OGS
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Local assembler of ThermoMechanics process.
In this assembler, the solid density can be expressed as an exponential function of temperature, if a temperature dependent solid density is assumed. The theory behind this is given below.
During the temperature variation, the solid mass balance is
\[ \rho_s^{n+1} V^{n+1} = \rho_s^n V^n, \]
with \(\rho_s\) the density, \(V\), the volume, and \(n\) the index of the time step. Under pure thermo-mechanics condition, the volume change along with the temperature change is given by
\[ V^{n+1} = V^{n} + \alpha_T dT V^{n} = (1+\alpha_T dT)V^{n}, \]
where \(\alpha_T\) is the volumetric thermal expansivity of the solid. This gives
\[ \rho_s^{n+1} + \alpha_T dT \rho_s^{n+1} = \rho_s^n. \]
Therefore, we obtain the differential expression of the temperature dependent solid density as
\[ \frac{d \rho_s}{d T} = -\alpha_T \rho_s. \]
The solution of the above ODE, i.e the density expression, is given by
\[ \rho_s = {\rho_0} \mathrm{exp} (- \alpha_T (T-T0)), \]
with reference density \(\rho_0\) at a reference temperature of \(T_0\).
An MPL property with the type of Exponential (see MaterialPropertyLib::Exponential) can be used for the temperature dependent solid property.
Definition at line 127 of file ThermoMechanicsFEM.h.
#include <ThermoMechanicsFEM.h>
Public Types | |
using | ShapeMatricesType |
using | ShapeMatrices = typename ShapeMatricesType::ShapeMatrices |
using | GlobalDimMatrixType = typename ShapeMatricesType::GlobalDimMatrixType |
using | BMatricesType = BMatrixPolicyType<ShapeFunction, DisplacementDim> |
using | Invariants = MathLib::KelvinVector::Invariants<KelvinVectorSize> |
using | NodalForceVectorType = typename BMatricesType::NodalForceVectorType |
using | RhsVector |
using | JacobianMatrix |
using | IpData |
Public Member Functions | |
ThermoMechanicsLocalAssembler (ThermoMechanicsLocalAssembler const &)=delete | |
ThermoMechanicsLocalAssembler (ThermoMechanicsLocalAssembler &&)=delete | |
ThermoMechanicsLocalAssembler (MeshLib::Element const &e, std::size_t const, NumLib::GenericIntegrationMethod const &integration_method, bool const is_axially_symmetric, ThermoMechanicsProcessData< DisplacementDim > &process_data) | |
std::size_t | setIPDataInitialConditions (std::string_view const name, double const *values, int const integration_order) override |
Returns number of read integration points. | |
void | assemble (double const, double const, std::vector< double > const &, std::vector< double > const &, std::vector< double > &, std::vector< double > &, std::vector< double > &) override |
void | assembleWithJacobianForStaggeredScheme (double const t, double const dt, Eigen::VectorXd const &local_x, Eigen::VectorXd const &local_x_prev, int const process_id, std::vector< double > &local_b_data, std::vector< double > &local_Jac_data) override |
void | assembleWithJacobian (double const t, double const dt, std::vector< double > const &local_x, std::vector< double > const &local_x_prev, std::vector< double > &local_rhs_data, std::vector< double > &local_Jac_data) override |
void | initializeConcrete () override |
void | postTimestepConcrete (Eigen::VectorXd const &, Eigen::VectorXd const &, double const, double const, int const) override |
Eigen::Map< const Eigen::RowVectorXd > | getShapeMatrix (const unsigned integration_point) const override |
Provides the shape matrix at the given integration point. | |
Public Member Functions inherited from ProcessLib::LocalAssemblerInterface | |
virtual | ~LocalAssemblerInterface ()=default |
virtual void | setInitialConditions (std::size_t const mesh_item_id, std::vector< NumLib::LocalToGlobalIndexMap const * > const &dof_tables, std::vector< GlobalVector * > const &x, double const t, int const process_id) |
virtual void | initialize (std::size_t const mesh_item_id, NumLib::LocalToGlobalIndexMap const &dof_table) |
virtual void | preAssemble (double const, double const, std::vector< double > const &) |
virtual void | assembleForStaggeredScheme (double const t, double const dt, Eigen::VectorXd const &local_x, Eigen::VectorXd const &local_x_prev, int const process_id, std::vector< double > &local_M_data, std::vector< double > &local_K_data, std::vector< double > &local_b_data) |
virtual void | computeSecondaryVariable (std::size_t const mesh_item_id, std::vector< NumLib::LocalToGlobalIndexMap const * > const &dof_tables, double const t, double const dt, std::vector< GlobalVector * > const &x, GlobalVector const &x_prev, int const process_id) |
virtual void | preTimestep (std::size_t const mesh_item_id, NumLib::LocalToGlobalIndexMap const &dof_table, GlobalVector const &x, double const t, double const delta_t) |
virtual void | postTimestep (std::size_t const mesh_item_id, std::vector< NumLib::LocalToGlobalIndexMap const * > const &dof_tables, std::vector< GlobalVector * > const &x, std::vector< GlobalVector * > const &x_prev, double const t, double const dt, int const process_id) |
void | postNonLinearSolver (std::size_t const mesh_item_id, std::vector< NumLib::LocalToGlobalIndexMap const * > const &dof_tables, std::vector< GlobalVector * > const &x, std::vector< GlobalVector * > const &x_prev, double const t, double const dt, int const process_id) |
virtual Eigen::Vector3d | getFlux (MathLib::Point3d const &, double const, std::vector< double > const &) const |
virtual Eigen::Vector3d | getFlux (MathLib::Point3d const &, double const, std::vector< std::vector< double > > const &) const |
Fits to staggered scheme. | |
Public Member Functions inherited from NumLib::ExtrapolatableElement | |
virtual | ~ExtrapolatableElement ()=default |
Static Public Attributes | |
static int const | KelvinVectorSize |
Private Member Functions | |
void | assembleWithJacobianForDeformationEquations (const double t, double const dt, Eigen::VectorXd const &local_x, Eigen::VectorXd const &local_x_prev, std::vector< double > &local_b_data, std::vector< double > &local_Jac_data) |
void | assembleWithJacobianForHeatConductionEquations (const double t, double const dt, Eigen::VectorXd const &local_x, Eigen::VectorXd const &local_x_prev, std::vector< double > &local_b_data, std::vector< double > &local_Jac_data) |
std::size_t | setSigma (double const *values) |
std::vector< double > | getSigma () const override |
std::vector< double > const & | getIntPtSigma (const double t, std::vector< GlobalVector * > const &x, std::vector< NumLib::LocalToGlobalIndexMap const * > const &dof_table, std::vector< double > &cache) const override |
std::size_t | setEpsilon (double const *values) |
std::vector< double > | getEpsilon () const override |
std::vector< double > const & | getIntPtEpsilon (const double t, std::vector< GlobalVector * > const &x, std::vector< NumLib::LocalToGlobalIndexMap const * > const &dof_table, std::vector< double > &cache) const override |
std::vector< double > const & | getIntPtEpsilonMechanical (const double t, std::vector< GlobalVector * > const &x, std::vector< NumLib::LocalToGlobalIndexMap const * > const &dof_table, std::vector< double > &cache) const override |
std::size_t | setEpsilonMechanical (double const *values) |
std::vector< double > | getEpsilonMechanical () const override |
unsigned | getNumberOfIntegrationPoints () const override |
int | getMaterialID () const override |
MaterialLib::Solids::MechanicsBase< DisplacementDim >::MaterialStateVariables const & | getMaterialStateVariablesAt (unsigned integration_point) const override |
Private Attributes | |
ThermoMechanicsProcessData< DisplacementDim > & | _process_data |
std::vector< IpData, Eigen::aligned_allocator< IpData > > | _ip_data |
NumLib::GenericIntegrationMethod const & | _integration_method |
MeshLib::Element const & | _element |
SecondaryData< typename ShapeMatrices::ShapeType > | _secondary_data |
bool const | _is_axially_symmetric |
Static Private Attributes | |
static const int | temperature_index = 0 |
static const int | temperature_size = ShapeFunction::NPOINTS |
static const int | displacement_index = ShapeFunction::NPOINTS |
static const int | displacement_size |
using ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssembler< ShapeFunction, DisplacementDim >::BMatricesType = BMatrixPolicyType<ShapeFunction, DisplacementDim> |
Definition at line 138 of file ThermoMechanicsFEM.h.
using ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssembler< ShapeFunction, DisplacementDim >::GlobalDimMatrixType = typename ShapeMatricesType::GlobalDimMatrixType |
Definition at line 137 of file ThermoMechanicsFEM.h.
using ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssembler< ShapeFunction, DisplacementDim >::Invariants = MathLib::KelvinVector::Invariants<KelvinVectorSize> |
Definition at line 142 of file ThermoMechanicsFEM.h.
using ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssembler< ShapeFunction, DisplacementDim >::IpData |
Definition at line 150 of file ThermoMechanicsFEM.h.
using ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssembler< ShapeFunction, DisplacementDim >::JacobianMatrix |
Definition at line 147 of file ThermoMechanicsFEM.h.
using ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssembler< ShapeFunction, DisplacementDim >::NodalForceVectorType = typename BMatricesType::NodalForceVectorType |
Definition at line 144 of file ThermoMechanicsFEM.h.
using ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssembler< ShapeFunction, DisplacementDim >::RhsVector |
Definition at line 145 of file ThermoMechanicsFEM.h.
using ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssembler< ShapeFunction, DisplacementDim >::ShapeMatrices = typename ShapeMatricesType::ShapeMatrices |
Definition at line 136 of file ThermoMechanicsFEM.h.
using ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssembler< ShapeFunction, DisplacementDim >::ShapeMatricesType |
Definition at line 131 of file ThermoMechanicsFEM.h.
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ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssembler< ShapeFunction, DisplacementDim >::ThermoMechanicsLocalAssembler | ( | MeshLib::Element const & | e, |
std::size_t const | , | ||
NumLib::GenericIntegrationMethod const & | integration_method, | ||
bool const | is_axially_symmetric, | ||
ThermoMechanicsProcessData< DisplacementDim > & | process_data ) |
Definition at line 27 of file ThermoMechanicsFEM-impl.h.
References ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssembler< ShapeFunction, DisplacementDim >::_element, ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssembler< ShapeFunction, DisplacementDim >::_integration_method, ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssembler< ShapeFunction, DisplacementDim >::_ip_data, ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssembler< ShapeFunction, DisplacementDim >::_process_data, ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssembler< ShapeFunction, DisplacementDim >::_secondary_data, MeshLib::Element::getID(), NumLib::GenericIntegrationMethod::getNumberOfPoints(), MathLib::WeightedPoint::getWeight(), NumLib::GenericIntegrationMethod::getWeightedPoint(), NumLib::initShapeMatrices(), MathLib::KelvinVector::kelvin_vector_dimensions(), ProcessLib::ThermoMechanics::SecondaryData< ShapeMatrixType >::N, MaterialLib::Solids::selectSolidConstitutiveRelation(), and ParameterLib::SpatialPosition::setElementID().
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Reimplemented from ProcessLib::LocalAssemblerInterface.
Definition at line 170 of file ThermoMechanicsFEM.h.
References OGS_FATAL.
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Reimplemented from ProcessLib::LocalAssemblerInterface.
Definition at line 115 of file ThermoMechanicsFEM-impl.h.
References ProcessLib::LinearBMatrix::computeBMatrix(), MathLib::createZeroedMatrix(), MathLib::createZeroedVector(), MaterialLib::Solids::CreepBGRa, MaterialPropertyLib::formEigenTensor(), MaterialPropertyLib::formKelvinVector(), NumLib::interpolateXCoordinate(), MathLib::KelvinVector::kelvinVectorToSymmetricTensor(), MaterialPropertyLib::VariableArray::mechanical_strain, OGS_FATAL, ParameterLib::SpatialPosition::setElementID(), ParameterLib::SpatialPosition::setIntegrationPoint(), MaterialPropertyLib::specific_heat_capacity, MaterialPropertyLib::VariableArray::stress, MaterialPropertyLib::VariableArray::temperature, MaterialPropertyLib::thermal_conductivity, and MaterialPropertyLib::thermal_expansivity.
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Assemble local matrices and vectors arise from the linearized discretized weak form of the residual of the momentum balance equation,
\[ \nabla (\sigma - \mathbf{D} \alpha_T (T-T_0) \mathrm{I}) = f \]
where \( \sigma\) is the effective stress tensor, \(\mathbf{D}\) is the tangential operator, \(T\) is the temperature, \(T_0\) is the initial temperature, \(\alpha_T\) is the linear thermal expansion, \(\mathrm{I}\) is the identity tensor, and \(f\) is the body force.
t | Time |
dt | Time increment |
local_x | Nodal values of \(x\) of all processes of an element. |
local_x_prev | Nodal values of \(x_{prev}\) of all processes of an element. |
local_b_data | Right hand side vector of an element. |
local_Jac_data | Element Jacobian matrix for the Newton-Raphson method. |
Definition at line 351 of file ThermoMechanicsFEM-impl.h.
References ProcessLib::LinearBMatrix::computeBMatrix(), MathLib::createZeroedMatrix(), MathLib::createZeroedVector(), MaterialPropertyLib::formKelvinVector(), NumLib::interpolateXCoordinate(), MaterialPropertyLib::VariableArray::mechanical_strain, OGS_FATAL, ParameterLib::SpatialPosition::setElementID(), ParameterLib::SpatialPosition::setIntegrationPoint(), MaterialPropertyLib::VariableArray::stress, MaterialPropertyLib::VariableArray::temperature, and MaterialPropertyLib::thermal_expansivity.
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Assemble local matrices and vectors arise from the linearized discretized weak form of the residual of the energy balance equation,
\[ \rho c_p \cdot{T} - \nabla (\mathbf{K} (\nabla T) = Q_T \]
where \( rho\) is the solid density, \( c_p\) is the specific heat capacity, \( \mathbf{K} \) is the thermal conductivity, and \( Q_T\) is the source/sink term.
t | Time |
dt | Time increment |
local_x | Nodal values of \(x\) of all processes of an element. |
local_x_prev | Nodal values of \(x_{prev}\) of all processes of an element. |
local_b_data | Right hand side vector of an element. |
local_Jac_data | Element Jacobian matrix for the Newton-Raphson method. |
Definition at line 489 of file ThermoMechanicsFEM-impl.h.
References MathLib::createZeroedMatrix(), MathLib::createZeroedVector(), MaterialPropertyLib::formEigenTensor(), ParameterLib::SpatialPosition::setElementID(), ParameterLib::SpatialPosition::setIntegrationPoint(), MaterialPropertyLib::VariableArray::temperature, and MaterialPropertyLib::thermal_conductivity.
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Reimplemented from ProcessLib::LocalAssemblerInterface.
Definition at line 329 of file ThermoMechanicsFEM-impl.h.
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Implements ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssemblerInterface< DisplacementDim >.
Definition at line 605 of file ThermoMechanicsFEM-impl.h.
References MathLib::KelvinVector::kelvin_vector_dimensions(), and ProcessLib::transposeInPlace().
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Implements ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssemblerInterface< DisplacementDim >.
Definition at line 649 of file ThermoMechanicsFEM-impl.h.
References MathLib::KelvinVector::kelvin_vector_dimensions(), and ProcessLib::transposeInPlace().
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Implements ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssemblerInterface< DisplacementDim >.
Definition at line 617 of file ThermoMechanicsFEM-impl.h.
References ProcessLib::getIntegrationPointKelvinVectorData().
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Implements ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssemblerInterface< DisplacementDim >.
Definition at line 629 of file ThermoMechanicsFEM-impl.h.
References ProcessLib::getIntegrationPointKelvinVectorData().
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Implements ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssemblerInterface< DisplacementDim >.
Definition at line 584 of file ThermoMechanicsFEM-impl.h.
References ProcessLib::getIntegrationPointKelvinVectorData().
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Implements ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssemblerInterface< DisplacementDim >.
Definition at line 668 of file ThermoMechanicsFEM-impl.h.
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Implements ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssemblerInterface< DisplacementDim >.
Definition at line 678 of file ThermoMechanicsFEM-impl.h.
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Implements ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssemblerInterface< DisplacementDim >.
Definition at line 661 of file ThermoMechanicsFEM-impl.h.
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Provides the shape matrix at the given integration point.
Implements NumLib::ExtrapolatableElement.
Definition at line 242 of file ThermoMechanicsFEM.h.
References ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssembler< ShapeFunction, DisplacementDim >::_secondary_data, and ProcessLib::ThermoMechanics::SecondaryData< ShapeMatrixType >::N.
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Implements ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssemblerInterface< DisplacementDim >.
Definition at line 572 of file ThermoMechanicsFEM-impl.h.
References MathLib::KelvinVector::kelvin_vector_dimensions(), and ProcessLib::transposeInPlace().
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Set initial stress from parameter.
Reimplemented from ProcessLib::LocalAssemblerInterface.
Definition at line 194 of file ThermoMechanicsFEM.h.
References ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssembler< ShapeFunction, DisplacementDim >::_element, ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssembler< ShapeFunction, DisplacementDim >::_integration_method, ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssembler< ShapeFunction, DisplacementDim >::_ip_data, ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssembler< ShapeFunction, DisplacementDim >::_process_data, MeshLib::Element::getID(), NumLib::GenericIntegrationMethod::getNumberOfPoints(), NumLib::interpolateCoordinates(), and MathLib::KelvinVector::symmetricTensorToKelvinVector().
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Reimplemented from ProcessLib::LocalAssemblerInterface.
Definition at line 228 of file ThermoMechanicsFEM.h.
References ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssembler< ShapeFunction, DisplacementDim >::_integration_method, ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssembler< ShapeFunction, DisplacementDim >::_ip_data, and NumLib::GenericIntegrationMethod::getNumberOfPoints().
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Definition at line 596 of file ThermoMechanicsFEM-impl.h.
References ProcessLib::setIntegrationPointKelvinVectorData().
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Definition at line 642 of file ThermoMechanicsFEM-impl.h.
References ProcessLib::setIntegrationPointKelvinVectorData().
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Returns number of read integration points.
Implements ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssemblerInterface< DisplacementDim >.
Definition at line 83 of file ThermoMechanicsFEM-impl.h.
References OGS_FATAL.
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Definition at line 563 of file ThermoMechanicsFEM-impl.h.
References ProcessLib::setIntegrationPointKelvinVectorData().
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Definition at line 351 of file ThermoMechanicsFEM.h.
Referenced by ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssembler< ShapeFunction, DisplacementDim >::ThermoMechanicsLocalAssembler(), and ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssembler< ShapeFunction, DisplacementDim >::initializeConcrete().
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Definition at line 350 of file ThermoMechanicsFEM.h.
Referenced by ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssembler< ShapeFunction, DisplacementDim >::ThermoMechanicsLocalAssembler(), ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssembler< ShapeFunction, DisplacementDim >::initializeConcrete(), and ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssembler< ShapeFunction, DisplacementDim >::postTimestepConcrete().
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Definition at line 348 of file ThermoMechanicsFEM.h.
Referenced by ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssembler< ShapeFunction, DisplacementDim >::ThermoMechanicsLocalAssembler(), ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssembler< ShapeFunction, DisplacementDim >::initializeConcrete(), and ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssembler< ShapeFunction, DisplacementDim >::postTimestepConcrete().
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Definition at line 353 of file ThermoMechanicsFEM.h.
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Definition at line 346 of file ThermoMechanicsFEM.h.
Referenced by ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssembler< ShapeFunction, DisplacementDim >::ThermoMechanicsLocalAssembler(), and ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssembler< ShapeFunction, DisplacementDim >::initializeConcrete().
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Definition at line 352 of file ThermoMechanicsFEM.h.
Referenced by ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssembler< ShapeFunction, DisplacementDim >::ThermoMechanicsLocalAssembler(), and ProcessLib::ThermoMechanics::ThermoMechanicsLocalAssembler< ShapeFunction, DisplacementDim >::getShapeMatrix().
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Definition at line 357 of file ThermoMechanicsFEM.h.
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Definition at line 358 of file ThermoMechanicsFEM.h.
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Definition at line 140 of file ThermoMechanicsFEM.h.
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Definition at line 355 of file ThermoMechanicsFEM.h.
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Definition at line 356 of file ThermoMechanicsFEM.h.