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finite_elasticity_routines.f90
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finite_elasticity_routines.f90
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!> \file
!> \author Chris Bradley
!> \brief This module handles all finite elasticity routines.
!>
!> \section LICENSE
!>
!> Version: MPL 1.1/GPL 2.0/LGPL 2.1
!>
!> The contents of this file are subject to the Mozilla Public License
!> Version 1.1 (the "License"); you may not use this file except in
!> compliance with the License. You may obtain a copy of the License at
!> http://www.mozilla.org/MPL/
!>
!> Software distributed under the License is distributed on an "AS IS"
!> basis, WITHOUT WARRANTY OF ANY KIND, either express or implied. See the
!> License for the specific language governing rights and limitations
!> under the License.
!>
!> The Original Code is OpenCMISS
!>
!> The Initial Developer of the Original Code is University of Auckland,
!> Auckland, New Zealand, the University of Oxford, Oxford, United
!> Kingdom and King's College, London, United Kingdom. Portions created
!> by the University of Auckland, the University of Oxford and King's
!> College, London are Copyright (C) 2007-2010 by the University of
!> Auckland, the University of Oxford and King's College, London.
!> All Rights Reserved.
!>
!> Contributor(s): Kumar Mithraratne, Jack Lee, Alice Hung, Sander Arens
!>
!> Alternatively, the contents of this file may be used under the terms of
!> either the GNU General Public License Version 2 or later (the "GPL"), or
!> the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
!> in which case the provisions of the GPL or the LGPL are applicable instead
!> of those above. If you wish to allow use of your version of this file only
!> under the terms of either the GPL or the LGPL, and not to allow others to
!> use your version of this file under the terms of the MPL, indicate your
!> decision by deleting the provisions above and replace them with the notice
!> and other provisions required by the GPL or the LGPL. If you do not delete
!> the provisions above, a recipient may use your version of this file under
!> the terms of any one of the MPL, the GPL or the LGPL.
!>
!>This module handles all finite elasticity routines.
MODULE FINITE_ELASTICITY_ROUTINES
USE BaseRoutines
USE BasisRoutines
USE BasisAccessRoutines
USE BOUNDARY_CONDITIONS_ROUTINES
USE ComputationEnvironment
USE Constants
USE CONTROL_LOOP_ROUTINES
USE ControlLoopAccessRoutines
USE COORDINATE_ROUTINES
USE CoordinateSystemAccessRoutines
USE DistributedMatrixVector
USE DOMAIN_MAPPINGS
USE EquationsRoutines
USE EquationsAccessRoutines
USE EquationsMappingRoutines
USE EquationsMappingAccessRoutines
USE EquationsMatricesRoutines
USE EquationsSetConstants
USE EquationsSetAccessRoutines
USE FIELD_ROUTINES
USE FieldAccessRoutines
USE FIELD_IO_ROUTINES
USE FLUID_MECHANICS_IO_ROUTINES
USE GENERATED_MESH_ROUTINES
USE INPUT_OUTPUT
USE ISO_VARYING_STRING
USE Kinds
USE Lapack
USE Maths
USE MatrixVector
USE MESH_ROUTINES
USE MeshAccessRoutines
#ifndef NOMPIMOD
USE MPI
#endif
USE PROBLEM_CONSTANTS
USE ProfilingRoutines
USE SOLVER_ROUTINES
USE SolverAccessRoutines
USE SolverMappingAccessRoutines
USE SolverMatricesAccessRoutines
USE Strings
USE Timer
USE Types
#include "macros.h"
IMPLICIT NONE
#ifdef NOMPIMOD
#include "mpif.h"
#endif
PRIVATE
!Module parameters
!> \addtogroup FINITE_ELASTICITY_ROUTINES_AnalyticParamIndices FINITE_ELASTICITY_ROUTINES::AnalyticParamIndices
!> \brief Indices for EQUATIONS_SET_ANALYTIC_TYPE%ANALYTIC_USER_PARAMS
!> \see FINITE_ELASTICITY_ROUTINES,OPENCMISS_AnalyticParamIndices
!>@{
INTEGER(INTG), PARAMETER :: FINITE_ELASTICITY_ANALYTIC_CYLINDER_PARAM_PIN_IDX=1 !<Inner pressure parameter index \see FINITE_ELASTICITY_ROUTINES_AnalyticParamIndices, FINITE_ELASTICITY_ROUTINES
INTEGER(INTG), PARAMETER :: FINITE_ELASTICITY_ANALYTIC_CYLINDER_PARAM_POUT_IDX=2 !<Outer pressure parameter index \see FINITE_ELASTICITY_ROUTINES_AnalyticParamIndices, FINITE_ELASTICITY_ROUTINES
INTEGER(INTG), PARAMETER :: FINITE_ELASTICITY_ANALYTIC_CYLINDER_PARAM_LAMBDA_IDX=3 !<Lambda parameter index \see FINITE_ELASTICITY_ROUTINES_AnalyticParamIndices, FINITE_ELASTICITY_ROUTINES
INTEGER(INTG), PARAMETER :: FINITE_ELASTICITY_ANALYTIC_CYLINDER_PARAM_TSI_IDX=4 !<Tsi parameter index \see FINITE_ELASTICITY_ROUTINES_AnalyticParamIndices, FINITE_ELASTICITY_ROUTINES
INTEGER(INTG), PARAMETER :: FINITE_ELASTICITY_ANALYTIC_CYLINDER_PARAM_RIN_IDX=5 !<Inner radius parameter index \see FINITE_ELASTICITY_ROUTINES_AnalyticParamIndices, FINITE_ELASTICITY_ROUTINES
INTEGER(INTG), PARAMETER :: FINITE_ELASTICITY_ANALYTIC_CYLINDER_PARAM_ROUT_IDX=6 !<Outer radius parameter index \see FINITE_ELASTICITY_ROUTINES_AnalyticParamIndices, FINITE_ELASTICITY_ROUTINES
INTEGER(INTG), PARAMETER :: FINITE_ELASTICITY_ANALYTIC_CYLINDER_PARAM_C1_IDX=7 !<c1 parameter index \see FINITE_ELASTICITY_ROUTINES_AnalyticParamIndices, FINITE_ELASTICITY_ROUTINES
INTEGER(INTG), PARAMETER :: FINITE_ELASTICITY_ANALYTIC_CYLINDER_PARAM_C2_IDX=8 !<c2 parameter index \see FINITE_ELASTICITY_ROUTINES_AnalyticParamIndices, FINITE_ELASTICITY_ROUTINES
!>@}
!Module types
!Module variables
!Interfaces
PUBLIC FINITE_ELASTICITY_ANALYTIC_CYLINDER_PARAM_PIN_IDX,FINITE_ELASTICITY_ANALYTIC_CYLINDER_PARAM_POUT_IDX, &
& FINITE_ELASTICITY_ANALYTIC_CYLINDER_PARAM_LAMBDA_IDX, FINITE_ELASTICITY_ANALYTIC_CYLINDER_PARAM_TSI_IDX, &
& FINITE_ELASTICITY_ANALYTIC_CYLINDER_PARAM_RIN_IDX, FINITE_ELASTICITY_ANALYTIC_CYLINDER_PARAM_ROUT_IDX, &
& FINITE_ELASTICITY_ANALYTIC_CYLINDER_PARAM_C1_IDX, FINITE_ELASTICITY_ANALYTIC_CYLINDER_PARAM_C2_IDX
PUBLIC FiniteElasticity_BoundaryConditionsAnalyticCalculate
PUBLIC FiniteElasticity_FiniteElementResidualEvaluate
PUBLIC FiniteElasticity_FiniteElementPreResidualEvaluate,FiniteElasticity_FiniteElementPostResidualEvaluate
PUBLIC FiniteElasticity_FiniteElementJacobianEvaluate
PUBLIC FINITE_ELASTICITY_EQUATIONS_SET_SETUP,FiniteElasticity_EquationsSetSolutionMethodSet, &
& FiniteElasticity_EquationsSetSpecificationSet,FiniteElasticity_ProblemSpecificationSet,FINITE_ELASTICITY_PROBLEM_SETUP, &
& FiniteElasticity_ContactProblemSpecificationSet,FiniteElasticity_ContactProblemSetup, &
& FiniteElasticity_PostSolve,FiniteElasticity_PostSolveOutputData, &
& FiniteElasticity_PreSolve,FiniteElasticity_ControlTimeLoopPreLoop,FiniteElasticity_ControlLoadIncrementLoopPostLoop, &
& EVALUATE_CHAPELLE_FUNCTION, GET_DARCY_FINITE_ELASTICITY_PARAMETERS, &
& FiniteElasticity_GaussDeformationGradientTensor,FINITE_ELASTICITY_LOAD_INCREMENT_APPLY, &
& FiniteElasticity_StressStrainCalculate
PUBLIC FiniteElasticityEquationsSet_DerivedVariableCalculate
PUBLIC FiniteElasticity_TensorInterpolateGaussPoint
PUBLIC FiniteElasticity_TensorInterpolateXi
CONTAINS
!
!================================================================================================================================
!
!>Calculates the analytic solution and sets the boundary conditions for an analytic problem
SUBROUTINE FiniteElasticity_BoundaryConditionsAnalyticCalculate(EQUATIONS_SET,BOUNDARY_CONDITIONS,err,error,*)
!Argument variables
TYPE(EQUATIONS_SET_TYPE), POINTER :: EQUATIONS_SET
TYPE(BOUNDARY_CONDITIONS_TYPE), POINTER :: BOUNDARY_CONDITIONS
INTEGER(INTG), INTENT(OUT) :: ERR !<The error code
TYPE(VARYING_STRING), INTENT(OUT) :: ERROR !<The error string
!Local variables
INTEGER(INTG) :: node_idx,component_idx,deriv_idx,variable_idx,dim_idx,local_ny,variable_type
INTEGER(INTG) :: NUMBER_OF_DIMENSIONS,user_node,global_node,local_node
REAL(DP) :: X(3),DEFORMED_X(3),P
REAL(DP), POINTER :: GEOMETRIC_PARAMETERS(:)
TYPE(DOMAIN_TYPE), POINTER :: DOMAIN,DOMAIN_PRESSURE
TYPE(DOMAIN_NODES_TYPE), POINTER :: DOMAIN_NODES,DOMAIN_PRESSURE_NODES
TYPE(DECOMPOSITION_TYPE), POINTER :: DECOMPOSITION
TYPE(MESH_TYPE), POINTER :: MESH
TYPE(GENERATED_MESH_TYPE), POINTER :: GENERATED_MESH
TYPE(DOMAIN_MAPPING_TYPE), POINTER :: NODES_MAPPING
TYPE(FIELD_TYPE), POINTER :: DEPENDENT_FIELD,GEOMETRIC_FIELD
TYPE(FIELD_VARIABLE_TYPE), POINTER :: FIELD_VARIABLE,GEOMETRIC_VARIABLE
!BC stuff
INTEGER(INTG),ALLOCATABLE :: INNER_SURFACE_NODES(:),OUTER_SURFACE_NODES(:),TOP_SURFACE_NODES(:),BOTTOM_SURFACE_NODES(:)
INTEGER(INTG) :: INNER_NORMAL_XI,OUTER_NORMAL_XI,TOP_NORMAL_XI,BOTTOM_NORMAL_XI,MESH_COMPONENT
INTEGER(INTG) :: myComputationalNodeNumber, DOMAIN_NUMBER, MPI_IERROR
REAL(DP) :: PIN,POUT,LAMBDA,DEFORMED_Z
LOGICAL :: X_FIXED,Y_FIXED,NODE_EXISTS, X_OKAY,Y_OKAY
TYPE(VARYING_STRING) :: LOCAL_ERROR
NULLIFY(GEOMETRIC_PARAMETERS)
ENTERS("FiniteElasticity_BoundaryConditionsAnalyticCalculate",err,error,*999)
myComputationalNodeNumber=ComputationalEnvironment_NodeNumberGet(err,error)
IF(ASSOCIATED(EQUATIONS_SET)) THEN
IF(ASSOCIATED(EQUATIONS_SET%ANALYTIC)) THEN
DEPENDENT_FIELD=>EQUATIONS_SET%DEPENDENT%DEPENDENT_FIELD
IF(ASSOCIATED(DEPENDENT_FIELD)) THEN
GEOMETRIC_FIELD=>EQUATIONS_SET%GEOMETRY%GEOMETRIC_FIELD
IF(ASSOCIATED(GEOMETRIC_FIELD)) THEN
CALL FIELD_NUMBER_OF_COMPONENTS_GET(GEOMETRIC_FIELD,FIELD_U_VARIABLE_TYPE,NUMBER_OF_DIMENSIONS,err,error,*999)
!Get access to geometric coordinates
NULLIFY(GEOMETRIC_VARIABLE)
CALL Field_VariableGet(GEOMETRIC_FIELD,FIELD_U_VARIABLE_TYPE,GEOMETRIC_VARIABLE,err,error,*999)
MESH_COMPONENT=GEOMETRIC_VARIABLE%COMPONENTS(1)%MESH_COMPONENT_NUMBER
CALL Field_ParameterSetDataGet(GEOMETRIC_FIELD,FIELD_U_VARIABLE_TYPE,FIELD_VALUES_SET_TYPE,GEOMETRIC_PARAMETERS, &
& err,error,*999)
!Assign BC here - it's complicated so separate from analytic calculations
IF(ASSOCIATED(BOUNDARY_CONDITIONS)) THEN
DECOMPOSITION=>DEPENDENT_FIELD%DECOMPOSITION
IF(ASSOCIATED(DECOMPOSITION)) THEN
MESH=>DECOMPOSITION%MESH
IF(ASSOCIATED(MESH)) THEN
GENERATED_MESH=>MESH%GENERATED_MESH
IF(ASSOCIATED(GENERATED_MESH)) THEN
NODES_MAPPING=>DECOMPOSITION%DOMAIN(1)%ptr%MAPPINGS%NODES !HACK - ALL CHECKING INTERMEDIATE SKIPPED
IF(ASSOCIATED(NODES_MAPPING)) THEN
!Get surfaces (hardcoded): fix two nodes on the bottom face, pressure conditions inside & outside
CALL GENERATED_MESH_SURFACE_GET(GENERATED_MESH,MESH_COMPONENT,1_INTG, &
& INNER_SURFACE_NODES,INNER_NORMAL_XI,err,error,*999) !Inner
CALL GENERATED_MESH_SURFACE_GET(GENERATED_MESH,MESH_COMPONENT,2_INTG, &
& OUTER_SURFACE_NODES,OUTER_NORMAL_XI,err,error,*999) !Outer
CALL GENERATED_MESH_SURFACE_GET(GENERATED_MESH,MESH_COMPONENT,3_INTG, &
& TOP_SURFACE_NODES,TOP_NORMAL_XI,err,error,*999) !Top
CALL GENERATED_MESH_SURFACE_GET(GENERATED_MESH,MESH_COMPONENT,4_INTG, &
& BOTTOM_SURFACE_NODES,BOTTOM_NORMAL_XI,err,error,*999) !Bottom
!Set all inner surface nodes to inner pressure (- sign is to make positive P into a compressive force) ?
PIN=EQUATIONS_SET%ANALYTIC%ANALYTIC_USER_PARAMS(FINITE_ELASTICITY_ANALYTIC_CYLINDER_PARAM_PIN_IDX)
DO node_idx=1,SIZE(INNER_SURFACE_NODES,1)
user_node=INNER_SURFACE_NODES(node_idx)
!Need to test if this node is in current decomposition
CALL DECOMPOSITION_NODE_DOMAIN_GET(DECOMPOSITION,user_node,1,DOMAIN_NUMBER,err,error,*999)
IF(DOMAIN_NUMBER==myComputationalNodeNumber) THEN
!Default to version 1 of each node derivative
CALL BOUNDARY_CONDITIONS_SET_NODE(BOUNDARY_CONDITIONS,DEPENDENT_FIELD,FIELD_DELUDELN_VARIABLE_TYPE,1,1, &
& user_node,ABS(INNER_NORMAL_XI),BOUNDARY_CONDITION_PRESSURE_INCREMENTED,PIN,err,error,*999)
ENDIF
ENDDO
!Set all outer surface nodes to outer pressure
POUT=EQUATIONS_SET%ANALYTIC%ANALYTIC_USER_PARAMS(FINITE_ELASTICITY_ANALYTIC_CYLINDER_PARAM_POUT_IDX)
DO node_idx=1,SIZE(OUTER_SURFACE_NODES,1)
user_node=OUTER_SURFACE_NODES(node_idx)
!Need to test if this node is in current decomposition
CALL DECOMPOSITION_NODE_DOMAIN_GET(DECOMPOSITION,user_node,1,DOMAIN_NUMBER,err,error,*999)
IF(DOMAIN_NUMBER==myComputationalNodeNumber) THEN
!Default to version 1 of each node derivative
CALL BOUNDARY_CONDITIONS_SET_NODE(BOUNDARY_CONDITIONS,DEPENDENT_FIELD,FIELD_DELUDELN_VARIABLE_TYPE,1,1, &
& user_node,ABS(OUTER_NORMAL_XI),BOUNDARY_CONDITION_PRESSURE_INCREMENTED,POUT,err,error,*999)
ENDIF
ENDDO
!Set all top nodes fixed in z plane at lambda*height
LAMBDA=EQUATIONS_SET%ANALYTIC%ANALYTIC_USER_PARAMS(FINITE_ELASTICITY_ANALYTIC_CYLINDER_PARAM_LAMBDA_IDX)
DO node_idx=1,SIZE(TOP_SURFACE_NODES,1)
user_node=TOP_SURFACE_NODES(node_idx)
!Need to test if this node is in current decomposition
CALL DECOMPOSITION_NODE_DOMAIN_GET(DECOMPOSITION,user_node,1,DOMAIN_NUMBER,err,error,*999)
IF(DOMAIN_NUMBER==myComputationalNodeNumber) THEN
CALL MeshTopology_NodeCheckExists(MESH,1,user_node,NODE_EXISTS,global_node,err,error,*999)
IF(.NOT.NODE_EXISTS) CYCLE
CALL DOMAIN_MAPPINGS_GLOBAL_TO_LOCAL_GET(NODES_MAPPING,global_node,NODE_EXISTS,local_node,err,error,*999)
!Default to version 1 of each node derivative
local_ny=GEOMETRIC_VARIABLE%COMPONENTS(3)%PARAM_TO_DOF_MAP%NODE_PARAM2DOF_MAP%NODES(local_node)% &
& DERIVATIVES(1)%VERSIONS(1)
DEFORMED_Z=GEOMETRIC_PARAMETERS(local_ny)*LAMBDA
!Default to version 1 of each node derivative
CALL BOUNDARY_CONDITIONS_SET_NODE(BOUNDARY_CONDITIONS,DEPENDENT_FIELD,FIELD_U_VARIABLE_TYPE,1,1, &
& user_node,ABS(TOP_NORMAL_XI),BOUNDARY_CONDITION_FIXED,DEFORMED_Z,err,error,*999)
ENDIF
ENDDO
!Set all bottom nodes fixed in z plane
DO node_idx=1,SIZE(BOTTOM_SURFACE_NODES,1)
user_node=BOTTOM_SURFACE_NODES(node_idx)
!Need to check this node exists in the current domain
CALL DECOMPOSITION_NODE_DOMAIN_GET(DECOMPOSITION,user_node,1,DOMAIN_NUMBER,err,error,*999)
IF(DOMAIN_NUMBER==myComputationalNodeNumber) THEN
!Default to version 1 of each node derivative
CALL BOUNDARY_CONDITIONS_SET_NODE(BOUNDARY_CONDITIONS,DEPENDENT_FIELD,FIELD_U_VARIABLE_TYPE,1,1, &
& user_node,ABS(BOTTOM_NORMAL_XI),BOUNDARY_CONDITION_FIXED,0.0_DP,err,error,*999)
ENDIF
ENDDO
!Set two nodes on the bottom surface to axial displacement only:
!Easier for parallel: Fix everything that can be fixed !!!
X_FIXED=.FALSE.
Y_FIXED=.FALSE.
DO node_idx=1,SIZE(BOTTOM_SURFACE_NODES,1)
user_node=BOTTOM_SURFACE_NODES(node_idx)
CALL DECOMPOSITION_NODE_DOMAIN_GET(DECOMPOSITION,user_node,1,DOMAIN_NUMBER,err,error,*999)
IF(DOMAIN_NUMBER==myComputationalNodeNumber) THEN
CALL MeshTopology_NodeCheckExists(MESH,1,user_node,NODE_EXISTS,global_node,err,error,*999)
IF(.NOT.NODE_EXISTS) CYCLE
CALL DOMAIN_MAPPINGS_GLOBAL_TO_LOCAL_GET(NODES_MAPPING,global_node,NODE_EXISTS,local_node,err,error,*999)
!Default to version 1 of each node derivative
local_ny=GEOMETRIC_VARIABLE%COMPONENTS(1)%PARAM_TO_DOF_MAP%NODE_PARAM2DOF_MAP%NODES(local_node)% &
& DERIVATIVES(1)%VERSIONS(1)
X(1)=GEOMETRIC_PARAMETERS(local_ny)
CALL MeshTopology_NodeCheckExists(MESH,1,user_node,NODE_EXISTS,global_node,err,error,*999)
IF(.NOT.NODE_EXISTS) CYCLE
CALL DOMAIN_MAPPINGS_GLOBAL_TO_LOCAL_GET(NODES_MAPPING,global_node,NODE_EXISTS,local_node, &
& err,error,*999)
!Default to version 1 of each node derivative
local_ny=GEOMETRIC_VARIABLE%COMPONENTS(2)%PARAM_TO_DOF_MAP%NODE_PARAM2DOF_MAP%NODES(local_node)% &
& DERIVATIVES(1)%VERSIONS(1)
X(2)=GEOMETRIC_PARAMETERS(local_ny)
IF(ABS(X(1))<1E-7_DP) THEN
!Default to version 1 of each node derivative
CALL BOUNDARY_CONDITIONS_SET_NODE(BOUNDARY_CONDITIONS,DEPENDENT_FIELD,FIELD_U_VARIABLE_TYPE,1,1, &
& user_node,1,BOUNDARY_CONDITION_FIXED,0.0_DP,err,error,*999)
X_FIXED=.TRUE.
ENDIF
IF(ABS(X(2))<1E-7_DP) THEN
!Default to version 1 of each node derivative
CALL BOUNDARY_CONDITIONS_SET_NODE(BOUNDARY_CONDITIONS,DEPENDENT_FIELD,FIELD_U_VARIABLE_TYPE,1,1, &
& user_node,2,BOUNDARY_CONDITION_FIXED,0.0_DP,err,error,*999)
Y_FIXED=.TRUE.
ENDIF
ENDIF
ENDDO
!Check it went well
CALL MPI_REDUCE(X_FIXED,X_OKAY,1,MPI_LOGICAL,MPI_LOR,0,computationalEnvironment%mpiCommunicator,MPI_IERROR)
CALL MPI_REDUCE(Y_FIXED,Y_OKAY,1,MPI_LOGICAL,MPI_LOR,0,computationalEnvironment%mpiCommunicator,MPI_IERROR)
IF(myComputationalNodeNumber==0) THEN
IF(.NOT.(X_OKAY.AND.Y_OKAY)) THEN
CALL FlagError("Could not fix nodes to prevent rigid body motion",err,error,*999)
ENDIF
ENDIF
ELSE
CALL FlagError("Domain nodes mapping is not associated.",err,error,*999)
ENDIF
ELSE
CALL FlagError("Generated mesh is not associated. For the Cylinder analytic solution, "// &
& "it must be available for automatic boundary condition assignment",err,error,*999)
ENDIF
ELSE
CALL FlagError("Mesh is not associated",err,error,*999)
ENDIF
ELSE
CALL FlagError("Decomposition is not associated",err,error,*999)
ENDIF
!Now calculate analytic solution
DO variable_idx=1,DEPENDENT_FIELD%NUMBER_OF_VARIABLES
variable_type=DEPENDENT_FIELD%VARIABLES(variable_idx)%VARIABLE_TYPE
FIELD_VARIABLE=>DEPENDENT_FIELD%VARIABLE_TYPE_MAP(variable_type)%ptr
IF(variable_idx==1) CALL WRITE_STRING_VALUE(GENERAL_OUTPUT_TYPE," Global number of dofs : ", &
& FIELD_VARIABLE%NUMBER_OF_GLOBAL_DOFS,err,error,*999)
IF(ASSOCIATED(FIELD_VARIABLE)) THEN
CALL FIELD_PARAMETER_SET_CREATE(DEPENDENT_FIELD,variable_type,FIELD_ANALYTIC_VALUES_SET_TYPE,err,error,*999)
component_idx=1 !Assuming components 1..3 use a common mesh component and 4 uses a different one
IF(FIELD_VARIABLE%COMPONENTS(component_idx)%INTERPOLATION_TYPE==FIELD_NODE_BASED_INTERPOLATION) THEN
DOMAIN=>FIELD_VARIABLE%COMPONENTS(component_idx)%DOMAIN
IF(ASSOCIATED(DOMAIN)) THEN
IF(ASSOCIATED(DOMAIN%TOPOLOGY)) THEN
DOMAIN_NODES=>DOMAIN%TOPOLOGY%NODES
IF(ASSOCIATED(DOMAIN_NODES)) THEN
!Also grab the equivalent pointer for pressure component
IF(FIELD_VARIABLE%COMPONENTS(4)%INTERPOLATION_TYPE==FIELD_NODE_BASED_INTERPOLATION) THEN
DOMAIN_PRESSURE=>FIELD_VARIABLE%COMPONENTS(4)%DOMAIN
IF(ASSOCIATED(DOMAIN_PRESSURE)) THEN
IF(ASSOCIATED(DOMAIN_PRESSURE%TOPOLOGY)) THEN
DOMAIN_PRESSURE_NODES=>DOMAIN_PRESSURE%TOPOLOGY%NODES
IF(ASSOCIATED(DOMAIN_PRESSURE_NODES)) THEN
!Loop over the local nodes excluding the ghosts.
DO node_idx=1,DOMAIN_NODES%NUMBER_OF_NODES
!!TODO \todo We should interpolate the geometric field here and the node position.
DO dim_idx=1,NUMBER_OF_DIMENSIONS
!Default to version 1 of each node derivative
local_ny=GEOMETRIC_VARIABLE%COMPONENTS(dim_idx)%PARAM_TO_DOF_MAP%NODE_PARAM2DOF_MAP% &
& NODES(node_idx)%DERIVATIVES(1)%VERSIONS(1)
X(dim_idx)=GEOMETRIC_PARAMETERS(local_ny)
ENDDO !dim_idx
!Loop over the derivatives
DO deriv_idx=1,DOMAIN_NODES%NODES(node_idx)%NUMBER_OF_DERIVATIVES
SELECT CASE(EQUATIONS_SET%ANALYTIC%ANALYTIC_FUNCTION_TYPE)
CASE(EQUATIONS_SET_FINITE_ELASTICITY_CYLINDER)
!Cylinder inflation, extension, torsion
SELECT CASE(variable_type)
CASE(FIELD_U_VARIABLE_TYPE)
SELECT CASE(DOMAIN_NODES%NODES(node_idx)%DERIVATIVES(deriv_idx)%GLOBAL_DERIVATIVE_INDEX)
CASE(NO_GLOBAL_DERIV)
!Do all components at the same time (r,theta,z)->(x,y,z) & p
CALL FiniteElasticity_CylinderAnalyticCalculate(X, &
& EQUATIONS_SET%ANALYTIC%ANALYTIC_USER_PARAMS,DEFORMED_X,P,err,error,*999)
CASE(GLOBAL_DERIV_S1)
CALL FlagError("Not implemented.",err,error,*999)
CASE(GLOBAL_DERIV_S2)
CALL FlagError("Not implemented.",err,error,*999)
CASE(GLOBAL_DERIV_S1_S2)
CALL FlagError("Not implemented.",err,error,*999)
CASE DEFAULT
LOCAL_ERROR="The global derivative index of "//TRIM(NumberToVString( &
DOMAIN_NODES%NODES(node_idx)%DERIVATIVES(deriv_idx)%GLOBAL_DERIVATIVE_INDEX,"*", &
& err,error))//" is invalid."
CALL FlagError(LOCAL_ERROR,err,error,*999)
END SELECT
CASE(FIELD_DELUDELN_VARIABLE_TYPE)
SELECT CASE(DOMAIN_NODES%NODES(node_idx)%DERIVATIVES(deriv_idx)%GLOBAL_DERIVATIVE_INDEX)
CASE(NO_GLOBAL_DERIV)
!Not implemented, but don't want to cause an error so do nothing
CASE(GLOBAL_DERIV_S1)
CALL FlagError("Not implemented.",err,error,*999)
CASE(GLOBAL_DERIV_S2)
CALL FlagError("Not implemented.",err,error,*999)
CASE(GLOBAL_DERIV_S1_S2)
CALL FlagError("Not implemented.",err,error,*999)
CASE DEFAULT
LOCAL_ERROR="The global derivative index of "//TRIM(NumberToVString( &
DOMAIN_NODES%NODES(node_idx)%DERIVATIVES(deriv_idx)%GLOBAL_DERIVATIVE_INDEX,"*", &
& err,error))//" is invalid."
CALL FlagError(LOCAL_ERROR,err,error,*999)
END SELECT
CASE DEFAULT
LOCAL_ERROR="The variable type "//TRIM(NumberToVString(variable_type,"*",err,error)) &
& //" is invalid."
CALL FlagError(LOCAL_ERROR,err,error,*999)
END SELECT
CASE DEFAULT
LOCAL_ERROR="The analytic function type of "// &
& TRIM(NumberToVString(EQUATIONS_SET%ANALYTIC%ANALYTIC_FUNCTION_TYPE,"*",err,error))// &
& " is invalid."
CALL FlagError(LOCAL_ERROR,err,error,*999)
END SELECT
!Set the analytic solution to parameter set
DO component_idx=1,NUMBER_OF_DIMENSIONS
!Default to version 1 of each node derivative
local_ny=FIELD_VARIABLE%COMPONENTS(component_idx)%PARAM_TO_DOF_MAP% &
& NODE_PARAM2DOF_MAP%NODES(node_idx)%DERIVATIVES(deriv_idx)%VERSIONS(1)
CALL Field_ParameterSetUpdateLocalDOF(DEPENDENT_FIELD,variable_type, &
& FIELD_ANALYTIC_VALUES_SET_TYPE,local_ny,DEFORMED_X(component_idx),err,error,*999)
ENDDO
!Don't forget the pressure component
user_node=DOMAIN_NODES%NODES(node_idx)%USER_NUMBER
CALL MeshTopology_NodeCheckExists(MESH,DOMAIN_PRESSURE%MESH_COMPONENT_NUMBER,user_node, &
& NODE_EXISTS,global_node,err,error,*999)
IF(NODE_EXISTS) THEN
CALL DECOMPOSITION_NODE_DOMAIN_GET(DECOMPOSITION,user_node, &
& DOMAIN_PRESSURE%MESH_COMPONENT_NUMBER,DOMAIN_NUMBER,err,error,*999)
IF(DOMAIN_NUMBER==myComputationalNodeNumber) THEN
!\todo: test the domain node mappings pointer properly
local_node=DOMAIN_PRESSURE%mappings%nodes%global_to_local_map(global_node)%local_number(1)
!Default to version 1 of each node derivative
local_ny=FIELD_VARIABLE%COMPONENTS(4)%PARAM_TO_DOF_MAP%NODE_PARAM2DOF_MAP% &
& NODES(local_node)%DERIVATIVES(deriv_idx)%VERSIONS(1)
!Because p=2.lambda in this particular constitutive law, we'll assign half the
!hydrostatic pressure to the analytic array
CALL Field_ParameterSetUpdateLocalDOF(DEPENDENT_FIELD,variable_type, &
& FIELD_ANALYTIC_VALUES_SET_TYPE,local_ny,P/2.0_dp,err,error,*999)
ENDIF
ENDIF
ENDDO !deriv_idx
ENDDO !node_idx
ELSE
CALL FlagError("Domain for pressure topology node is not associated",err,error,*999)
ENDIF
ELSE
CALL FlagError("Domain for pressure topology is not associated",err,error,*999)
ENDIF
ELSE
CALL FlagError("Domain for pressure component is not associated",err,error,*999)
ENDIF
ELSE
CALL FlagError("Non-nodal based interpolation of pressure cannot be used with analytic solutions", &
& err,error,*999)
ENDIF
ELSE
CALL FlagError("Domain topology nodes is not associated.",err,error,*999)
ENDIF
ELSE
CALL FlagError("Domain topology is not associated.",err,error,*999)
ENDIF
ELSE
CALL FlagError("Domain is not associated.",err,error,*999)
ENDIF
ELSE
CALL FlagError("Only node based interpolation is implemented.",err,error,*999)
ENDIF
CALL Field_ParameterSetUpdateStart(DEPENDENT_FIELD,variable_type,FIELD_ANALYTIC_VALUES_SET_TYPE, &
& err,error,*999)
CALL Field_ParameterSetUpdateFinish(DEPENDENT_FIELD,variable_type,FIELD_ANALYTIC_VALUES_SET_TYPE, &
& err,error,*999)
ELSE
CALL FlagError("Field variable is not associated.",err,error,*999)
ENDIF
ENDDO !variable_idx
CALL Field_ParameterSetDataRestore(GEOMETRIC_FIELD,FIELD_U_VARIABLE_TYPE,FIELD_VALUES_SET_TYPE, &
& GEOMETRIC_PARAMETERS,err,error,*999)
ELSE
CALL FlagError("Boundary conditions is not associated.",err,error,*999)
ENDIF
ELSE
CALL FlagError("Equations set geometric field is not associated.",err,error,*999)
ENDIF
ELSE
CALL FlagError("Equations set dependent field is not associated.",err,error,*999)
ENDIF
ELSE
CALL FlagError("Equations set analytic is not associated.",err,error,*999)
ENDIF
ELSE
CALL FlagError("Equations set is not associated.",err,error,*999)
ENDIF
EXITS("FiniteElasticity_BoundaryConditionsAnalyticCalculate")
RETURN
999 ERRORS("FiniteElasticity_BoundaryConditionsAnalyticCalculate",err,error)
EXITS("FiniteElasticity_BoundaryConditionsAnalyticCalculate")
RETURN 1
END SUBROUTINE FiniteElasticity_BoundaryConditionsAnalyticCalculate
!
!================================================================================================================================
!
!>Calcualates the analytic solution (deformed coordinates and hydrostatic pressure) for cylinder inflation+extension+torsion problem
SUBROUTINE FiniteElasticity_CylinderAnalyticCalculate(X,ANALYTIC_USER_PARAMS,DEFORMED_X,P,err,error,*)
!Argument variables
REAL(DP), INTENT(IN) :: X(:) !<Undeformed coordinates
REAL(DP), INTENT(IN) :: ANALYTIC_USER_PARAMS(:) !<Array containing the problem parameters
REAL(DP), INTENT(OUT) :: DEFORMED_X(3) !<Deformed coordinates
REAL(DP), INTENT(OUT) :: P !<Hydrostatic pressure at the given material coordintae
INTEGER(INTG), INTENT(OUT) :: ERR !<The error code
TYPE(VARYING_STRING), INTENT(OUT) :: ERROR !<The error string
!Local variables
REAL(DP) :: PIN,POUT,LAMBDA,TSI,A1,A2,C1,C2 !A1=external radius, A2=internal radius
REAL(DP) :: MU1,MU2,MU,K
REAL(DP) :: F,F2,DF
REAL(DP) :: R,THETA ! Undeformed coordinates in radial coordinates
REAL(DP) :: DEFORMED_R,DEFORMED_THETA
REAL(DP) :: DELTA,RES
REAL(DP), PARAMETER :: STEP=1E-5_DP, RELTOL=1E-12_DP
ENTERS("FiniteElasticity_CylinderAnalyticCalculate",err,error,*999)
!Grab problem parameters
PIN=ANALYTIC_USER_PARAMS(FINITE_ELASTICITY_ANALYTIC_CYLINDER_PARAM_PIN_IDX)
POUT=ANALYTIC_USER_PARAMS(FINITE_ELASTICITY_ANALYTIC_CYLINDER_PARAM_POUT_IDX)
LAMBDA=ANALYTIC_USER_PARAMS(FINITE_ELASTICITY_ANALYTIC_CYLINDER_PARAM_LAMBDA_IDX)
TSI=ANALYTIC_USER_PARAMS(FINITE_ELASTICITY_ANALYTIC_CYLINDER_PARAM_TSI_IDX)
A1=ANALYTIC_USER_PARAMS(FINITE_ELASTICITY_ANALYTIC_CYLINDER_PARAM_ROUT_IDX) ! external radius
A2=ANALYTIC_USER_PARAMS(FINITE_ELASTICITY_ANALYTIC_CYLINDER_PARAM_RIN_IDX) ! internal radius
C1=ANALYTIC_USER_PARAMS(FINITE_ELASTICITY_ANALYTIC_CYLINDER_PARAM_C1_IDX)
C2=ANALYTIC_USER_PARAMS(FINITE_ELASTICITY_ANALYTIC_CYLINDER_PARAM_C2_IDX)
!Solve for MU1 - Newton's method (\todo: Implement here, or separate out for general use?)
MU1=1.0_DP !Initial guess - need a better way!
DO
!Calculate f(MU1)
F=FINITE_ELASTICITY_CYLINDER_ANALYTIC_FUNC_EVALUATE(MU1,PIN,POUT,LAMBDA,TSI,A1,A2,C1,C2,err,error)
IF(ERR/=0) GOTO 999
!Calculate f'(MU1) by finite differencing
F2=FINITE_ELASTICITY_CYLINDER_ANALYTIC_FUNC_EVALUATE(MU1+STEP,PIN,POUT,LAMBDA,TSI,A1,A2,C1,C2,err,error)
IF(ERR/=0) GOTO 999
DF=(F2-F)/STEP
!Next increment for MU1
DELTA=-F/DF
!Ensure that the step actually reduces residual
F2=FINITE_ELASTICITY_CYLINDER_ANALYTIC_FUNC_EVALUATE(MU1+DELTA,PIN,POUT,LAMBDA,TSI,A1,A2,C1,C2,err,error)
IF(ERR/=0) GOTO 999
DO
IF (ABS(F2)<ABS(F).OR.ABS(F2)<ZERO_TOLERANCE) THEN ! PASS
MU1=MU1+DELTA
EXIT
ELSEIF (DELTA<1E-3_DP) THEN ! FAIL: It's likely that the initial guess is too far away
CALL FlagError("FiniteElasticity_CylinderAnalyticCalculate failed to converge.",err,error,*999)
ELSE ! KEEP GOING
DELTA=DELTA/2.0_DP
F2=FINITE_ELASTICITY_CYLINDER_ANALYTIC_FUNC_EVALUATE(MU1+DELTA,PIN,POUT,LAMBDA,TSI,A1,A2,C1,C2,err,error)
IF(ERR/=0) GOTO 999
ENDIF
ENDDO
!Test for convergence: relative residual
RES=DELTA/(1.0_DP+MU1)
IF (RES<RELTOL) EXIT
ENDDO
!Calculate MU2
MU2=SQRT(((A1/A2)**2*(LAMBDA*MU1**2-1.0_DP)+1.0_DP)/LAMBDA)
!Calculate radius and angle from undeformed coordinates
R=SQRT(X(1)**2+X(2)**2)
THETA=ATAN2(X(2),X(1)) ! in radians
!Calculate deformed coordinates
K=A1**2*(LAMBDA*MU1**2-1.0_DP)
MU=SQRT(1.0_DP/LAMBDA*(1.0_DP+K/R**2))
DEFORMED_R=MU*R
DEFORMED_THETA=THETA+TSI*LAMBDA*X(3)
DEFORMED_X(1)=DEFORMED_R*COS(DEFORMED_THETA)
DEFORMED_X(2)=DEFORMED_R*SIN(DEFORMED_THETA)
DEFORMED_X(3)=LAMBDA*X(3)
!Calculate pressure
P=POUT-(C1/LAMBDA+C2*LAMBDA)*(1.0_DP/LAMBDA/MU1**2-R**2/(R**2+K)+LOG(MU**2/MU1**2))+C1*TSI**2*LAMBDA*(R**2-A1**2) &
& -2.0_DP*(C1/LAMBDA**2/MU**2+C2*(1.0_DP/LAMBDA**2+1.0_DP/MU**2+TSI**2*R**2))
EXITS("FiniteElasticity_CylinderAnalyticCalculate")
RETURN
999 ERRORSEXITS("FiniteElasticity_CylinderAnalyticCalculate",err,error)
RETURN 1
END SUBROUTINE FiniteElasticity_CylinderAnalyticCalculate
!
!================================================================================================================================
!
!>Evaluates the residual function required to solve for MU1, in the cylinder analytic example
FUNCTION FINITE_ELASTICITY_CYLINDER_ANALYTIC_FUNC_EVALUATE(MU1,PIN,POUT,LAMBDA,TSI,A1,A2,C1,C2,err,error)
!Argument variables
REAL(DP) :: FINITE_ELASTICITY_CYLINDER_ANALYTIC_FUNC_EVALUATE
REAL(DP) :: MU1,PIN,POUT,LAMBDA,TSI,A1,A2,C1,C2
INTEGER(INTG) :: ERR
TYPE(VARYING_STRING) :: ERROR
!Local variables
REAL(DP) :: MU,K
ENTERS("FINITE_ELASTICITY_CYLINDER_ANALYTIC_FUNC_EVALUATE",err,error,*999)
K=A1**2*(LAMBDA*MU1**2-1.0_DP)
MU=SQRT(1.0_DP/LAMBDA*(1.0_DP+K/A2**2))
FINITE_ELASTICITY_CYLINDER_ANALYTIC_FUNC_EVALUATE= &
& 2.0_DP*(C1/LAMBDA**2/MU**2 + C2*(1.0_DP/LAMBDA**2+1.0_DP/MU**2+TSI**2*A2**2))+ &
& POUT-(C1/LAMBDA+C2*LAMBDA)*(1.0_DP/LAMBDA/MU1**2-A2**2/(A2**2+K)+2*LOG(MU/MU1))+ &
& C1*TSI**2*LAMBDA*(A2**2-A1**2)-2.0_DP*(C1/LAMBDA**2/MU**2+C2*(1.0_DP/LAMBDA**2+ &
& 1.0_DP/MU**2+TSI**2*A2**2))+PIN
EXITS("FINITE_ELASTICITY_CYLINDER_ANALYTIC_FUNC_EVALUATE")
RETURN
999 ERRORS("FINITE_ELASTICITY_CYLINDER_ANALYTIC_FUNC_EVALUATE",err,error)
EXITS("FINITE_ELASTICITY_CYLINDER_ANALYTIC_FUNC_EVALUATE")
RETURN
END FUNCTION FINITE_ELASTICITY_CYLINDER_ANALYTIC_FUNC_EVALUATE
!
!================================================================================================================================
!
!>Evaluates the spatial elasticity and stress tensor in Voigt form at a given Gauss point.
SUBROUTINE FINITE_ELASTICITY_GAUSS_ELASTICITY_TENSOR(EQUATIONS_SET,DEPENDENT_INTERPOLATED_POINT, &
& MATERIALS_INTERPOLATED_POINT,ELASTICITY_TENSOR,HYDRO_ELASTICITY_VOIGT,STRESS_TENSOR,DZDNU, &
& Jznu,ELEMENT_NUMBER,GAUSS_POINT_NUMBER,ERR,ERROR,*)
!Argument variables
TYPE(EQUATIONS_SET_TYPE), POINTER, INTENT(IN) :: EQUATIONS_SET !<A pointer to the equations set
TYPE(FIELD_INTERPOLATED_POINT_TYPE), POINTER :: DEPENDENT_INTERPOLATED_POINT,MATERIALS_INTERPOLATED_POINT
REAL(DP), INTENT(OUT) :: ELASTICITY_TENSOR(:,:) !< Rank 4 elasticity tensor in Voigt notation
REAL(DP), INTENT(OUT) :: HYDRO_ELASTICITY_VOIGT(:) !<Rank 2 hydrostatic portion of the elasticity tensor in Voigt notation
REAL(DP), INTENT(OUT) :: STRESS_TENSOR(:) !< Rank 2 stress tensor in Voigt notation
REAL(DP), INTENT(IN) :: DZDNU(:,:)!< The deformation gradient
REAL(DP), INTENT(IN) :: Jznu !< The Jacobian
INTEGER(INTG), INTENT(IN) :: ELEMENT_NUMBER,GAUSS_POINT_NUMBER !<Element/Gauss point number
INTEGER(INTG), INTENT(OUT) :: ERR !<The error code
TYPE(VARYING_STRING), INTENT(OUT) :: ERROR !<The error string
!Local Variables
INTEGER(INTG) :: PRESSURE_COMPONENT,i,j,dof_idx
REAL(DP) :: P, I1, I3
REAL(DP) :: DZDNUT(3,3),AZL(3,3),AZU(3,3),TEMP(3,3)
REAL(DP) :: AZLv(6), AZUv(6) !<Voigt forms of the C and C^-1 tensors.
REAL(DP) :: TEMPTERM1,TEMPTERM2,VALUE
REAL(DP), POINTER :: C(:) !Parameters for constitutive laws
REAL(DP) :: B(6),E(6),DQ_DE(6),Q
REAL(DP) :: I3EE(6,6) !<Derivative of I3 wrt E
REAL(DP) :: ADJCC(6,6) !<Derivative of adj(C) wrt C
REAL(DP) :: AZUE(6,6) !<Derivative of C^-1 wrt E
TYPE(FIELD_VARIABLE_TYPE), POINTER :: FIELD_VARIABLE
TYPE(VARYING_STRING) :: LOCAL_ERROR
ENTERS("FINITE_ELASTICITY_GAUSS_ELASTICITY_TENSOR",ERR,ERROR,*999)
NULLIFY(FIELD_VARIABLE,C)
!AZL = F'*F (deformed covariant or right cauchy deformation tensor, C)
!AZU - deformed contravariant tensor; I3 = det(C)
!E = Green-Lagrange strain tensor = 0.5*(C-I)
!P is the hydrostatic pressure
! Evaluate the Cauchy strain tensor C.
CALL MatrixTranspose(DZDNU,DZDNUT,ERR,ERROR,*999)
CALL MatrixProduct(DZDNUT,DZDNU,AZL,ERR,ERROR,*999)
CALL Invert(AZL,AZU,I3,ERR,ERROR,*999)
! Evaluate the derivative of AZU wrt to E (AZUE) for the hydrostatic term. Formulation from Nam-Ho Kim book, pg.198.
AZLv(1) = AZL(1,1)
AZLv(2) = AZL(2,2)
AZLv(3) = AZL(3,3)
AZLv(4) = AZL(1,2)
AZLv(5) = AZL(1,3)
AZLv(6) = AZL(2,3)
AZUv(1) = AZU(1,1)
AZUv(2) = AZU(2,2)
AZUv(3) = AZU(3,3)
AZUv(4) = AZU(1,2)
AZUv(5) = AZU(1,3)
AZUv(6) = AZU(2,3)
I3EE = RESHAPE([0.0_DP, 4.0_DP*AZLv(3), 4.0_DP*AZLv(2), 0.0_DP, 0.0_DP,-4.0_DP*AZLv(6), &
& 4.0_DP*AZLv(3), 0.0_DP, 4.0_DP*AZLv(1), 0.0_DP,-4.0_DP*AZLv(5), 0.0_DP, &
& 4.0_DP*AZLv(2), 4.0_DP*AZLv(1), 0.0_DP, -2.0_DP*AZLv(4), 0.0_DP, 0.0_DP, &
& 0.0_DP, 0.0_DP, -4.0_DP*AZLv(4), -2.0_DP*AZLv(3), 2.0_DP*AZLv(6), 2.0_DP*AZLv(5), &
& 0.0_DP, -4.0_DP*AZLv(5), 0.0_DP, 2.0_DP*AZLv(6), -2.0_DP*AZLv(2), 2.0_DP*AZLv(4), &
& -4.0_DP*AZLv(6), 0.0_DP, 0.0_DP, 2.0_DP*AZLv(5), 2.0_DP*AZLv(4), -2.0_DP*AZLv(1)], [6,6])
ADJCC = RESHAPE([0.0_DP, AZLv(3), AZLv(2), 0.0_DP, 0.0_DP,-AZLv(6), &
& AZLv(3), 0.0_DP, AZLv(1), 0.0_DP,-AZLv(5), 0.0_DP, &
& AZLv(2), AZLv(1), 0.0_DP, -AZLv(4), 0.0_DP, 0.0_DP, &
& 0.0_DP, 0.0_DP, -AZLv(4), -0.5_DP*AZLv(3), 0.5_DP*AZLv(6), 0.5_DP*AZLv(5), &
& 0.0_DP, -AZLv(5), 0.0_DP,0.5_DP*AZLv(6), -0.5_DP*AZLv(2), 0.5_DP*AZLv(4), &
& -AZLv(6), 0.0_DP, 0.0_DP, 0.5_DP*AZLv(5), 0.5_DP*AZLv(4), -0.5_DP*AZLv(1)], [6,6])
!DO i=1,6
! DO j=1,6
! AZUE(i,j) = -2.0_DP*AZUv(i)*AZUv(j) + 2.0_DP*ADJCC(i,j)/I3
! ENDDO
!ENDDO
DO i=1,6
DO j=1,6
AZUE(i,j) = -2.0_DP*AZUv(i)*AZUv(j) + 0.5_DP*I3EE(i,j)/I3
ENDDO
ENDDO
C=>MATERIALS_INTERPOLATED_POINT%VALUES(:,NO_PART_DERIV)
ELASTICITY_TENSOR=0.0_DP
SELECT CASE(EQUATIONS_SET%specification(3))
CASE(EQUATIONS_SET_MOONEY_RIVLIN_ACTIVECONTRACTION_SUBTYPE, &
& EQUATIONS_SET_MOONEY_RIVLIN_SUBTYPE, &
& EQUATIONS_SET_MR_AND_GROWTH_LAW_IN_CELLML_SUBTYPE)
LOCAL_ERROR="Analytic Jacobian has not been validated for the Mooney-Rivlin equations, please use finite differences instead."
CALL FlagWarning(LOCAL_ERROR,ERR,ERROR,*999)
PRESSURE_COMPONENT=DEPENDENT_INTERPOLATED_POINT%INTERPOLATION_PARAMETERS%FIELD_VARIABLE%NUMBER_OF_COMPONENTS
P=DEPENDENT_INTERPOLATED_POINT%VALUES(PRESSURE_COMPONENT,NO_PART_DERIV)
!Form of constitutive model is:
! W=c1*(I1-3)+c2*(I2-3)+p/2*(I3-1)
! Calculate isochoric fictitious 2nd Piola tensor (in Voigt form)
I1=AZL(1,1)+AZL(2,2)+AZL(3,3)
TEMPTERM1=-2.0_DP*C(2)
TEMPTERM2=2.0_DP*(C(1)+I1*C(2))
STRESS_TENSOR(1)=TEMPTERM1*AZL(1,1)+TEMPTERM2
STRESS_TENSOR(2)=TEMPTERM1*AZL(2,2)+TEMPTERM2
STRESS_TENSOR(3)=TEMPTERM1*AZL(3,3)+TEMPTERM2
STRESS_TENSOR(4)=TEMPTERM1*AZL(2,1)
STRESS_TENSOR(5)=TEMPTERM1*AZL(3,1)
STRESS_TENSOR(6)=TEMPTERM1*AZL(3,2)
IF(EQUATIONS_SET%specification(3)==EQUATIONS_SET_MOONEY_RIVLIN_ACTIVECONTRACTION_SUBTYPE) THEN
!add active contraction stress values
!Be aware for modified DZDNU, should active contraction be added here? Normally should be okay as modified DZDNU and DZDNU
!converge during the Newton iteration.
CALL Field_VariableGet(EQUATIONS_SET%INDEPENDENT%INDEPENDENT_FIELD,FIELD_U_VARIABLE_TYPE,FIELD_VARIABLE,ERR,ERROR,*999)
DO i=1,FIELD_VARIABLE%NUMBER_OF_COMPONENTS
dof_idx=FIELD_VARIABLE%COMPONENTS(i)%PARAM_TO_DOF_MAP%GAUSS_POINT_PARAM2DOF_MAP% &
& GAUSS_POINTS(GAUSS_POINT_NUMBER,ELEMENT_NUMBER)
CALL FIELD_PARAMETER_SET_GET_LOCAL_DOF(EQUATIONS_SET%INDEPENDENT%INDEPENDENT_FIELD,FIELD_U_VARIABLE_TYPE, &
& FIELD_VALUES_SET_TYPE,dof_idx,VALUE,ERR,ERROR,*999)
STRESS_TENSOR(i)=STRESS_TENSOR(i)+VALUE
ENDDO
ENDIF
! Calculate material elasticity tensor (in Voigt form) as
! this will be compensated for in the push-forward with the modified deformation gradient.
TEMPTERM1=4.0_DP*C(2)
TEMPTERM2=-2.0_DP*C(2)
ELASTICITY_TENSOR(2,1)=TEMPTERM1
ELASTICITY_TENSOR(3,1)=TEMPTERM1
ELASTICITY_TENSOR(1,2)=TEMPTERM1
ELASTICITY_TENSOR(3,2)=TEMPTERM1
ELASTICITY_TENSOR(1,3)=TEMPTERM1
ELASTICITY_TENSOR(2,3)=TEMPTERM1
ELASTICITY_TENSOR(4,4)=TEMPTERM2
ELASTICITY_TENSOR(5,5)=TEMPTERM2
ELASTICITY_TENSOR(6,6)=TEMPTERM2
!Add volumetric part of elasticity tensor - p*d(C^-1)/dE.
ELASTICITY_TENSOR=ELASTICITY_TENSOR + P*AZUE
!Hydrostatic portion of the elasticity tensor (dS/dp)
HYDRO_ELASTICITY_VOIGT = AZUv
! Do push-forward of 2nd Piola tensor and the material elasticity tensor.
CALL FINITE_ELASTICITY_PUSH_STRESS_TENSOR(STRESS_TENSOR,DZDNU,Jznu,ERR,ERROR,*999)
CALL FINITE_ELASTICITY_PUSH_STRESS_TENSOR(HYDRO_ELASTICITY_VOIGT,DZDNU,Jznu,ERR,ERROR,*999)
CALL FINITE_ELASTICITY_PUSH_ELASTICITY_TENSOR(ELASTICITY_TENSOR,DZDNU,Jznu,ERR,ERROR,*999)
! Add volumetric parts.
STRESS_TENSOR(1:3)=STRESS_TENSOR(1:3)+P
CASE(EQUATIONS_SET_TRANSVERSE_ISOTROPIC_GUCCIONE_SUBTYPE,EQUATIONS_SET_GUCCIONE_ACTIVECONTRACTION_SUBTYPE, &
& EQUATIONS_SET_REFERENCE_STATE_TRANSVERSE_GUCCIONE_SUBTYPE)
PRESSURE_COMPONENT=DEPENDENT_INTERPOLATED_POINT%INTERPOLATION_PARAMETERS%FIELD_VARIABLE%NUMBER_OF_COMPONENTS
P=DEPENDENT_INTERPOLATED_POINT%VALUES(PRESSURE_COMPONENT,NO_PART_DERIV)
B=[2.0_DP*C(2),2.0_DP*C(3),2.0_DP*C(3),C(4),C(4),C(3)] ![2*b_f,2*b_t,2*b_t,b_ft,b_ft,b_t]
E=[0.5_DP*(AZL(1,1)-1.0_DP),0.5_DP*(AZL(2,2)-1.0_DP),0.5_DP*(AZL(3,3)-1.0_DP),AZL(2,1),AZL(3,1),AZL(3,2)] !(Modified) strain tensor in Voigt form.
DQ_DE=B*E
TEMPTERM1=0.5_DP*C(1)*EXP(0.5_DP*DOT_PRODUCT(E,DQ_DE))
!Calculate 2nd Piola tensor (in Voigt form)
STRESS_TENSOR=TEMPTERM1*DQ_DE + P*AZUv
IF(EQUATIONS_SET%specification(3)==EQUATIONS_SET_GUCCIONE_ACTIVECONTRACTION_SUBTYPE) THEN
!add active contraction stress values
CALL Field_VariableGet(EQUATIONS_SET%INDEPENDENT%INDEPENDENT_FIELD,FIELD_U_VARIABLE_TYPE,FIELD_VARIABLE,ERR,ERROR,*999)
DO i=1,FIELD_VARIABLE%NUMBER_OF_COMPONENTS
dof_idx=FIELD_VARIABLE%COMPONENTS(i)%PARAM_TO_DOF_MAP%GAUSS_POINT_PARAM2DOF_MAP% &
& GAUSS_POINTS(GAUSS_POINT_NUMBER,ELEMENT_NUMBER)
CALL FIELD_PARAMETER_SET_GET_LOCAL_DOF(EQUATIONS_SET%INDEPENDENT%INDEPENDENT_FIELD,FIELD_U_VARIABLE_TYPE, &
& FIELD_VALUES_SET_TYPE,dof_idx,VALUE,ERR,ERROR,*999)
STRESS_TENSOR(i)=STRESS_TENSOR(i)+VALUE
ENDDO
ENDIF
!\todo blas has routines specifically for symmetric matrices, so it would be worth to check if these could give some speedup.
! Calculate material elasticity tensor c (in Voigt form).
! First calculate lower part of 6X6 matrix
DO j=1,6
DO i=j,6
ELASTICITY_TENSOR(i,j)=TEMPTERM1*DQ_DE(i)*DQ_DE(j)
ENDDO
ENDDO
B=[2.0_DP*C(2),2.0_DP*C(3),2.0_DP*C(3),C(4),C(4),C(3)]
DO i=1,6
ELASTICITY_TENSOR(i,i)=ELASTICITY_TENSOR(i,i)+TEMPTERM1*B(i)
ENDDO
! Then calculate upper part.
DO j=2,6
DO i=1,j-1
ELASTICITY_TENSOR(i,j)=ELASTICITY_TENSOR(j,i)
ENDDO
ENDDO
!Add volumetric part of elasticity tensor - p*d(C^-1)/dE.
ELASTICITY_TENSOR=ELASTICITY_TENSOR + P*AZUE
!Hydrostatic portion of the elasticity tensor (dS/dp)
HYDRO_ELASTICITY_VOIGT = AZUv
!Do push-forward of 2nd Piola tensor and the material elasticity tensor.
CALL FINITE_ELASTICITY_PUSH_STRESS_TENSOR(STRESS_TENSOR,DZDNU,Jznu,ERR,ERROR,*999)
CALL FINITE_ELASTICITY_PUSH_STRESS_TENSOR(HYDRO_ELASTICITY_VOIGT,DZDNU,Jznu,ERR,ERROR,*999)
CALL FINITE_ELASTICITY_PUSH_ELASTICITY_TENSOR(ELASTICITY_TENSOR,DZDNU,Jznu,ERR,ERROR,*999)
CASE DEFAULT
LOCAL_ERROR="Analytic Jacobian has not been implemented for the third equations set specification of "// &
& TRIM(NumberToVString(EQUATIONS_SET%specification(3),"*",ERR,ERROR))
CALL FlagError(LOCAL_ERROR,ERR,ERROR,*999)
END SELECT
EXITS("FINITE_ELASTICITY_GAUSS_ELASTICITY_TENSOR")
RETURN
999 ERRORSEXITS("FINITE_ELASTICITY_GAUSS_ELASTICITY_TENSOR",ERR,ERROR)
RETURN 1
END SUBROUTINE FINITE_ELASTICITY_GAUSS_ELASTICITY_TENSOR
!
!================================================================================================================================
!
!>Evaluates the element Jacobian matrix for the given element number for a finite elasticity class finite element equation set.
SUBROUTINE FiniteElasticity_FiniteElementJacobianEvaluate(EQUATIONS_SET,ELEMENT_NUMBER,err,error,*)
!Argument variables
TYPE(EQUATIONS_SET_TYPE), POINTER :: EQUATIONS_SET !<A pointer to the equations set
INTEGER(INTG), INTENT(IN) :: ELEMENT_NUMBER !<The element number to evaluate the Jacobian for
INTEGER(INTG), INTENT(OUT) :: ERR !<The error code
TYPE(VARYING_STRING), INTENT(OUT) :: ERROR !<The error string
!Local Variables
INTEGER(INTG) :: FIELD_VAR_TYPE,ng,nh,ns,nhs,ni,mh,ms,mhs,oh
INTEGER(INTG) :: PRESSURE_COMPONENT
INTEGER(INTG) :: SUM_ELEMENT_PARAMETERS,TOTAL_NUMBER_OF_SURFACE_PRESSURE_CONDITIONS
INTEGER(INTG) :: NUMBER_OF_DIMENSIONS,NUMBER_OF_XI
INTEGER(INTG) :: ELEMENT_BASE_DOF_INDEX(4),component_idx,component_idx2
INTEGER(INTG), PARAMETER :: OFF_DIAG_COMP(3)=[0,1,3],OFF_DIAG_DEP_VAR1(3)=[1,1,2],OFF_DIAG_DEP_VAR2(3)=[2,3,3]
INTEGER(INTG) :: MESH_COMPONENT_NUMBER,NUMBER_OF_ELEMENT_PARAMETERS(4)
REAL(DP) :: DZDNU(3,3),CAUCHY_TENSOR(3,3),HYDRO_ELASTICITY_TENSOR(3,3)
REAL(DP) :: JGW_SUB_MAT(3,3)
REAL(DP) :: TEMPVEC(3)
REAL(DP) :: STRESS_TENSOR(6),ELASTICITY_TENSOR(6,6),HYDRO_ELASTICITY_VOIGT(6)
REAL(DP) :: DPHIDZ(3,64,3),DJDZ(64,3)
REAL(DP) :: JGW_DPHINS_DZ,JGW_DPHIMS_DZ,PHIMS,PHINS,TEMPTERM
REAL(DP) :: Jznu,JGW,SUM1,SUM2
TYPE(QUADRATURE_SCHEME_PTR_TYPE) :: QUADRATURE_SCHEMES(4)
TYPE(BASIS_TYPE), POINTER :: DEPENDENT_BASIS
TYPE(BOUNDARY_CONDITIONS_VARIABLE_TYPE), POINTER :: BOUNDARY_CONDITIONS_VARIABLE
TYPE(BOUNDARY_CONDITIONS_TYPE), POINTER :: BOUNDARY_CONDITIONS
TYPE(FIELD_INTERPOLATED_POINT_TYPE), POINTER :: geometricInterpPoint,fibreInterpPoint, &
& materialsInterpPoint,dependentInterpPoint
TYPE(FIELD_INTERPOLATED_POINT_METRICS_TYPE), POINTER :: geometricInterpPointMetrics, &
& dependentInterpPointMetrics
TYPE(EquationsType), POINTER :: equations
TYPE(EquationsMappingVectorType), POINTER :: vectorMapping
TYPE(EquationsMappingNonlinearType), POINTER :: nonlinearMapping
TYPE(EquationsMatricesVectorType), POINTER :: vectorMatrices
TYPE(EquationsMatricesNonlinearType), POINTER :: nonlinearMatrices
TYPE(EquationsJacobianType), POINTER :: jacobianMatrix
TYPE(EquationsVectorType), POINTER :: vectorEquations
TYPE(FIELD_TYPE), POINTER :: DEPENDENT_FIELD,GEOMETRIC_FIELD,MATERIALS_FIELD,FIBRE_FIELD
TYPE(FIELD_VARIABLE_TYPE), POINTER :: FIELD_VARIABLE
TYPE(QUADRATURE_SCHEME_TYPE), POINTER :: DEPENDENT_QUADRATURE_SCHEME
INTEGER(INTG) :: EQUATIONS_SET_SUBTYPE
ENTERS("FiniteElasticity_FiniteElementJacobianEvaluate",err,error,*999)
IF(ASSOCIATED(EQUATIONS_SET)) THEN
EQUATIONS=>EQUATIONS_SET%EQUATIONS
EQUATIONS_SET_SUBTYPE = EQUATIONS_SET%SPECIFICATION(3)
IF(ASSOCIATED(EQUATIONS)) THEN
NULLIFY(vectorEquations)
CALL Equations_VectorEquationsGet(equations,vectorEquations,err,error,*999)
vectorMatrices=>vectorEquations%vectorMatrices
nonlinearMatrices=>vectorMatrices%nonlinearMatrices
jacobianMatrix=>nonlinearMatrices%jacobians(1)%ptr
IF(jacobianMatrix%updateJacobian) THEN
IF (EQUATIONS_SET_SUBTYPE == EQUATIONS_SET_REFERENCE_STATE_TRANSVERSE_GUCCIONE_SUBTYPE) THEN
DEPENDENT_FIELD=>equations%interpolation%geometricField
GEOMETRIC_FIELD=>equations%interpolation%dependentField
ELSE
DEPENDENT_FIELD=>equations%interpolation%dependentField
GEOMETRIC_FIELD=>equations%interpolation%geometricField
END IF
MATERIALS_FIELD=>equations%interpolation%materialsField
FIBRE_FIELD=>equations%interpolation%fibreField
DEPENDENT_BASIS=>DEPENDENT_FIELD%DECOMPOSITION%DOMAIN(DEPENDENT_FIELD%DECOMPOSITION%MESH_COMPONENT_NUMBER)%ptr% &
& TOPOLOGY%ELEMENTS%ELEMENTS(ELEMENT_NUMBER)%BASIS
DEPENDENT_QUADRATURE_SCHEME=>DEPENDENT_BASIS%QUADRATURE%QUADRATURE_SCHEME_MAP(BASIS_DEFAULT_QUADRATURE_SCHEME)%ptr
NUMBER_OF_DIMENSIONS=EQUATIONS_SET%REGION%COORDINATE_SYSTEM%NUMBER_OF_DIMENSIONS
NUMBER_OF_XI=DEPENDENT_BASIS%NUMBER_OF_XI
vectorMapping=>vectorEquations%vectorMapping
nonlinearMapping=>vectorMapping%nonlinearMapping
FIELD_VARIABLE=>nonlinearMapping%residualVariables(1)%ptr
FIELD_VAR_TYPE=FIELD_VARIABLE%VARIABLE_TYPE
PRESSURE_COMPONENT=FIELD_VARIABLE%NUMBER_OF_COMPONENTS
BOUNDARY_CONDITIONS=>EQUATIONS_SET%BOUNDARY_CONDITIONS
CALL BOUNDARY_CONDITIONS_VARIABLE_GET(BOUNDARY_CONDITIONS,EQUATIONS_SET%equations%vectorEquations%vectorMapping% &
& rhsMapping%rhsVariable,BOUNDARY_CONDITIONS_VARIABLE,err,error,*999)
TOTAL_NUMBER_OF_SURFACE_PRESSURE_CONDITIONS=BOUNDARY_CONDITIONS_VARIABLE%DOF_COUNTS(BOUNDARY_CONDITION_PRESSURE)+ &
& BOUNDARY_CONDITIONS_VARIABLE%DOF_COUNTS(BOUNDARY_CONDITION_PRESSURE_INCREMENTED)
CALL FIELD_INTERPOLATION_PARAMETERS_ELEMENT_GET(FIELD_VALUES_SET_TYPE,ELEMENT_NUMBER,equations%interpolation% &
& dependentInterpParameters(FIELD_VAR_TYPE)%ptr,err,error,*999)
CALL FIELD_INTERPOLATION_PARAMETERS_ELEMENT_GET(FIELD_VALUES_SET_TYPE,ELEMENT_NUMBER,equations%interpolation% &
& geometricInterpParameters(FIELD_U_VARIABLE_TYPE)%ptr,err,error,*999)
CALL FIELD_INTERPOLATION_PARAMETERS_ELEMENT_GET(FIELD_VALUES_SET_TYPE,ELEMENT_NUMBER,equations%interpolation% &
& materialsInterpParameters(FIELD_U_VARIABLE_TYPE)%ptr,err,error,*999)
IF(ASSOCIATED(FIBRE_FIELD)) THEN
CALL FIELD_INTERPOLATION_PARAMETERS_ELEMENT_GET(FIELD_VALUES_SET_TYPE,ELEMENT_NUMBER,equations%interpolation% &
& fibreInterpParameters(FIELD_U_VARIABLE_TYPE)%ptr,err,error,*999)
END IF
!Point interpolation pointer
geometricInterpPoint=>equations%interpolation%geometricInterpPoint(FIELD_U_VARIABLE_TYPE)%ptr
geometricInterpPointMetrics=>equations%interpolation%geometricInterpPointMetrics(FIELD_U_VARIABLE_TYPE)%ptr
IF (EQUATIONS_SET_SUBTYPE == EQUATIONS_SET_REFERENCE_STATE_TRANSVERSE_GUCCIONE_SUBTYPE) THEN
dependentInterpPoint=>equations%interpolation%geometricInterpPoint(FIELD_U_VARIABLE_TYPE)%ptr
dependentInterpPointMetrics=>equations%interpolation%geometricInterpPointMetrics(FIELD_U_VARIABLE_TYPE)%ptr
geometricInterpPoint=>equations%interpolation%dependentInterpPoint(FIELD_VAR_TYPE)%ptr
geometricInterpPointMetrics=>equations%interpolation%dependentInterpPointMetrics(FIELD_VAR_TYPE)%ptr
ELSE
geometricInterpPoint=>equations%interpolation%geometricInterpPoint(FIELD_U_VARIABLE_TYPE)%ptr
geometricInterpPointMetrics=>equations%interpolation%geometricInterpPointMetrics(FIELD_U_VARIABLE_TYPE)%ptr
dependentInterpPoint=>equations%interpolation%dependentInterpPoint(FIELD_VAR_TYPE)%ptr
dependentInterpPointMetrics=>equations%interpolation%dependentInterpPointMetrics(FIELD_VAR_TYPE)%ptr
END IF
IF(ASSOCIATED(FIBRE_FIELD)) THEN
fibreInterpPoint=>equations%interpolation%fibreInterpPoint(FIELD_U_VARIABLE_TYPE)%ptr
END IF
materialsInterpPoint=>equations%interpolation%materialsInterpPoint(FIELD_U_VARIABLE_TYPE)%ptr
SUM_ELEMENT_PARAMETERS=0
!Loop over geometric dependent basis functions.
DO nh=1,FIELD_VARIABLE%NUMBER_OF_COMPONENTS
MESH_COMPONENT_NUMBER=FIELD_VARIABLE%COMPONENTS(nh)%MESH_COMPONENT_NUMBER
DEPENDENT_BASIS=>DEPENDENT_FIELD%DECOMPOSITION%DOMAIN(MESH_COMPONENT_NUMBER)%ptr% &
& TOPOLOGY%ELEMENTS%ELEMENTS(ELEMENT_NUMBER)%BASIS
QUADRATURE_SCHEMES(nh)%ptr=>DEPENDENT_BASIS%QUADRATURE%QUADRATURE_SCHEME_MAP(BASIS_DEFAULT_QUADRATURE_SCHEME)%ptr
IF(FIELD_VARIABLE%COMPONENTS(nh)%INTERPOLATION_TYPE==FIELD_NODE_BASED_INTERPOLATION) THEN
NUMBER_OF_ELEMENT_PARAMETERS(nh)=DEPENDENT_BASIS%NUMBER_OF_ELEMENT_PARAMETERS
ELSEIF(FIELD_VARIABLE%COMPONENTS(nh)%INTERPOLATION_TYPE==FIELD_ELEMENT_BASED_INTERPOLATION) THEN
NUMBER_OF_ELEMENT_PARAMETERS(nh)=1
ENDIF
ELEMENT_BASE_DOF_INDEX(nh)=SUM_ELEMENT_PARAMETERS
SUM_ELEMENT_PARAMETERS=SUM_ELEMENT_PARAMETERS+NUMBER_OF_ELEMENT_PARAMETERS(nh)
ENDDO !nh
!Loop over all Gauss points
DO ng=1,DEPENDENT_QUADRATURE_SCHEME%NUMBER_OF_GAUSS
CALL FIELD_INTERPOLATE_GAUSS(FIRST_PART_DERIV,BASIS_DEFAULT_QUADRATURE_SCHEME,ng, &
& dependentInterpPoint,err,error,*999)
CALL FIELD_INTERPOLATE_GAUSS(FIRST_PART_DERIV,BASIS_DEFAULT_QUADRATURE_SCHEME,ng, &
& geometricInterpPoint,err,error,*999)