoSys Community (http://www.opengeosys.org) + * Distributed under a Modified BSD License. + * See accompanying file LICENSE.txt or + * http://www.opengeosys.org/project/license + * + */ + +#include "LinearElasticIsotropicPhaseField.h" + +namespace MaterialLib +{ +namespace Solids +{ + +template class LinearElasticIsotropicPhaseField<2>; +template class LinearElasticIsotropicPhaseField<3>; + +} // namespace Solids +} // namespace MaterialLib diff --git a/MaterialLib/SolidModels/LinearElasticIsotropicPhaseField.h b/MaterialLib/SolidModels/LinearElasticIsotropicPhaseField.h new file mode 100644 index 00000000000..1a5eeaf141d --- /dev/null +++ b/MaterialLib/SolidModels/LinearElasticIsotropicPhaseField.h @@ -0,0 +1,135 @@ +/** + * \copyright + * Copyright (c) 2012-2017, OpenGeoSys Community (http://www.opengeosys.org) + * Distributed under a Modified BSD License. + * See accompanying file LICENSE.txt or + * http://www.opengeosys.org/project/license + * + */ + +#pragma once + +#include "PhaseFieldExtension.h" +#include "LinearElasticIsotropic.h" +#include "KelvinVector.h" + +namespace MaterialLib +{ +namespace Solids +{ +template <int DisplacementDim> +class LinearElasticIsotropicPhaseField final + : public LinearElasticIsotropic<DisplacementDim>, + public PhaseFieldExtension<DisplacementDim> +{ +public: + static int const KelvinVectorSize = + ProcessLib::KelvinVectorDimensions<DisplacementDim>::value; + using KelvinVector = ProcessLib::KelvinVectorType<DisplacementDim>; + using KelvinMatrix = ProcessLib::KelvinMatrixType<DisplacementDim>; + + explicit LinearElasticIsotropicPhaseField( + typename LinearElasticIsotropic< + DisplacementDim>::MaterialProperties&& material_properties) + : LinearElasticIsotropic<DisplacementDim>(std::move(material_properties)) + { + } + + std::unique_ptr< + typename MechanicsBase<DisplacementDim>::MaterialStateVariables> + createMaterialStateVariables() override + { + return LinearElasticIsotropic< + DisplacementDim>::createMaterialStateVariables(); + } + + boost::optional<std::tuple<KelvinVector, + std::unique_ptr<typename MechanicsBase< + DisplacementDim>::MaterialStateVariables>, + KelvinMatrix>> + integrateStress( + double const t, + ProcessLib::SpatialPosition const& x, + double const dt, + KelvinVector const& eps_prev, + KelvinVector const& eps, + KelvinVector const& sigma_prev, + typename MechanicsBase<DisplacementDim>::MaterialStateVariables const& + material_state_variables) override + { + return LinearElasticIsotropic<DisplacementDim>:: + integrateStress(t, + x, + dt, + eps_prev, + eps, + sigma_prev, + material_state_variables); + } + + /** Decompose the stiffness into tensile and compressive part. + * Judging by the physical observations, compression perpendicular + * to a crack does not cause crack propagation. Thus, + * the phase-field parameter is only involved into the tensile part + * to degrade the elastic strain energy. + */ + bool calculateDegradedStress(double const t, + ProcessLib::SpatialPosition const& x, + KelvinVector const& eps, + double& strain_energy_tensile, + KelvinVector& sigma_tensile, + KelvinVector& sigma_compressive, + KelvinMatrix& C_tensile, + KelvinMatrix& C_compressive, + KelvinVector& sigma_real, + double const degradation) const override + { + using Invariants = + MaterialLib::SolidModels::Invariants<KelvinVectorSize>; + // calculation of deviatoric parts + auto const& P_dev = Invariants::deviatoric_projection; + KelvinVector const epsd_curr = P_dev * eps; + + // Hydrostatic part for the stress and the tangent. + double const eps_curr_trace = Invariants::trace(eps); + + auto const& K = + LinearElasticIsotropic<DisplacementDim>::_mp.bulk_modulus(t, x); + auto const& mu = + LinearElasticIsotropic<DisplacementDim>::_mp.mu(t, x); + + C_tensile = KelvinMatrix::Zero(); + C_compressive = KelvinMatrix::Zero(); + + if (eps_curr_trace >= 0) + { + strain_energy_tensile = + K / 2 * eps_curr_trace * eps_curr_trace + + mu * epsd_curr.transpose() * epsd_curr; + sigma_tensile.noalias() = + K * eps_curr_trace * Invariants::identity2 + + 2 * mu * epsd_curr; + sigma_compressive.noalias() = KelvinVector::Zero(); + C_tensile.template topLeftCorner<3, 3>().setConstant(K); + C_tensile.noalias() += 2 * mu * P_dev * KelvinMatrix::Identity(); + } + else + { + strain_energy_tensile = mu * epsd_curr.transpose() * epsd_curr; + sigma_tensile.noalias() = 2 * mu * epsd_curr; + sigma_compressive.noalias() = + K * eps_curr_trace * Invariants::identity2; + C_tensile.noalias() = 2 * mu * P_dev * KelvinMatrix::Identity(); + C_compressive.template topLeftCorner<3, 3>().setConstant(K); + } + + sigma_real.noalias() = degradation * sigma_tensile + sigma_compressive; + return true; + } +}; + +extern template class LinearElasticIsotropicPhaseField<2>; +extern template class LinearElasticIsotropicPhaseField<3>; + +} // namespace Solids +} // namespace MaterialLib diff --git a/MaterialLib/SolidModels/PhaseFieldExtension.h b/MaterialLib/SolidModels/PhaseFieldExtension.h new file mode 100644 index 00000000000..77bb5a40027 --- /dev/null +++ b/MaterialLib/SolidModels/PhaseFieldExtension.h @@ -0,0 +1,89 @@ +/** + * \file + * \copyright + * Copyright (c) 2012-2017, OpenGeoSys Community (http://www.opengeosys.org) + * Distributed under a Modified BSD License. + * See accompanying file LICENSE.txt or + * http://www.opengeosys.org/project/license + * + */ + +#pragma once + +#include "ProcessLib/Deformation/BMatrixPolicy.h" +#include "ProcessLib/Parameter/SpatialPosition.h" +#include "MechanicsBase.h" + +namespace MaterialLib +{ +namespace Solids +{ + +template <int DisplacementDim> +struct PhaseFieldExtension : public MechanicsBase<DisplacementDim> +{ + using KelvinVector = ProcessLib::KelvinVectorType<DisplacementDim>; + using KelvinMatrix = ProcessLib::KelvinMatrixType<DisplacementDim>; + virtual bool calculateDegradedStress(double const t, + ProcessLib::SpatialPosition const& x, + KelvinVector const& eps, + double& strain_energy_tensile, + KelvinVector& sigma_tensile, + KelvinVector& sigma_compressive, + KelvinMatrix& C_tensile, + KelvinMatrix& C_compressive, + KelvinVector& sigma_real, + double const degradation) const = 0; + + /// Dynamic size Kelvin vector and matrix wrapper for the polymorphic + /// constitutive relation compute function. + bool calculateDegradedStress( + double const t, + ProcessLib::SpatialPosition const& x, + Eigen::Matrix<double, Eigen::Dynamic, 1> const& eps, + double& strain_energy_tensile, + Eigen::Matrix<double, Eigen::Dynamic, 1>& sigma_tensile, + Eigen::Matrix<double, Eigen::Dynamic, 1>& sigma_compressive, + Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor>& + C_tensile, + Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor>& + C_compressive, + Eigen::Matrix<double, Eigen::Dynamic, 1>& sigma_real, + double const degradation) const + { + // TODO Avoid copies of data: + // Using MatrixBase<Derived> not possible because template functions + // cannot be virtual. Maybe there is a workaround for this. Using + // Map<Matrix<double, ...>> makes the interface (for the material model + // implementation) unnecessary difficult. + KelvinVector const eps_{eps}; + KelvinVector sigma_tensile_{sigma_tensile}; + KelvinVector sigma_compressive_{sigma_compressive}; + KelvinMatrix C_tensile_{C_tensile}; + KelvinMatrix C_compressive_{C_compressive}; + KelvinVector sigma_real_{sigma_real}; + + bool const result = calculateDegradedStress(t, + x, + eps_, + strain_energy_tensile, + sigma_tensile_, + sigma_compressive_, + C_tensile_, + C_compressive_, + sigma_real_, + degradation); + + sigma_tensile = sigma_tensile_; + sigma_compressive = sigma_compressive_; + C_tensile = C_tensile_; + C_compressive = C_compressive_; + sigma_real = sigma_real_; + return result; + } + + virtual ~PhaseFieldExtension() = default; +}; + +} // namespace Solids +} // namespace MaterialLib diff --git a/ProcessLib/CMakeLists.txt b/ProcessLib/CMakeLists.txt index e64cf8f6782..f73380f5ba8 100644 --- a/ProcessLib/CMakeLists.txt +++ b/ProcessLib/CMakeLists.txt @@ -17,6 +17,7 @@ APPEND_SOURCE_FILES(SOURCES LIE/SmallDeformation) APPEND_SOURCE_FILES(SOURCES LIE/SmallDeformation/LocalAssembler) APPEND_SOURCE_FILES(SOURCES LiquidFlow) APPEND_SOURCE_FILES(SOURCES Parameter) +APPEND_SOURCE_FILES(SOURCES PhaseField) APPEND_SOURCE_FILES(SOURCES RichardsFlow) APPEND_SOURCE_FILES(SOURCES SmallDeformation) APPEND_SOURCE_FILES(SOURCES TES) @@ -58,6 +59,7 @@ include(HydroMechanics/Tests.cmake) include(LIE/HydroMechanics/Tests.cmake) include(LIE/SmallDeformation/Tests.cmake) include(LiquidFlow/Tests.cmake) +include(PhaseField/Tests.cmake) include(RichardsFlow/Tests.cmake) include(SmallDeformation/Tests.cmake) include(TES/Tests.cmake) diff --git a/ProcessLib/PhaseField/CreatePhaseFieldProcess.cpp b/ProcessLib/PhaseField/CreatePhaseFieldProcess.cpp new file mode 100644 index 00000000000..0dcadcb9de6 --- /dev/null +++ b/ProcessLib/PhaseField/CreatePhaseFieldProcess.cpp @@ -0,0 +1,208 @@ +/** + * \copyright + * Copyright (c) 2012-2017, OpenGeoSys Community (http://www.opengeosys.org) + * Distributed under a Modified BSD License. + * See accompanying file LICENSE.txt or + * http://www.opengeosys.org/project/license + * + */ + +#include "CreatePhaseFieldProcess.h" + +#include <cassert> + +#include "MaterialLib/SolidModels/CreateLinearElasticIsotropic.h" +#include "MaterialLib/SolidModels/LinearElasticIsotropic.h" +#include "ProcessLib/Utils/ParseSecondaryVariables.h" + +#include "PhaseFieldProcess.h" +#include "PhaseFieldProcessData.h" + +namespace ProcessLib +{ +namespace PhaseField +{ +template <int DisplacementDim> +class PhaseFieldProcess; + +extern template class PhaseFieldProcess<2>; +extern template class PhaseFieldProcess<3>; + +template <int DisplacementDim> +std::unique_ptr<Process> createPhaseFieldProcess( + MeshLib::Mesh& mesh, + std::unique_ptr<ProcessLib::AbstractJacobianAssembler>&& jacobian_assembler, + std::vector<ProcessVariable> const& variables, + std::vector<std::unique_ptr<ParameterBase>> const& parameters, + unsigned const integration_order, + BaseLib::ConfigTree const& config) +{ + //! \ogs_file_param{prj__processes__process__type} + config.checkConfigParameter("type", "PHASE_FIELD"); + DBUG("Create PhaseFieldProcess."); + + // Process variable. + + //! \ogs_file_param{prj__processes__process__PHASE_FIELD__process_variables} + auto const pv_config = config.getConfigSubtree("process_variables"); + + auto process_variables = findProcessVariables( + variables, pv_config, + {//! \ogs_file_param_special{prj__processes__process__PHASE_FIELD__process_variables__phasefield} + "phasefield", + //! \ogs_file_param_special{prj__processes__process__PHASE_FIELD__process_variables__displacement} + "displacement"}); + + DBUG("Associate displacement with process variable \'%s\'.", + process_variables[1].get().getName().c_str()); + + if (process_variables[1].get().getNumberOfComponents() != DisplacementDim) + { + OGS_FATAL( + "Number of components of the process variable '%s' is different " + "from the displacement dimension: got %d, expected %d", + process_variables[1].get().getName().c_str(), + process_variables[1].get().getNumberOfComponents(), + DisplacementDim); + } + + DBUG("Associate phase field with process variable \'%s\'.", + process_variables[0].get().getName().c_str()); + if (process_variables[0].get().getNumberOfComponents() != 1) + { + OGS_FATAL( + "Phase field process variable '%s' is not a scalar variable but has " + "%d components.", + process_variables[0].get().getName().c_str(), + process_variables[0].get().getNumberOfComponents(), + DisplacementDim); + } + + // Constitutive relation. + // read type; + auto const constitutive_relation_config = + //! \ogs_file_param{prj__processes__process__PHASE_FIELD__constitutive_relation} + config.getConfigSubtree("constitutive_relation"); + + auto const phasefield_parameters_config = + //! \ogs_file_param{prj__processes__process__PHASE_FIELD__phasefield_parameters} + config.getConfigSubtree("phasefield_parameters"); + + auto const type = + //! \ogs_file_param{prj__processes__process__PHASE_FIELD__constitutive_relation__type} + constitutive_relation_config.peekConfigParameter<std::string>("type"); + + std::unique_ptr<MaterialLib::Solids::PhaseFieldExtension<DisplacementDim>> + material = nullptr; + if (type == "LinearElasticIsotropic") + { + auto elastic_model = MaterialLib::Solids::createLinearElasticIsotropic< + DisplacementDim>(parameters, constitutive_relation_config); + material = + std::make_unique<MaterialLib::Solids::LinearElasticIsotropicPhaseField< + DisplacementDim>>(std::move(elastic_model->getMaterialProperties())); + } + else + { + OGS_FATAL( + "Cannot construct constitutive relation of given type \'%s\'.", + type.c_str()); + } + + // Residual stiffness + auto& residual_stiffness = findParameter<double>( + phasefield_parameters_config, + //! \ogs_file_param_special{prj__processes__process__PHASE_FIELD__phasefield_parameters__residual_stiffness} + "residual_stiffness", parameters, 1); + DBUG("Use \'%s\' as residual stiffness.", residual_stiffness.name.c_str()); + + // Crack resistance + auto& crack_resistance = findParameter<double>( + phasefield_parameters_config, + //! \ogs_file_param_special{prj__processes__process__PHASE_FIELD__phasefield_parameters__crack_resistance} + "crack_resistance", parameters, 1); + DBUG("Use \'%s\' as crack resistance.", crack_resistance.name.c_str()); + + // Crack length scale + auto& crack_length_scale = findParameter<double>( + phasefield_parameters_config, + //! \ogs_file_param_special{prj__processes__process__PHASE_FIELD__phasefield_parameters__crack_length_scale} + "crack_length_scale", parameters, 1); + DBUG("Use \'%s\' as crack length scale.", crack_length_scale.name.c_str()); + + // Kinetic coefficient + auto& kinetic_coefficient = findParameter<double>( + phasefield_parameters_config, + //! \ogs_file_param_special{prj__processes__process__PHASE_FIELD__phasefield_parameters__kinetic_coefficient} + "kinetic_coefficient", parameters, 1); + DBUG("Use \'%s\' as kinetic coefficient.", + kinetic_coefficient.name.c_str()); + + // Solid density + auto& solid_density = findParameter<double>( + config, + //! \ogs_file_param_special{prj__processes__process__PHASE_FIELD__solid_density} + "solid_density", parameters, 1); + DBUG("Use \'%s\' as solid density parameter.", solid_density.name.c_str()); + + // History field + auto& history_field = findParameter<double>( + phasefield_parameters_config, + //! \ogs_file_param_special{prj__processes__process__PHASE_FIELD__phasefield_parameters__history_field} + "history_field", parameters, 1); + DBUG("Use \'%s\' as history field.", history_field.name.c_str()); + + // Specific body force + Eigen::Matrix<double, DisplacementDim, 1> specific_body_force; + { + std::vector<double> const b = + //! \ogs_file_param{prj__processes__process__PHASE_FIELD__specific_body_force} + config.getConfigParameter<std::vector<double>>( + "specific_body_force"); + if (specific_body_force.size() != DisplacementDim) + OGS_FATAL( + "The size of the specific body force vector does not match the " + "displacement dimension. Vector size is %d, displacement " + "dimension is %d", + specific_body_force.size(), DisplacementDim); + + std::copy_n(b.data(), b.size(), specific_body_force.data()); + } + + PhaseFieldProcessData<DisplacementDim> process_data{ + std::move(material), residual_stiffness, crack_resistance, + crack_length_scale, kinetic_coefficient, solid_density, + history_field, specific_body_force}; + + SecondaryVariableCollection secondary_variables; + + NumLib::NamedFunctionCaller named_function_caller( + {"PhaseField_displacement"}); + + ProcessLib::parseSecondaryVariables(config, secondary_variables, + named_function_caller); + + return std::make_unique<PhaseFieldProcess<DisplacementDim>>( + mesh, std::move(jacobian_assembler), parameters, integration_order, + std::move(process_variables), std::move(process_data), + std::move(secondary_variables), std::move(named_function_caller)); +} + +template std::unique_ptr<Process> createPhaseFieldProcess<2>( + MeshLib::Mesh& mesh, + std::unique_ptr<ProcessLib::AbstractJacobianAssembler>&& jacobian_assembler, + std::vector<ProcessVariable> const& variables, + std::vector<std::unique_ptr<ParameterBase>> const& parameters, + unsigned const integration_order, + BaseLib::ConfigTree const& config); + +template std::unique_ptr<Process> createPhaseFieldProcess<3>( + MeshLib::Mesh& mesh, + std::unique_ptr<ProcessLib::AbstractJacobianAssembler>&& jacobian_assembler, + std::vector<ProcessVariable> const& variables, + std::vector<std::unique_ptr<ParameterBase>> const& parameters, + unsigned const integration_order, + BaseLib::ConfigTree const& config); + +} // namespace PhaseField +} // namespace ProcessLib diff --git a/ProcessLib/PhaseField/CreatePhaseFieldProcess.h b/ProcessLib/PhaseField/CreatePhaseFieldProcess.h new file mode 100644 index 00000000000..770b8e7bd22 --- /dev/null +++ b/ProcessLib/PhaseField/CreatePhaseFieldProcess.h @@ -0,0 +1,28 @@ +/** + * \copyright + * Copyright (c) 2012-2017, OpenGeoSys Community (http://www.opengeosys.org) + * Distributed under a Modified BSD License. + * See accompanying file LICENSE.txt or + * http://www.opengeosys.org/project/license + * + */ + +#pragma once + +#include "ProcessLib/Process.h" + +namespace ProcessLib +{ +namespace PhaseField +{ +template <int DisplacementDim> +std::unique_ptr<Process> createPhaseFieldProcess( + MeshLib::Mesh& mesh, + std::unique_ptr<ProcessLib::AbstractJacobianAssembler>&& jacobian_assembler, + std::vector<ProcessVariable> const& variables, + std::vector<std::unique_ptr<ParameterBase>> const& parameters, + unsigned const integration_order, + BaseLib::ConfigTree const& config); + +} // namespace PhaseField +} // namespace ProcessLib diff --git a/ProcessLib/PhaseField/PhaseFieldFEM.h b/ProcessLib/PhaseField/PhaseFieldFEM.h new file mode 100644 index 00000000000..f3be2299be4 --- /dev/null +++ b/ProcessLib/PhaseField/PhaseFieldFEM.h @@ -0,0 +1,653 @@ +/** + * \copyright + * Copyright (c) 2012-2017, OpenGeoSys Community (http://www.opengeosys.org) + * Distributed under a Modified BSD License. + * See accompanying file LICENSE.txt or + * http://www.opengeosys.org/project/license + * + */ + +#pragma once + +#include <memory> +#include <vector> + +#include "MaterialLib/SolidModels/KelvinVector.h" +#include "MaterialLib/SolidModels/LinearElasticIsotropicPhaseField.h" +#include "MaterialLib/SolidModels/LinearElasticIsotropic.h" +#include "MathLib/LinAlg/Eigen/EigenMapTools.h" +#include "NumLib/Extrapolation/ExtrapolatableElement.h" +#include "NumLib/Fem/FiniteElement/TemplateIsoparametric.h" +#include "NumLib/Fem/ShapeMatrixPolicy.h" +#include "NumLib/Function/Interpolation.h" +#include "ProcessLib/Deformation/BMatrixPolicy.h" +#include "ProcessLib/Deformation/LinearBMatrix.h" +#include "ProcessLib/LocalAssemblerInterface.h" +#include "ProcessLib/LocalAssemblerTraits.h" +#include "ProcessLib/Parameter/Parameter.h" +#include "ProcessLib/Utils/InitShapeMatrices.h" + +#include "PhaseFieldProcessData.h" + +namespace ProcessLib +{ +namespace PhaseField +{ +template <typename BMatricesType, typename ShapeMatrixType, int DisplacementDim> +struct IntegrationPointData final +{ + explicit IntegrationPointData( + MaterialLib::Solids::MechanicsBase<DisplacementDim>& solid_material) + : solid_material(solid_material), + material_state_variables( + solid_material.createMaterialStateVariables()) + { + } + + typename ShapeMatrixType::NodalRowVectorType N; + typename ShapeMatrixType::GlobalDimNodalMatrixType dNdx; + + typename BMatricesType::KelvinVectorType eps, eps_prev; + + typename BMatricesType::KelvinVectorType sigma_tensile, sigma_compressive, + sigma_real_prev, sigma_real; + double strain_energy_tensile; + + MaterialLib::Solids::MechanicsBase<DisplacementDim>& solid_material; + std::unique_ptr<typename MaterialLib::Solids::MechanicsBase< + DisplacementDim>::MaterialStateVariables> material_state_variables; + + typename BMatricesType::KelvinMatrixType C_tensile, C_compressive; + double integration_weight; + double history_variable; + double history_variable_prev; + + void pushBackState() + { + if (history_variable_prev < + history_variable) + { + history_variable_prev = + history_variable; + } + eps_prev = eps; + sigma_real_prev = sigma_real; + material_state_variables->pushBackState(); + } + + template <typename DisplacementVectorType> + void updateConstitutiveRelation( + double const t, + SpatialPosition const& x_position, + double const dt, + DisplacementVectorType const& /*u*/, + double const degradation) + { + static_cast<MaterialLib::Solids::PhaseFieldExtension<DisplacementDim>&>( + solid_material) + .calculateDegradedStress(t, x_position, eps, strain_energy_tensile, + sigma_tensile, sigma_compressive, C_tensile, + C_compressive, sigma_real, degradation); + } + +}; + +/// Used by for extrapolation of the integration point values. It is ordered +/// (and stored) by integration points. +template <typename ShapeMatrixType> +struct SecondaryData +{ + std::vector<ShapeMatrixType, Eigen::aligned_allocator<ShapeMatrixType>> N; +}; + +struct PhaseFieldLocalAssemblerInterface + : public ProcessLib::LocalAssemblerInterface, + public NumLib::ExtrapolatableElement +{ + virtual std::vector<double> const& getIntPtSigmaXX( + const double /*t*/, + GlobalVector const& /*current_solution*/, + NumLib::LocalToGlobalIndexMap const& /*dof_table*/, + std::vector<double>& cache) const = 0; + + virtual std::vector<double> const& getIntPtSigmaYY( + const double /*t*/, + GlobalVector const& /*current_solution*/, + NumLib::LocalToGlobalIndexMap const& /*dof_table*/, + std::vector<double>& cache) const = 0; + + virtual std::vector<double> const& getIntPtSigmaZZ( + const double /*t*/, + GlobalVector const& /*current_solution*/, + NumLib::LocalToGlobalIndexMap const& /*dof_table*/, + std::vector<double>& cache) const = 0; + + virtual std::vector<double> const& getIntPtSigmaXY( + const double /*t*/, + GlobalVector const& /*current_solution*/, + NumLib::LocalToGlobalIndexMap const& /*dof_table*/, + std::vector<double>& cache) const = 0; + + virtual std::vector<double> const& getIntPtSigmaXZ( + const double /*t*/, + GlobalVector const& /*current_solution*/, + NumLib::LocalToGlobalIndexMap const& /*dof_table*/, + std::vector<double>& cache) const = 0; + + virtual std::vector<double> const& getIntPtSigmaYZ( + const double /*t*/, + GlobalVector const& /*current_solution*/, + NumLib::LocalToGlobalIndexMap const& /*dof_table*/, + std::vector<double>& cache) const = 0; + + virtual std::vector<double> const& getIntPtEpsilonXX( + const double /*t*/, + GlobalVector const& /*current_solution*/, + NumLib::LocalToGlobalIndexMap const& /*dof_table*/, + std::vector<double>& cache) const = 0; + + virtual std::vector<double> const& getIntPtEpsilonYY( + const double /*t*/, + GlobalVector const& /*current_solution*/, + NumLib::LocalToGlobalIndexMap const& /*dof_table*/, + std::vector<double>& cache) const = 0; + + virtual std::vector<double> const& getIntPtEpsilonZZ( + const double /*t*/, + GlobalVector const& /*current_solution*/, + NumLib::LocalToGlobalIndexMap const& /*dof_table*/, + std::vector<double>& cache) const = 0; + + virtual std::vector<double> const& getIntPtEpsilonXY( + const double /*t*/, + GlobalVector const& /*current_solution*/, + NumLib::LocalToGlobalIndexMap const& /*dof_table*/, + std::vector<double>& cache) const = 0; + + virtual std::vector<double> const& getIntPtEpsilonXZ( + const double /*t*/, + GlobalVector const& /*current_solution*/, + NumLib::LocalToGlobalIndexMap const& /*dof_table*/, + std::vector<double>& cache) const = 0; + + virtual std::vector<double> const& getIntPtEpsilonYZ( + const double /*t*/, + GlobalVector const& /*current_solution*/, + NumLib::LocalToGlobalIndexMap const& /*dof_table*/, + std::vector<double>& cache) const = 0; +}; + +template <typename ShapeFunction, typename IntegrationMethod, + int DisplacementDim> +class PhaseFieldLocalAssembler : public PhaseFieldLocalAssemblerInterface +{ +public: + using ShapeMatricesType = + ShapeMatrixPolicyType<ShapeFunction, DisplacementDim>; + + // Types for displacement. + // (Higher order elements = ShapeFunction). + using ShapeMatrices = typename ShapeMatricesType::ShapeMatrices; + using BMatricesType = BMatrixPolicyType<ShapeFunction, DisplacementDim>; + + using NodalForceVectorType = typename BMatricesType::NodalForceVectorType; + using RhsVector = typename ShapeMatricesType::template VectorType< + ShapeFunction::NPOINTS + ShapeFunction::NPOINTS * DisplacementDim>; + using JacobianMatrix = typename ShapeMatricesType::template MatrixType< + ShapeFunction::NPOINTS + ShapeFunction::NPOINTS * DisplacementDim, + ShapeFunction::NPOINTS + ShapeFunction::NPOINTS * DisplacementDim>; + + PhaseFieldLocalAssembler(PhaseFieldLocalAssembler const&) = delete; + PhaseFieldLocalAssembler(PhaseFieldLocalAssembler&&) = delete; + + PhaseFieldLocalAssembler( + MeshLib::Element const& e, + std::size_t const /*local_matrix_size*/, + bool const is_axially_symmetric, + unsigned const integration_order, + PhaseFieldProcessData<DisplacementDim>& process_data) + : _process_data(process_data), + _integration_method(integration_order), + _element(e), + _is_axially_symmetric(is_axially_symmetric) + { + unsigned const n_integration_points = + _integration_method.getNumberOfPoints(); + + _ip_data.reserve(n_integration_points); + _secondary_data.N.resize(n_integration_points); + + auto const shape_matrices = + initShapeMatrices<ShapeFunction, ShapeMatricesType, + IntegrationMethod, DisplacementDim>( + e, is_axially_symmetric, _integration_method); + + SpatialPosition x_position; + x_position.setElementID(_element.getID()); + + for (unsigned ip = 0; ip < n_integration_points; ip++) + { + // displacement (subscript u) + _ip_data.emplace_back(*_process_data.material); + auto& ip_data = _ip_data[ip]; + ip_data.integration_weight = + _integration_method.getWeightedPoint(ip).getWeight() * + shape_matrices[ip].integralMeasure * shape_matrices[ip].detJ; + + ip_data.eps.setZero(kelvin_vector_size); + ip_data.eps_prev.resize(kelvin_vector_size); + ip_data.C_tensile.setZero(kelvin_vector_size, kelvin_vector_size); + ip_data.C_compressive.setZero(kelvin_vector_size, + kelvin_vector_size); + ip_data.sigma_tensile.setZero(kelvin_vector_size); + ip_data.sigma_compressive.setZero(kelvin_vector_size); + ip_data.history_variable = + process_data.history_field(0, x_position)[0]; + ip_data.history_variable_prev = + process_data.history_field(0, x_position)[0]; + ip_data.sigma_real.setZero(kelvin_vector_size); + + ip_data.N = shape_matrices[ip].N; + ip_data.dNdx = shape_matrices[ip].dNdx; + + _secondary_data.N[ip] = shape_matrices[ip].N; + } + } + + void assemble(double const /*t*/, std::vector<double> const& /*local_x*/, + std::vector<double>& /*local_M_data*/, + std::vector<double>& /*local_K_data*/, + std::vector<double>& /*local_rhs_data*/) override + { + OGS_FATAL( + "PhaseFieldLocalAssembler: assembly without jacobian is not " + "implemented."); + } + + void assembleWithJacobian(double const t, + std::vector<double> const& local_x, + std::vector<double> const& local_xdot, + const double /*dxdot_dx*/, const double /*dx_dx*/, + std::vector<double>& /*local_M_data*/, + std::vector<double>& /*local_K_data*/, + std::vector<double>& local_rhs_data, + std::vector<double>& local_Jac_data) override + { + auto const local_matrix_size = local_x.size(); + assert(local_matrix_size == phasefield_size + displacement_size); + + auto d = Eigen::Map<typename ShapeMatricesType::template VectorType< + phasefield_size> const>(local_x.data() + phasefield_index, + phasefield_size); + + auto u = Eigen::Map<typename ShapeMatricesType::template VectorType< + displacement_size> const>(local_x.data() + displacement_index, + displacement_size); + + auto d_dot = Eigen::Map<typename ShapeMatricesType::template VectorType< + phasefield_size> const>(local_xdot.data() + phasefield_index, + phasefield_size); + + auto local_Jac = MathLib::createZeroedMatrix<JacobianMatrix>( + local_Jac_data, local_matrix_size, local_matrix_size); + + auto local_rhs = MathLib::createZeroedVector<RhsVector>( + local_rhs_data, local_matrix_size); + + typename ShapeMatricesType::template MatrixType<displacement_size, + phasefield_size> Kud; + Kud.setZero(displacement_size, phasefield_size); + + typename ShapeMatricesType::template MatrixType<phasefield_size, + displacement_size> Kdu; + Kdu.setZero(phasefield_size, displacement_size); + + typename ShapeMatricesType::NodalMatrixType Kdd; + Kdd.setZero(phasefield_size, phasefield_size); + + typename ShapeMatricesType::NodalMatrixType Ddd; + Ddd.setZero(phasefield_size, phasefield_size); + + double const& dt = _process_data.dt; + + SpatialPosition x_position; + x_position.setElementID(_element.getID()); + + unsigned const n_integration_points = + _integration_method.getNumberOfPoints(); + for (unsigned ip = 0; ip < n_integration_points; ip++) + { + x_position.setIntegrationPoint(ip); + auto const& w = _ip_data[ip].integration_weight; + + auto const& dNdx = _ip_data[ip].dNdx; + auto const& N = _ip_data[ip].N; + + auto const x_coord = + interpolateXCoordinate<ShapeFunction, ShapeMatricesType>( + _element, N); + auto const& B = LinearBMatrix::computeBMatrix< + DisplacementDim, ShapeFunction::NPOINTS, + typename BMatricesType::BMatrixType>(dNdx, N, x_coord, + _is_axially_symmetric); + + auto const& C_tensile = _ip_data[ip].C_tensile; + auto const& C_compressive = _ip_data[ip].C_compressive; + + auto& eps = _ip_data[ip].eps; + auto const& strain_energy_tensile = + _ip_data[ip].strain_energy_tensile; + auto const& sigma_tensile = _ip_data[ip].sigma_tensile; + + auto& history_variable = _ip_data[ip].history_variable; + auto& history_variable_prev = _ip_data[ip].history_variable_prev; + + auto const& sigma_real = _ip_data[ip].sigma_real; + + // Kdd_1 defines one term which both used in Kdd and local_rhs for + // phase field + double const gc = _process_data.crack_resistance(t, x_position)[0]; + double const ls = + _process_data.crack_length_scale(t, x_position)[0]; + typename ShapeMatricesType::NodalMatrixType const Kdd_1 = + dNdx.transpose() * 2 * gc * ls * dNdx; + + // + // displacement equation, displacement part + // + double const k = _process_data.residual_stiffness(t, x_position)[0]; + double const d_ip = N.dot(d); + double const degradation = d_ip * d_ip * (1 - k) + k; + eps.noalias() = B * u; + _ip_data[ip].updateConstitutiveRelation(t, x_position, dt, u, + degradation); + + local_Jac.template block<displacement_size, displacement_size>( + displacement_index, displacement_index) + .noalias() += B.transpose() * + (degradation * C_tensile + C_compressive) * B * w; + + typename ShapeMatricesType::template MatrixType<DisplacementDim, + displacement_size> + N_u = ShapeMatricesType::template MatrixType< + DisplacementDim, + displacement_size>::Zero(DisplacementDim, + displacement_size); + + for (int i = 0; i < DisplacementDim; ++i) + N_u.template block<1, displacement_size / DisplacementDim>( + i, i * displacement_size / DisplacementDim) + .noalias() = N; + + auto const rho_sr = _process_data.solid_density(t, x_position)[0]; + auto const& b = _process_data.specific_body_force; + local_rhs.template block<displacement_size, 1>(displacement_index, 0) + .noalias() -= + (B.transpose() * sigma_real - N_u.transpose() * rho_sr * b) * w; + + // + // displacement equation, phasefield part + // + Kud.noalias() += B.transpose() * 2 * d_ip * sigma_tensile * N * w; + + double const d_dot_ip = N.dot(d_dot); + + if (history_variable_prev < strain_energy_tensile) + { + history_variable = strain_energy_tensile; + Kdu.noalias() = Kud.transpose(); + } + else + { + history_variable = history_variable_prev; + } + + // + // phasefield equation, phasefield part. + // + Kdd.noalias() += (Kdd_1 + N.transpose() * 2 * history_variable * N + + N.transpose() * 0.5 * gc / ls * N) * + w; + double const M = + _process_data.kinetic_coefficient(t, x_position)[0]; + local_rhs.template segment<phasefield_size>(phasefield_index) + .noalias() -= (N.transpose() * d_dot_ip / M + Kdd_1 * d + + N.transpose() * d_ip * 2 * history_variable - + N.transpose() * 0.5 * gc / ls * (1 - d_ip)) * + w; + + Ddd.noalias() += N.transpose() / M * N * w; + } + // displacement equation, phasefield part + local_Jac.template block<displacement_size, phasefield_size>( + displacement_index, phasefield_index) + .noalias() += Kud; + + // phasefield equation, phasefield part. + local_Jac.template block<phasefield_size, phasefield_size>( + phasefield_index, phasefield_index) + .noalias() += Kdd + Ddd / dt; + + // phasefield equation, displacement part. + local_Jac.template block<phasefield_size, displacement_size>( + phasefield_index, displacement_index) + .noalias() += Kdu; + + } + + void preTimestepConcrete(std::vector<double> const& /*local_x*/, + double const /*t*/, + double const /*delta_t*/) override + { + unsigned const n_integration_points = + _integration_method.getNumberOfPoints(); + + for (unsigned ip = 0; ip < n_integration_points; ip++) + { + _ip_data[ip].pushBackState(); + } + } + + Eigen::Map<const Eigen::RowVectorXd> getShapeMatrix( + const unsigned integration_point) const override + { + auto const& N = _secondary_data.N[integration_point]; + + // assumes N is stored contiguously in memory + return Eigen::Map<const Eigen::RowVectorXd>(N.data(), N.size()); + } + + std::vector<double> const& getIntPtSigmaXX( + const double /*t*/, + GlobalVector const& /*current_solution*/, + NumLib::LocalToGlobalIndexMap const& /*dof_table*/, + std::vector<double>& cache) const override + { + return getIntPtSigma(cache, 0); + } + + std::vector<double> const& getIntPtSigmaYY( + const double /*t*/, + GlobalVector const& /*current_solution*/, + NumLib::LocalToGlobalIndexMap const& /*dof_table*/, + std::vector<double>& cache) const override + { + return getIntPtSigma(cache, 1); + } + + std::vector<double> const& getIntPtSigmaZZ( + const double /*t*/, + GlobalVector const& /*current_solution*/, + NumLib::LocalToGlobalIndexMap const& /*dof_table*/, + std::vector<double>& cache) const override + { + return getIntPtSigma(cache, 2); + } + + std::vector<double> const& getIntPtSigmaXY( + const double /*t*/, + GlobalVector const& /*current_solution*/, + NumLib::LocalToGlobalIndexMap const& /*dof_table*/, + std::vector<double>& cache) const override + { + return getIntPtSigma(cache, 3); + } + + std::vector<double> const& getIntPtSigmaYZ( + const double /*t*/, + GlobalVector const& /*current_solution*/, + NumLib::LocalToGlobalIndexMap const& /*dof_table*/, + std::vector<double>& cache) const override + { + assert(DisplacementDim == 3); + return getIntPtSigma(cache, 4); + } + + std::vector<double> const& getIntPtSigmaXZ( + const double /*t*/, + GlobalVector const& /*current_solution*/, + NumLib::LocalToGlobalIndexMap const& /*dof_table*/, + std::vector<double>& cache) const override + { + assert(DisplacementDim == 3); + return getIntPtSigma(cache, 5); + } + + std::vector<double> const& getIntPtEpsilonXX( + const double /*t*/, + GlobalVector const& /*current_solution*/, + NumLib::LocalToGlobalIndexMap const& /*dof_table*/, + std::vector<double>& cache) const override + { + return getIntPtEpsilon(cache, 0); + } + + std::vector<double> const& getIntPtEpsilonYY( + const double /*t*/, + GlobalVector const& /*current_solution*/, + NumLib::LocalToGlobalIndexMap const& /*dof_table*/, + std::vector<double>& cache) const override + { + return getIntPtEpsilon(cache, 1); + } + + std::vector<double> const& getIntPtEpsilonZZ( + const double /*t*/, + GlobalVector const& /*current_solution*/, + NumLib::LocalToGlobalIndexMap const& /*dof_table*/, + std::vector<double>& cache) const override + { + return getIntPtEpsilon(cache, 2); + } + + std::vector<double> const& getIntPtEpsilonXY( + const double /*t*/, + GlobalVector const& /*current_solution*/, + NumLib::LocalToGlobalIndexMap const& /*dof_table*/, + std::vector<double>& cache) const override + { + return getIntPtEpsilon(cache, 3); + } + + std::vector<double> const& getIntPtEpsilonYZ( + const double /*t*/, + GlobalVector const& /*current_solution*/, + NumLib::LocalToGlobalIndexMap const& /*dof_table*/, + std::vector<double>& cache) const override + { + assert(DisplacementDim == 3); + return getIntPtEpsilon(cache, 4); + } + + std::vector<double> const& getIntPtEpsilonXZ( + const double /*t*/, + GlobalVector const& /*current_solution*/, + NumLib::LocalToGlobalIndexMap const& /*dof_table*/, + std::vector<double>& cache) const override + { + assert(DisplacementDim == 3); + return getIntPtEpsilon(cache, 5); + } + +private: + std::vector<double> const& getIntPtSigma(std::vector<double>& cache, + std::size_t const component) const + { + cache.clear(); + cache.reserve(_ip_data.size()); + + for (auto const& ip_data : _ip_data) + { + if (component < 3) // xx, yy, zz components + cache.push_back(ip_data.sigma_real[component]); + else // mixed xy, yz, xz components + cache.push_back(ip_data.sigma_real[component] / std::sqrt(2)); + } + + return cache; + } + + std::vector<double> const& getIntPtEpsilon( + std::vector<double>& cache, std::size_t const component) const + { + cache.clear(); + cache.reserve(_ip_data.size()); + + for (auto const& ip_data : _ip_data) + { + if (component < 3) // xx, yy, zz components + cache.push_back(ip_data.eps[component]); + else // mixed xy, yz, xz components + cache.push_back(ip_data.eps[component] / std::sqrt(2)); + } + + return cache; + } + + PhaseFieldProcessData<DisplacementDim>& _process_data; + + std::vector< + IntegrationPointData<BMatricesType, ShapeMatricesType, DisplacementDim>, + Eigen::aligned_allocator<IntegrationPointData< + BMatricesType, ShapeMatricesType, DisplacementDim>>> + _ip_data; + + IntegrationMethod _integration_method; + MeshLib::Element const& _element; + bool const _is_axially_symmetric; + SecondaryData<typename ShapeMatrices::ShapeType> _secondary_data; + + static const int phasefield_index = 0; + static const int phasefield_size = ShapeFunction::NPOINTS; + static const int displacement_index = ShapeFunction::NPOINTS; + static const int displacement_size = + ShapeFunction::NPOINTS * DisplacementDim; + static const int kelvin_vector_size = + KelvinVectorDimensions<DisplacementDim>::value; +}; + +template <typename ShapeFunction, typename IntegrationMethod, + unsigned GlobalDim, int DisplacementDim> +class LocalAssemblerData final + : public PhaseFieldLocalAssembler<ShapeFunction, IntegrationMethod, + DisplacementDim> +{ +public: + LocalAssemblerData(LocalAssemblerData const&) = delete; + LocalAssemblerData(LocalAssemblerData&&) = delete; + + LocalAssemblerData(MeshLib::Element const& e, + std::size_t const local_matrix_size, + bool is_axially_symmetric, + unsigned const integration_order, + PhaseFieldProcessData<DisplacementDim>& process_data) + : PhaseFieldLocalAssembler<ShapeFunction, IntegrationMethod, + DisplacementDim>( + e, local_matrix_size, is_axially_symmetric, integration_order, + process_data) + { + } +}; + +} // namespace PhaseField +} // namespace ProcessLib diff --git a/ProcessLib/PhaseField/PhaseFieldProcess.cpp b/ProcessLib/PhaseField/PhaseFieldProcess.cpp new file mode 100644 index 00000000000..6e3243e76ce --- /dev/null +++ b/ProcessLib/PhaseField/PhaseFieldProcess.cpp @@ -0,0 +1,20 @@ +/** + * \copyright + * Copyright (c) 2012-2017, OpenGeoSys Community (http://www.opengeosys.org) + * Distributed under a Modified BSD License. + * See accompanying file LICENSE.txt or + * http://www.opengeosys.org/project/license + * + */ + +#include "PhaseFieldProcess.h" + +namespace ProcessLib +{ +namespace PhaseField +{ +template class PhaseFieldProcess<2>; +template class PhaseFieldProcess<3>; + +} // namespace PhaseField +} // namespace ProcessLib diff --git a/ProcessLib/PhaseField/PhaseFieldProcess.h b/ProcessLib/PhaseField/PhaseFieldProcess.h new file mode 100644 index 00000000000..df885f24062 --- /dev/null +++ b/ProcessLib/PhaseField/PhaseFieldProcess.h @@ -0,0 +1,244 @@ +/** + * \copyright + * Copyright (c) 2012-2017, OpenGeoSys Community (http://www.opengeosys.org) + * Distributed under a Modified BSD License. + * See accompanying file LICENSE.txt or + * http://www.opengeosys.org/project/license + * + */ + +#pragma once + +#include <cassert> + +#include "NumLib/DOF/DOFTableUtil.h" +#include "ProcessLib/Process.h" +#include "ProcessLib/SmallDeformation/CreateLocalAssemblers.h" + +#include "PhaseFieldFEM.h" +#include "PhaseFieldProcessData.h" + +namespace ProcessLib +{ +namespace PhaseField +{ + +/** + * \brief A class to simulate mechanical fracturing process + * using phase-field approach in solids described by + * + * \f[ + * \mathrm{div} \left[ \left(d^2 + k \right) \boldsymbol{\sigma}_0^+ + * + \boldsymbol{\sigma}_0^- \right] + + * \varrho \boldsymbol{b} = \boldsymbol{0} + * \f] + * \f[ + * 2d H(\boldsymbol{\epsilon}_\mathrm{el}) + * - \frac{1 - d}{2 \varepsilon} g_\mathrm{c} + * - 2 \varepsilon g_\mathrm{c} \mathrm{div}(\mathrm{grad} d) = 0 + * \f] + * where + * \f{eqnarray*}{ + * &d:& \mbox{order parameter,}\\ + * &\varrho:& \mbox{density,}\\ + * &H:& \mbox{history field,}\\ + * &g_\mathrm{c}:& \mbox{fracture energy,}\\ + * &\varepsilon:& \mbox{length scale}\\ + * \f} + * + * Detailed model description can refer + * <a href="Miao_Biot2017.pdff" target="_blank"><b>Phase field method</b></a> + */ +template <int DisplacementDim> +class PhaseFieldProcess final : public Process +{ + using Base = Process; + +public: + PhaseFieldProcess( + MeshLib::Mesh& mesh, + std::unique_ptr<ProcessLib::AbstractJacobianAssembler>&& + jacobian_assembler, + std::vector<std::unique_ptr<ParameterBase>> const& parameters, + unsigned const integration_order, + std::vector<std::reference_wrapper<ProcessVariable>>&& + process_variables, + PhaseFieldProcessData<DisplacementDim>&& process_data, + SecondaryVariableCollection&& secondary_variables, + NumLib::NamedFunctionCaller&& named_function_caller) + : Process(mesh, std::move(jacobian_assembler), parameters, + integration_order, std::move(process_variables), + std::move(secondary_variables), + std::move(named_function_caller)), + _process_data(std::move(process_data)) + { + } + + //! \name ODESystem interface + //! @{ + + bool isLinear() const override { return false; } + //! @} + +private: + using LocalAssemblerInterface = PhaseFieldLocalAssemblerInterface; + + void initializeConcreteProcess( + NumLib::LocalToGlobalIndexMap const& dof_table, + MeshLib::Mesh const& mesh, + unsigned const integration_order) override + { + ProcessLib::SmallDeformation::createLocalAssemblers< + DisplacementDim, PhaseFieldLocalAssembler>( + mesh.getElements(), dof_table, _local_assemblers, + mesh.isAxiallySymmetric(), integration_order, _process_data); + + // TODO move the two data members somewhere else. + // for extrapolation of secondary variables + std::vector<MeshLib::MeshSubsets> all_mesh_subsets_single_component; + all_mesh_subsets_single_component.emplace_back( + _mesh_subset_all_nodes.get()); + _local_to_global_index_map_single_component.reset( + new NumLib::LocalToGlobalIndexMap( + std::move(all_mesh_subsets_single_component), + // by location order is needed for output + NumLib::ComponentOrder::BY_LOCATION)); + + Base::_secondary_variables.addSecondaryVariable( + "sigma_xx", + makeExtrapolator( + 1, getExtrapolator(), _local_assemblers, + &PhaseFieldLocalAssemblerInterface::getIntPtSigmaXX)); + + Base::_secondary_variables.addSecondaryVariable( + "sigma_yy", + makeExtrapolator( + 1, getExtrapolator(), _local_assemblers, + &PhaseFieldLocalAssemblerInterface::getIntPtSigmaYY)); + + Base::_secondary_variables.addSecondaryVariable( + "sigma_zz", + makeExtrapolator( + 1, getExtrapolator(), _local_assemblers, + &PhaseFieldLocalAssemblerInterface::getIntPtSigmaZZ)); + + Base::_secondary_variables.addSecondaryVariable( + "sigma_xy", + makeExtrapolator( + 1, getExtrapolator(), _local_assemblers, + &PhaseFieldLocalAssemblerInterface::getIntPtSigmaXY)); + + if (DisplacementDim == 3) + { + Base::_secondary_variables.addSecondaryVariable( + "sigma_xz", + makeExtrapolator( + 1, getExtrapolator(), _local_assemblers, + &PhaseFieldLocalAssemblerInterface::getIntPtSigmaXZ)); + + Base::_secondary_variables.addSecondaryVariable( + "sigma_yz", + makeExtrapolator( + 1, getExtrapolator(), _local_assemblers, + &PhaseFieldLocalAssemblerInterface::getIntPtSigmaYZ)); + } + Base::_secondary_variables.addSecondaryVariable( + "epsilon_xx", + makeExtrapolator( + 1, getExtrapolator(), _local_assemblers, + &PhaseFieldLocalAssemblerInterface::getIntPtEpsilonXX)); + + Base::_secondary_variables.addSecondaryVariable( + "epsilon_yy", + makeExtrapolator( + 1, getExtrapolator(), _local_assemblers, + &PhaseFieldLocalAssemblerInterface::getIntPtEpsilonYY)); + + Base::_secondary_variables.addSecondaryVariable( + "epsilon_zz", + makeExtrapolator( + 1, getExtrapolator(), _local_assemblers, + &PhaseFieldLocalAssemblerInterface::getIntPtEpsilonZZ)); + + Base::_secondary_variables.addSecondaryVariable( + "epsilon_xy", + makeExtrapolator( + 1, getExtrapolator(), _local_assemblers, + &PhaseFieldLocalAssemblerInterface::getIntPtEpsilonXY)); + if (DisplacementDim == 3) + { + Base::_secondary_variables.addSecondaryVariable( + "epsilon_yz", + makeExtrapolator(1, getExtrapolator(), _local_assemblers, + &PhaseFieldLocalAssemblerInterface:: + getIntPtEpsilonYZ)); + + Base::_secondary_variables.addSecondaryVariable( + "epsilon_xz", + makeExtrapolator(1, getExtrapolator(), _local_assemblers, + &PhaseFieldLocalAssemblerInterface:: + getIntPtEpsilonXZ)); + } + } + + void assembleConcreteProcess( + const double t, GlobalVector const& x, GlobalMatrix& M, GlobalMatrix& K, + GlobalVector& b, StaggeredCouplingTerm const& coupling_term) override + { + DBUG("Assemble PhaseFieldProcess."); + + // Call global assembler for each local assembly item. + GlobalExecutor::executeMemberDereferenced( + _global_assembler, &VectorMatrixAssembler::assemble, + _local_assemblers, *_local_to_global_index_map, t, x, M, K, b, + coupling_term); + } + + void assembleWithJacobianConcreteProcess( + const double t, GlobalVector const& x, GlobalVector const& xdot, + const double dxdot_dx, const double dx_dx, GlobalMatrix& M, + GlobalMatrix& K, GlobalVector& b, GlobalMatrix& Jac, + StaggeredCouplingTerm const& coupling_term) override + { + // DBUG("AssembleJacobian PhaseFieldProcess."); + + // Call global assembler for each local assembly item. + GlobalExecutor::executeMemberDereferenced( + _global_assembler, &VectorMatrixAssembler::assembleWithJacobian, + _local_assemblers, *_local_to_global_index_map, t, x, xdot, + dxdot_dx, dx_dx, M, K, b, Jac, coupling_term); + } + + void preTimestepConcreteProcess(GlobalVector const& x, double const t, + double const dt) override + { + DBUG("PreTimestep PhaseFieldProcess."); + + _process_data.dt = dt; + _process_data.t = t; + + GlobalExecutor::executeMemberOnDereferenced( + &PhaseFieldLocalAssemblerInterface::preTimestep, _local_assemblers, + *_local_to_global_index_map, x, t, dt); + } + + void postTimestepConcreteProcess(GlobalVector const& x) override + { + DBUG("PostTimestep PhaseFieldProcess."); + + GlobalExecutor::executeMemberOnDereferenced( + &PhaseFieldLocalAssemblerInterface::postTimestep, _local_assemblers, + *_local_to_global_index_map, x); + } + +private: + PhaseFieldProcessData<DisplacementDim> _process_data; + + std::vector<std::unique_ptr<LocalAssemblerInterface>> _local_assemblers; + + std::unique_ptr<NumLib::LocalToGlobalIndexMap> + _local_to_global_index_map_single_component; +}; + +} // namespace PhaseField +} // namespace ProcessLib diff --git a/ProcessLib/PhaseField/PhaseFieldProcessData.h b/ProcessLib/PhaseField/PhaseFieldProcessData.h new file mode 100644 index 00000000000..bea1a24b92e --- /dev/null +++ b/ProcessLib/PhaseField/PhaseFieldProcessData.h @@ -0,0 +1,82 @@ +/** + * \copyright + * Copyright (c) 2012-2017, OpenGeoSys Community (http://www.opengeosys.org) + * Distributed under a Modified BSD License. + * See accompanying file LICENSE.txt or + * http://www.opengeosys.org/project/license + * + */ + +#pragma once + +namespace MeshLib +{ +class Element; +} + +namespace ProcessLib +{ +namespace PhaseField +{ +template <int DisplacementDim> +struct PhaseFieldProcessData +{ + PhaseFieldProcessData( + std::unique_ptr<MaterialLib::Solids::MechanicsBase<DisplacementDim>>&& + material_, + Parameter<double> const& residual_stiffness_, + Parameter<double> const& crack_resistance_, + Parameter<double> const& crack_length_scale_, + Parameter<double> const& kinetic_coefficient_, + Parameter<double> const& solid_density_, + Parameter<double>& history_field_, + Eigen::Matrix<double, DisplacementDim, 1> const& specific_body_force_) + : material{std::move(material_)}, + residual_stiffness(residual_stiffness_), + crack_resistance(crack_resistance_), + crack_length_scale(crack_length_scale_), + kinetic_coefficient(kinetic_coefficient_), + solid_density(solid_density_), + history_field(history_field_), + specific_body_force(specific_body_force_) + { + } + + PhaseFieldProcessData(PhaseFieldProcessData&& other) + : material{std::move(other.material)}, + residual_stiffness(other.residual_stiffness), + crack_resistance(other.crack_resistance), + crack_length_scale(other.crack_length_scale), + kinetic_coefficient(other.kinetic_coefficient), + solid_density(other.solid_density), + history_field(other.history_field), + specific_body_force(other.specific_body_force), + dt(other.dt), + t(other.t) + { + } + + //! Copies are forbidden. + PhaseFieldProcessData(PhaseFieldProcessData const&) = delete; + + //! Assignments are not needed. + void operator=(PhaseFieldProcessData const&) = delete; + + //! Assignments are not needed. + void operator=(PhaseFieldProcessData&&) = delete; + + std::unique_ptr<MaterialLib::Solids::MechanicsBase<DisplacementDim>> + material; + Parameter<double> const& residual_stiffness; + Parameter<double> const& crack_resistance; + Parameter<double> const& crack_length_scale; + Parameter<double> const& kinetic_coefficient; + Parameter<double> const& solid_density; + Parameter<double>& history_field; + Eigen::Matrix<double, DisplacementDim, 1> const& specific_body_force; + double dt; + double t; +}; + +} // namespace PhaseField +} // namespace ProcessLib diff --git a/ProcessLib/PhaseField/Tests.cmake b/ProcessLib/PhaseField/Tests.cmake new file mode 100644 index 00000000000..8a267e8658d --- /dev/null +++ b/ProcessLib/PhaseField/Tests.cmake @@ -0,0 +1,13 @@ +AddTest( + NAME PhaseField_3D_Unconfined_Compression + PATH PhaseField + EXECUTABLE ogs + EXECUTABLE_ARGS cube_1e0.prj + WRAPPER time + TESTER vtkdiff + REQUIREMENTS NOT (OGS_USE_LIS OR OGS_USE_MPI) + 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zv=jdv;jbC+rWb;)*#(oNlmGG|LJ1`j{ofnhSuB6QO8@`9!T-1>{yRngzpla6gP-5U W9+7#KB()2ER1`EWzrSSq;C}!J;@q<U literal 0 HcmV?d00001 diff --git a/web/content/docs/benchmarks/phase-field/phasefield.md b/web/content/docs/benchmarks/phase-field/phasefield.md new file mode 100644 index 00000000000..af1d34b6b75 --- /dev/null +++ b/web/content/docs/benchmarks/phase-field/phasefield.md @@ -0,0 +1,50 @@ ++++ +project = "https://github.com/ufz/ogs-data/blob/master/PhaseField/beam3d.prj" +author = "Xing-Yuan Miao" +date = "2017-05-19T09:10:33+01:00" +title = "Crack beam under tension" +weight = 158 + +[menu] + [menu.benchmarks] + parent = "phase-field" + ++++ + +{{< project-link >}} + +## Problem description + +We solve a homogeneous beam model under a given displacement loading. The length of the beam is 2\,mm. Detailed model description can refer [this PDF](../Miao_Biot2017.pdf). +## Results and evaluation + +Results show crack phase-field and displacement field distributions through the length of the beam: + +{{< img src="../beam.png" >}} +{{< img src="../beam_d.png" >}} +{{< img src="../beam_u.png" >}} + +For highlighting the deviation between the analytical and numerical solution, we provide the absolute error of the analytical solution and numerical simulation as follows: +{{< img src="../error_u.png" >}} + +The analytical solution is: +$$ +\begin{equation} +d (x) = 1 - {\mathrm{e}}^{\frac{- |x|}{2 \varepsilon}} +\end{equation} +$$ +$$ +\begin{equation} +u (x) = \dfrac{\sigma}{E} \int_0^x \dfrac{1}{d (x)^2 + k} \mathrm{d}x +\end{equation} +$$ +with +$$ +\begin{equation} +\sigma = \dfrac{E u_0}{I (\varepsilon, k)} +\end{equation} +$$ +\begin{equation} +I (\varepsilon, k) = \int_0^1 \dfrac{1}{d (x)^2 + k} \mathrm{d}x +\end{equation} +$$ \ No newline at end of file -- GitLab