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DAMASK_EICMD
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DAMASK_EICMD/constitutive.f90

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! ---------------------------
MODULE constitutive
! ---------------------------
! *** constitutive equations ***
use prec, only: pRe,pIn
implicit none
! ***************************
! *** Material parameters ***
! ***************************
real(pRe), allocatable :: Cslip_66(:,:,:),Cslip_3333(:,:,:,:,:)
real(pRe), allocatable :: s0_slip(:),gdot0_slip(:)
real(pRe), allocatable :: h0(:),w0(:),s_sat(:),q0(:),n_slip(:)
real(pRe), allocatable :: hardening_matrix(:,:,:)
character*80, allocatable :: TCfile(:), ODFfile(:)
real(pRe), parameter :: latent=1.4_pRe
integer(pIn), parameter :: Nslip(3)
integer(pIn) Nmats
real(pRe) sn(3,48,3),sd(3,48,3)
real(pRe) Sslip(3,48,3,3),Sslip_v(3,48,6)
! *** Vectors n and d for each fcc slip systems ***
! MISSING needs to be generalized to fcc and bcc (and hcp?)
! 1: fcc, 2: bcc, 3: hcp
! the respective crystal structure has to be defined
! via material parameter 'crystal_structure' in [material]
data sd( 1,:)/ 0, 1,-1/ ; data sn( 1,:)/ 1, 1, 1/
data sd( 2,:)/-1, 0, 1/ ; data sn( 2,:)/ 1, 1, 1/
data sd( 3,:)/ 1,-1, 0/ ; data sn( 3,:)/ 1, 1, 1/
data sd( 4,:)/ 0,-1,-1/ ; data sn( 4,:)/-1,-1, 1/
data sd( 5,:)/ 1, 0, 1/ ; data sn( 5,:)/-1,-1, 1/
data sd( 6,:)/-1, 1, 0/ ; data sn( 6,:)/-1,-1, 1/
data sd( 7,:)/ 0,-1, 1/ ; data sn( 7,:)/ 1,-1,-1/
data sd( 8,:)/-1, 0,-1/ ; data sn( 8,:)/ 1,-1,-1/
data sd( 9,:)/ 1, 1, 0/ ; data sn( 9,:)/ 1,-1,-1/
data sd(10,:)/ 0, 1, 1/ ; data sn(10,:)/-1, 1,-1/
data sd(11,:)/ 1, 0,-1/ ; data sn(11,:)/-1, 1,-1/
data sd(12,:)/-1,-1, 0/ ; data sn(12,:)/-1, 1,-1/
contains
! **************************************
! *** module Init ***
! **************************************
subroutine constitutive_init()
call constitutive_calc_SchmidM()
call constitutive_calc_hardeningM()
call constitutive_parse_materialDat()
end subroutine
! **************************************
! *** Calculation of Schmid matrices ***
! **************************************
subroutine constitutive_calc_SchmidM()
use prec, only: pRe,pIn
implicit none
integer(pIn) i,j,k,l
real(pRe) invNorm
do j=1,3 ! iterate over crystal system
do i=1,Nslip(j) ! iterate over slip systems
do k=1,3
do l=1,3
Sslip(j,i,k,l)=sd(j,i,k)*sn(j,i,l)
enddo
enddo
invNorm = dsqrt(1.0_pRe/
& (sn(j,i,1)**2+sn(j,1,2)**2+sn(j,i,3)**2)/
& (sd(j,i,1)**2+sd(j,1,2)**2+sd(j,i,3)**2))
Sslip(j,i,:,:) = Sslip(j,i,:,:)*invNorm
Sslip_v(j,i,1)=Sslip(j,i,1,1)
Sslip_v(j,i,2)=Sslip(j,i,2,2)
Sslip_v(j,i,3)=Sslip(j,i,3,3)
Sslip_v(j,i,4)=Sslip(j,i,1,2)+Sslip(j,i,2,1)
Sslip_v(j,i,5)=Sslip(j,i,2,3)+Sslip(j,i,3,2)
Sslip_v(j,i,6)=Sslip(j,i,1,3)+Sslip(j,i,3,1)
enddo
enddo
end subroutine
! ****************************************
! *** Hardening matrix (see Kalidindi) ***
! ****************************************
subroutine constitutive_calc_hardeningM()
use prec, only: pRe,pIn
implicit none
integer(pIn) i,j,k,l
! MISSING iteration over crystal systems
! PE does not understand the j,k looping
hardening_matrix=latent
do i=1,10,3
do j=1,3
do k=1,3
hardening_matrix(i-1+j,i-1+k)=1.0_ZdRe
enddo
enddo
enddo
! ****************************************
! *** Reading 'material.mpie' ***
! ****************************************
subroutine constitutive_parse_materialDat()
use prec, only: pRe,pIn
implicit none
character*80 line
integer(pIn) i,j,k,l,positions(4)
! MISSING: needs to be 2 pass
! first pass to count Nmats and allocate
! 2nd pass to read actual parameters
write(6,*) '## constitutive_parse_materialDat ##'
write(6,*)
constitutive_Nmats = 1
open(200,FILE='material.mpie',ACTION='READ',STATUS='OLD',ERR=100)
read(200,610,ERR=200,END=200) line
IF( line(1:1).ne.'[' )THEN
WRITE(6,*) 'Problem with mat file: no mat. in 1st line'
ELSE
WRITE(6,*) 'Reading mat. data'
DO WHILE( .true. )
READ(200,610,END=220) line
IF( line(1:1).eq.'[' )THEN
constitutive_Nmats = constitutive_Nmats+1
ELSE
positions = IO_stringPos(line,2) ! parse 2 parts
SELECT CASE (IO_stringValue(line,positions,1))
CASE ('s0_slip')
s0_slip(mat) = IO_floatValue(line,positions,2)
CASE ('g0_slip')
g0_slip(mat) = IO_floatValue(line,positions,2)
CASE ('n_slip')
n_slip(mat) = IO_intValue(line,positions,2)
CASE ('h0')
h0(mat) = IO_floatValue(line,positions,2)
CASE ('w0')
w0(mat) = IO_floatValue(line,positions,2)
CASE ('tauc_sat')
tauc_sat(mat) = IO_floatValue(line,positions,2)
CASE ('C11')
C11(mat) = IO_floatValue(line,positions,2)
CASE ('C12')
C12(mat) = IO_floatValue(line,positions,2)
CASE ('C44')
C44(mat) = IO_floatValue(line,positions,2)
CASE ('TCfile')
TCfile(mat) = IO_stringValue(line,positions,2)
CASE ('ODFfile')
ODFfile(mat) = IO_stringValue(line,positions,2)
CASE ('Ngrains')
Ngrains(mat) = IO_intValue(line,positions,2)
CASE DEFAULT
WRITE(6,*) 'Unknown mat. parameter ',line
END IF
END DO
END IF
220 continue
close(200)
! ** Defintion of stiffness matrices **
! MISSING: this needs to be iterated over the materials
Cslip_66 = 0.0_pRe
do i=1,3
do j=1,3
Cslip_66(i,j) = C12
enddo
Cslip_66(i,i) = C11
Cslip_66(i+3,i+3) = C44
enddo
Cslip_3333(:,:,:,:) = math_66to3333(Cslip_66(:,:))
! *** Transformation to get the MARC order ***
! *** 11,22,33,12,23,13 ***
! MISSING this should be outsourced to FEM-spec
temp=Cslip_66(4,:)
Cslip_66(4,:)=Cslip_66(6,:)
Cslip_66(6,:)=Cslip_66(5,:)
Cslip_66(5,:)=temp
temp=Cslip_66(:,4)
Cslip_66(:,4)=2.0d0*Cslip_66(:,6)
Cslip_66(:,6)=2.0d0*Cslip_66(:,5)
Cslip_66(:,5)=2.0d0*temp
! *** Output to MARC output file ***
write(6,*) 'Material data:'
write(6,*) 'Slip parameter:(s0_slip,g0_slip,n_slip)'
write(6,*) s0_slip,g0_slip,n_slip
write(6,*) 'Slip hardening parameter:(h0,tauc_sat,w0)'
write(6,*) h0,tauc_sat,w0
write(6,*) 'Elasticity matrix:'
write(6,*) Cslip_66(1,:)
write(6,*) Cslip_66(2,:)
write(6,*) Cslip_66(3,:)
write(6,*) Cslip_66(4,:)/2.0d0
write(6,*) Cslip_66(5,:)/2.0d0
write(6,*) Cslip_66(6,:)/2.0d0
write(6,*)
call flush(6)
! END OF MISSING mat iterations
return
100 call _error(110)
200 call _error(210)
end
subroutine READ_ORIENTATIONS
!***********************************************************************
!*** This routine reads orientations from 'orientations.mpie' ***
!***********************************************************************
use mpie
use Zahlendarstellung, only: ZdRe,ZdIn
implicit none
! *** Definition of variables ***
integer(ZdIn) i,j
! *** Read 'orientations.mpie' file ***
open(100,FILE='orientations.mpie',ACTION='READ',STATUS='OLD',
& ERR=100)
read(100,*,ERR=200,END=200)
! *** Read number of states, maximum of components over the states ***
read(100,*,ERR=200,END=200) mpie_nmat,mpie_norimx
! *** Allocate memory for the arrays ***
allocate(mpie_mat(mpie_nmat,2+7*mpie_norimx))
allocate(mpie_cko(mpie_nmat,4:35,3,0:35,2))
allocate(mpie_ckofile(mpie_nmat,80))
allocate(mpie_odfmax(mpie_nmat))
mpie_mat=0.0_ZdRe
mpie_cko=0.0_ZdRe
mpie_ckofile=''
mpie_odfmax=0.0_ZdRe
! *** Read the different states ***
do i=1,mpie_nmat
read(100,*,ERR=200,END=200)
! *** Number of component and symmetry ***
read(100,*,ERR=200,END=200) mpie_mat(i,1),mpie_mat(i,2)
! *** If symmetry = 2, use direct ODF sampling,i.e. read coefficience ***
if (mpie_mat(i,2)==2_ZdIn) then
read(100,'(80A)',ERR=200,END=201) mpie_ckofile(i,:)
201 call mpie_read_ckofile(mpie_cko(i,:,:,:,:),
& mpie_ckofile(i,:))
call mpie_odf_max(mpie_cko(i,:,:,:,:),mpie_odfmax(i))
! *** Set volume fraction to inverse of orientation number for each orientation ***
do j=1,int(mpie_mat(i,1),ZdIn)
mpie_mat(i,2+7*j)=1/mpie_mat(i,1)
enddo
else
! *** Read for every component: ***
! *** gauss: euler angles (phi1, PHI, phi2), dummy, scatter, volume fraction ***
! *** fiber: alpha1, alpha2, beta1, beta2, scatter, volume fraction ***
do j=1,int(mpie_mat(i,1),ZdIn)
read(100,*,ERR=200,END=200) mpie_mat(i,7*j-4),
& mpie_mat(i,7*j-3),mpie_mat(i,7*j-2),
& mpie_mat(i,7*j-1),mpie_mat(i,7*j),
& mpie_mat(i,7*j+1),mpie_mat(i,7*j+2)
enddo
endif
enddo
close(100)
! *** Output to MARC output file ***
write(6,*) 'MPIE Material Routine Ver. 0.1 by L. Hantcherli'
write(6,*)
write(6,*) 'Orientations data:'
write(6,*) 'Number of materials: ', mpie_nmat
write(6,*) 'Maximum number of components: ', mpie_norimx
write(6,*)
do i=1,mpie_nmat
write(6,*) 'State', i
if (mpie_mat(i,2)==2_ZdIn) then
write(6,*) mpie_ckofile(i,:),mpie_mat(i,9),mpie_odfmax(i)
else
write(6,*) mpie_mat(i,:)
endif
write(6,*)
enddo
call flush(6)
return
100 call _error(100)
200 call _error(200)
end
subroutine slip_rate (tau_slip,tauc_slip_new,gdot_slip,
& dgdot_dtaucslip)
C ********************************************************************
C Subroutine contains the constitutive equation for the slip
C rate on each slip system
C Input: tau_slip : shear stress on each slip system
C tauc_slip_new : critical shear stress on each slip system
C Output: gdot_slip : slip rate on each slip system
C dgdot_dtaucslip: derivative of slip rate on each slip system
C ********************************************************************
use mpie
use Zahlendarstellung
implicit none
real(ZdRe) tau_slip(nslip),tauc_slip_new(nslip),
& gdot_slip(nslip),dgdot_dtaucslip(nslip)
integer(ZdIn) i
do i=1,nslip
gdot_slip(i)=g0_slip*(abs(tau_slip(i))/tauc_slip_new(i))
& **n_slip*sign(1.0_ZdRe,tau_slip(i))
dgdot_dtaucslip(i)=g0_slip*(abs(tau_slip(i))/tauc_slip_new(i))
& **(n_slip-1) *n_slip/tauc_slip_new(i)
enddo
return
end
subroutine hardening (tauc_slip_new,gdot_slip,dtauc_slip)
C *********************************************************************
C Subroutine calculates the increment in critical shear stress due
C to plastic deformation on each slip system
C Input: tauc_slip_new :critical shear stress needed for slip on each
C slip system
C gdot_slip :slip rate on each slip system
C Output: dtauc_slip :increment of hardening due to slip on each
C slip system
C Local : selfhr
C *********************************************************************
use mpie
use Zahlendarstellung
implicit none
real(ZdRe) tauc_slip_new(nslip),gdot_slip(nslip),
& dtauc_slip(nslip)
real(ZdRe) selfhr(nslip)
integer(ZdIn) i
do i=1,nslip
selfhr(i)=h0*(1.0_ZdRe-tauc_slip_new(i)/
& tauc_sat)**w0
& *abs(gdot_slip(i))
enddo
dtauc_slip=matmul(hardening_matrix,selfhr)
return
end
subroutine plastic_vel_grad(dt,tau_slip,tauc_slip_new,Lp)
C *************************************************************
C Subroutine calculates the plastic velocity gradient given the
C slip rates
C Input: dt : time step
C tau_slip : shear stress on each slip system on each
C slip system
C tauc_slip_new : critical shear stress needed for slip on each
C slip system
C Output: Lp : plastic velocity gradient
C gdot_slip : slip rate on each slip system
C *************************************************************
use mpie
use Zahlendarstellung
implicit none
real(ZdRe) dt,tau_slip(nslip),tauc_slip_new(nslip),
& Lp(3,3),gdot_slip(nslip)
integer(ZdIn) i
Lp=0
do i=1,nslip
gdot_slip(i)=g0_slip*(abs(tau_slip(i))/tauc_slip_new(i))
& **n_slip*sign(1.0_ZdRe,tau_slip(i))
Lp=Lp+gdot_slip(i)*Sslip(i,:,:)
enddo
return
end
function CPFEM_Cauchy(Estar_v,Fe,C66)
C ***************************************************************
C Subroutine calculates the cauchy from the elastic strain tensor
C Input: Estar_v : elastic strain tensor (in vector form)
C Fe : elastic deformation gradient
C C66 : Stiffness Tensor
C Output: cs : cauchy stress
C Local: Tstar_v,Tstar,mm,det
C ***************************************************************
use math
use prec
implicit none
real(pRe) Estar_v(6),Fe(3,3),C66(6,6),CPFEM_Cauchy(6)
real(pRe) det,mm(3,3),Tstar(3,3)
integer(pIn) i
det = math_det(Fe)
Tstar = math_6to33(matmul(C66,Estar_v))
mm=matmul(matmul(Fe,Tstar),transpose(Fe))/det
CPFEM_Cauchy = math_33to6(mm)
return
end function
end module
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