functions only used within updatestate
This commit is contained in:
Martin Diehl
parent
c16fdec749
commit
0aa21e507a
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@ -74,11 +74,6 @@ module homogenization_RGC
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homogenization_RGC_updateState, &
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homogenization_RGC_postResults
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private :: &
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stressPenalty, &
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volumePenalty, &
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grainDeformation, &
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surfaceCorrection, &
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equivalentModuli, &
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relaxationVector, &
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interfaceNormal, &
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getInterface, &
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@ -798,6 +793,328 @@ function homogenization_RGC_updateState(P,F,F0,avgF,dt,dPdF,ip,el)
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!$OMP END CRITICAL (write2out)
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endif
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contains
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!--------------------------------------------------------------------------------------------------
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!> @brief calculate stress-like penalty due to deformation mismatch
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!--------------------------------------------------------------------------------------------------
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subroutine stressPenalty(rPen,nMis,avgF,fDef,ip,el,instance)
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use debug, only: &
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debug_level, &
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debug_homogenization,&
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debug_levelExtensive, &
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debug_e, &
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debug_i
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use mesh, only: &
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mesh_homogenizationAt
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use constitutive, only: &
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constitutive_homogenizedC
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use math, only: &
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math_civita
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use material, only: &
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homogenization_maxNgrains,&
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homogenization_Ngrains
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use numerics, only: &
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xSmoo_RGC
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implicit none
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real(pReal), dimension (3,3,homogenization_maxNgrains), intent(out) :: rPen !< stress-like penalty
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real(pReal), dimension (3,homogenization_maxNgrains), intent(out) :: nMis !< total amount of mismatch
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real(pReal), dimension (3,3,homogenization_maxNgrains), intent(in) :: fDef !< deformation gradients
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real(pReal), dimension (3,3), intent(in) :: avgF !< initial effective stretch tensor
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integer(pInt), intent(in) :: ip,el,instance
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integer(pInt), dimension (4) :: intFace
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integer(pInt), dimension (3) :: iGrain3,iGNghb3,nGDim
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real(pReal), dimension (3,3) :: gDef,nDef
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real(pReal), dimension (3) :: nVect,surfCorr
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real(pReal), dimension (2) :: Gmoduli
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integer(pInt) :: iGrain,iGNghb,iFace,i,j,k,l
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real(pReal) :: muGrain,muGNghb,nDefNorm,bgGrain,bgGNghb
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type(tParameters) :: prm
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integer(pInt), parameter :: nFace = 6_pInt
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real(pReal), parameter :: nDefToler = 1.0e-10_pReal
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nGDim = param(instance)%Nconstituents
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rPen = 0.0_pReal
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nMis = 0.0_pReal
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!--------------------------------------------------------------------------------------------------
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! get the correction factor the modulus of penalty stress representing the evolution of area of
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! the interfaces due to deformations
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surfCorr = surfaceCorrection(avgF,ip,el)
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associate(prm => param(instance))
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!--------------------------------------------------------------------------------------------------
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! debugging the surface correction factor
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if (iand(debug_level(debug_homogenization),debug_levelExtensive) /= 0_pInt &
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.and. debug_e == el .and. debug_i == ip) then
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!$OMP CRITICAL (write2out)
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write(6,'(1x,a20,2(1x,i3))')'Correction factor: ',ip,el
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write(6,'(1x,3(e11.4,1x))')(surfCorr(i), i = 1,3)
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!$OMP END CRITICAL (write2out)
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endif
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!--------------------------------------------------------------------------------------------------
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! computing the mismatch and penalty stress tensor of all grains
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do iGrain = 1_pInt,homogenization_Ngrains(mesh_homogenizationAt(el))
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Gmoduli = equivalentModuli(iGrain,ip,el)
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muGrain = Gmoduli(1) ! collecting the equivalent shear modulus of grain
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bgGrain = Gmoduli(2) ! and the lengthh of Burgers vector
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iGrain3 = grain1to3(iGrain,instance) ! get the grain ID in local 3-dimensional index (x,y,z)-position
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!* Looping over all six interfaces of each grain
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do iFace = 1_pInt,nFace
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intFace = getInterface(iFace,iGrain3) ! get the 4-dimensional index of the interface in local numbering system of the grain
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nVect = interfaceNormal(intFace,ip,el) ! get the interface normal
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iGNghb3 = iGrain3 ! identify the neighboring grain across the interface
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iGNghb3(abs(intFace(1))) = iGNghb3(abs(intFace(1))) + int(real(intFace(1),pReal)/real(abs(intFace(1)),pReal),pInt)
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if (iGNghb3(1) < 1) iGNghb3(1) = nGDim(1) ! with periodicity along e1 direction
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if (iGNghb3(1) > nGDim(1)) iGNghb3(1) = 1_pInt
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if (iGNghb3(2) < 1) iGNghb3(2) = nGDim(2) ! with periodicity along e2 direction
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if (iGNghb3(2) > nGDim(2)) iGNghb3(2) = 1_pInt
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if (iGNghb3(3) < 1) iGNghb3(3) = nGDim(3) ! with periodicity along e3 direction
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if (iGNghb3(3) > nGDim(3)) iGNghb3(3) = 1_pInt
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iGNghb = grain3to1(iGNghb3,instance) ! get the ID of the neighboring grain
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Gmoduli = equivalentModuli(iGNghb,ip,el) ! collecting the shear modulus and Burgers vector of the neighbor
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muGNghb = Gmoduli(1)
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bgGNghb = Gmoduli(2)
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gDef = 0.5_pReal*(fDef(1:3,1:3,iGNghb) - fDef(1:3,1:3,iGrain)) ! compute the difference/jump in deformation gradeint across the neighbor
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!--------------------------------------------------------------------------------------------------
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! compute the mismatch tensor of all interfaces
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nDefNorm = 0.0_pReal
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nDef = 0.0_pReal
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do i = 1_pInt,3_pInt; do j = 1_pInt,3_pInt
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do k = 1_pInt,3_pInt; do l = 1_pInt,3_pInt
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nDef(i,j) = nDef(i,j) - nVect(k)*gDef(i,l)*math_civita(j,k,l) ! compute the interface mismatch tensor from the jump of deformation gradient
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enddo; enddo
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nDefNorm = nDefNorm + nDef(i,j)*nDef(i,j) ! compute the norm of the mismatch tensor
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enddo; enddo
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nDefNorm = max(nDefToler,sqrt(nDefNorm)) ! approximation to zero mismatch if mismatch is zero (singularity)
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nMis(abs(intFace(1)),iGrain) = nMis(abs(intFace(1)),iGrain) + nDefNorm ! total amount of mismatch experienced by the grain (at all six interfaces)
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!--------------------------------------------------------------------------------------------------
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! debuggin the mismatch tensor
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if (iand(debug_level(debug_homogenization),debug_levelExtensive) /= 0_pInt &
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.and. debug_e == el .and. debug_i == ip) then
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!$OMP CRITICAL (write2out)
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write(6,'(1x,a20,i2,1x,a20,1x,i3)')'Mismatch to face: ',intFace(1),'neighbor grain: ',iGNghb
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do i = 1,3
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write(6,'(1x,3(e11.4,1x))')(nDef(i,j), j = 1,3)
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enddo
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write(6,'(1x,a20,e11.4)')'with magnitude: ',nDefNorm
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!$OMP END CRITICAL (write2out)
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endif
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!--------------------------------------------------------------------------------------------------
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! compute the stress penalty of all interfaces
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do i = 1_pInt,3_pInt; do j = 1_pInt,3_pInt
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do k = 1_pInt,3_pInt; do l = 1_pInt,3_pInt
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rPen(i,j,iGrain) = rPen(i,j,iGrain) + 0.5_pReal*(muGrain*bgGrain + muGNghb*bgGNghb)*prm%xiAlpha &
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*surfCorr(abs(intFace(1)))/prm%dAlpha(abs(intFace(1))) &
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*cosh(prm%ciAlpha*nDefNorm) &
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*0.5_pReal*nVect(l)*nDef(i,k)/nDefNorm*math_civita(k,l,j) &
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*tanh(nDefNorm/xSmoo_RGC)
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enddo; enddo
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enddo; enddo
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enddo
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!--------------------------------------------------------------------------------------------------
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! debugging the stress-like penalty
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if (iand(debug_level(debug_homogenization),debug_levelExtensive) /= 0_pInt &
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.and. debug_e == el .and. debug_i == ip) then
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!$OMP CRITICAL (write2out)
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write(6,'(1x,a20,i2)')'Penalty of grain: ',iGrain
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do i = 1,3
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write(6,'(1x,3(e11.4,1x))')(rPen(i,j,iGrain), j = 1,3)
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enddo
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!$OMP END CRITICAL (write2out)
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endif
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enddo
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end associate
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end subroutine stressPenalty
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!--------------------------------------------------------------------------------------------------
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!> @brief calculate stress-like penalty due to volume discrepancy
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!--------------------------------------------------------------------------------------------------
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subroutine volumePenalty(vPen,vDiscrep,fDef,fAvg,ip,el)
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use debug, only: &
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debug_level, &
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debug_homogenization,&
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debug_levelExtensive, &
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debug_e, &
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debug_i
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use mesh, only: &
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mesh_homogenizationAt
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use math, only: &
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math_det33, &
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math_inv33
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use material, only: &
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homogenization_maxNgrains,&
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homogenization_Ngrains
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use numerics, only: &
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maxVolDiscr_RGC,&
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volDiscrMod_RGC,&
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volDiscrPow_RGC
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implicit none
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real(pReal), dimension (3,3,homogenization_maxNgrains), intent(out) :: vPen ! stress-like penalty due to volume
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real(pReal), intent(out) :: vDiscrep ! total volume discrepancy
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real(pReal), dimension (3,3,homogenization_maxNgrains), intent(in) :: fDef ! deformation gradients
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real(pReal), dimension (3,3), intent(in) :: fAvg ! overall deformation gradient
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integer(pInt), intent(in) :: ip,& ! integration point
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el
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real(pReal), dimension (homogenization_maxNgrains) :: gVol
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integer(pInt) :: iGrain,nGrain,i,j
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nGrain = homogenization_Ngrains(mesh_homogenizationAt(el))
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!--------------------------------------------------------------------------------------------------
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! compute the volumes of grains and of cluster
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vDiscrep = math_det33(fAvg) ! compute the volume of the cluster
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do iGrain = 1_pInt,nGrain
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gVol(iGrain) = math_det33(fDef(1:3,1:3,iGrain)) ! compute the volume of individual grains
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vDiscrep = vDiscrep - gVol(iGrain)/real(nGrain,pReal) ! calculate the difference/dicrepancy between
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! the volume of the cluster and the the total volume of grains
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enddo
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!--------------------------------------------------------------------------------------------------
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! calculate the stress and penalty due to volume discrepancy
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vPen = 0.0_pReal
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do iGrain = 1_pInt,nGrain
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vPen(:,:,iGrain) = -1.0_pReal/real(nGrain,pReal)*volDiscrMod_RGC*volDiscrPow_RGC/maxVolDiscr_RGC* &
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sign((abs(vDiscrep)/maxVolDiscr_RGC)**(volDiscrPow_RGC - 1.0),vDiscrep)* &
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gVol(iGrain)*transpose(math_inv33(fDef(:,:,iGrain)))
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!--------------------------------------------------------------------------------------------------
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! debugging the stress-like penalty
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if (iand(debug_level(debug_homogenization),debug_levelExtensive) /= 0_pInt &
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.and. debug_e == el .and. debug_i == ip) then
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!$OMP CRITICAL (write2out)
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write(6,'(1x,a30,i2)')'Volume penalty of grain: ',iGrain
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do i = 1,3
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write(6,'(1x,3(e11.4,1x))')(vPen(i,j,iGrain), j = 1,3)
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enddo
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!$OMP END CRITICAL (write2out)
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endif
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enddo
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end subroutine volumePenalty
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!--------------------------------------------------------------------------------------------------
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!> @brief compute the correction factor accouted for surface evolution (area change) due to
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! deformation
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!--------------------------------------------------------------------------------------------------
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function surfaceCorrection(avgF,ip,el)
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use math, only: &
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math_invert33, &
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math_mul33x33
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implicit none
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real(pReal), dimension(3) :: surfaceCorrection
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real(pReal), dimension(3,3), intent(in) :: avgF !< average F
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integer(pInt), intent(in) :: ip,& !< integration point number
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el !< element number
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real(pReal), dimension(3,3) :: invC
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real(pReal), dimension(3) :: nVect
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real(pReal) :: detF
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integer(pInt) :: i,j,iBase
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logical :: error
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call math_invert33(math_mul33x33(transpose(avgF),avgF),invC,detF,error)
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surfaceCorrection = 0.0_pReal
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do iBase = 1_pInt,3_pInt
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nVect = interfaceNormal([iBase,1_pInt,1_pInt,1_pInt],ip,el) ! get the normal of the interface
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do i = 1_pInt,3_pInt; do j = 1_pInt,3_pInt
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surfaceCorrection(iBase) = surfaceCorrection(iBase) + invC(i,j)*nVect(i)*nVect(j) ! compute the component of (the inverse of) the stretch in the direction of the normal
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enddo; enddo
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surfaceCorrection(iBase) = sqrt(surfaceCorrection(iBase))*detF ! get the surface correction factor (area contraction/enlargement)
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enddo
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end function surfaceCorrection
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!--------------------------------------------------------------------------------------------------
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!> @brief compute the equivalent shear and bulk moduli from the elasticity tensor
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!--------------------------------------------------------------------------------------------------
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function equivalentModuli(grainID,ip,el)
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use constitutive, only: &
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constitutive_homogenizedC
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implicit none
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integer(pInt), intent(in) :: &
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grainID,&
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ip, & !< integration point number
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el !< element number
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real(pReal), dimension (6,6) :: elasTens
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real(pReal), dimension(2) :: equivalentModuli
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real(pReal) :: &
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cEquiv_11, &
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cEquiv_12, &
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cEquiv_44
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elasTens = constitutive_homogenizedC(grainID,ip,el)
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!--------------------------------------------------------------------------------------------------
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! compute the equivalent shear modulus after Turterltaub and Suiker, JMPS (2005)
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cEquiv_11 = (elasTens(1,1) + elasTens(2,2) + elasTens(3,3))/3.0_pReal
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cEquiv_12 = (elasTens(1,2) + elasTens(2,3) + elasTens(3,1) + &
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elasTens(1,3) + elasTens(2,1) + elasTens(3,2))/6.0_pReal
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cEquiv_44 = (elasTens(4,4) + elasTens(5,5) + elasTens(6,6))/3.0_pReal
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equivalentModuli(1) = 0.2_pReal*(cEquiv_11 - cEquiv_12) + 0.6_pReal*cEquiv_44
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!--------------------------------------------------------------------------------------------------
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! obtain the length of Burgers vector (could be model dependend)
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equivalentModuli(2) = 2.5e-10_pReal
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end function equivalentModuli
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!--------------------------------------------------------------------------------------------------
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!> @brief calculating the grain deformation gradient (the same with
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! homogenization_RGC_partionDeformation, but used only for perturbation scheme)
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!--------------------------------------------------------------------------------------------------
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subroutine grainDeformation(F, avgF, ip, el)
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use mesh, only: &
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mesh_homogenizationAt
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use material, only: &
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homogenization_maxNgrains,&
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homogenization_typeInstance
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implicit none
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real(pReal), dimension (3,3,homogenization_maxNgrains), intent(out) :: F !< partioned F per grain
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real(pReal), dimension (3,3), intent(in) :: avgF !<
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integer(pInt), intent(in) :: &
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el, & !< element number
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ip !< integration point number
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real(pReal), dimension (3) :: aVect,nVect
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integer(pInt), dimension (4) :: intFace
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integer(pInt), dimension (3) :: iGrain3
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integer(pInt) :: instance, iGrain,iFace,i,j
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!--------------------------------------------------------------------------------------------------
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! compute the deformation gradient of individual grains due to relaxations
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instance = homogenization_typeInstance(mesh_homogenizationAt(el))
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F = 0.0_pReal
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do iGrain = 1_pInt,product(param(instance)%Nconstituents)
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iGrain3 = grain1to3(iGrain,instance)
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do iFace = 1_pInt,6_pInt
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intFace = getInterface(iFace,iGrain3)
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aVect = relaxationVector(intFace,instance, ip, el)
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nVect = interfaceNormal(intFace,ip,el)
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forall (i=1_pInt:3_pInt,j=1_pInt:3_pInt) &
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F(i,j,iGrain) = F(i,j,iGrain) + aVect(i)*nVect(j) ! effective relaxations
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enddo
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F(1:3,1:3,iGrain) = F(1:3,1:3,iGrain) + avgF ! relaxed deformation gradient
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enddo
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end subroutine grainDeformation
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end function homogenization_RGC_updateState
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@ -887,285 +1204,7 @@ pure function homogenization_RGC_postResults(ip,el) result(postResults)
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end function homogenization_RGC_postResults
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!--------------------------------------------------------------------------------------------------
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!> @brief calculate stress-like penalty due to deformation mismatch
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!--------------------------------------------------------------------------------------------------
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subroutine stressPenalty(rPen,nMis,avgF,fDef,ip,el,instance)
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use debug, only: &
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debug_level, &
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debug_homogenization,&
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debug_levelExtensive, &
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debug_e, &
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debug_i
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use mesh, only: &
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mesh_homogenizationAt
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use constitutive, only: &
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constitutive_homogenizedC
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use math, only: &
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math_civita
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use material, only: &
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homogenization_maxNgrains,&
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homogenization_Ngrains
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use numerics, only: &
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xSmoo_RGC
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implicit none
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real(pReal), dimension (3,3,homogenization_maxNgrains), intent(out) :: rPen !< stress-like penalty
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real(pReal), dimension (3,homogenization_maxNgrains), intent(out) :: nMis !< total amount of mismatch
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real(pReal), dimension (3,3,homogenization_maxNgrains), intent(in) :: fDef !< deformation gradients
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real(pReal), dimension (3,3), intent(in) :: avgF !< initial effective stretch tensor
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integer(pInt), intent(in) :: ip,el,instance
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integer(pInt), dimension (4) :: intFace
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integer(pInt), dimension (3) :: iGrain3,iGNghb3,nGDim
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real(pReal), dimension (3,3) :: gDef,nDef
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real(pReal), dimension (3) :: nVect,surfCorr
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real(pReal), dimension (2) :: Gmoduli
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integer(pInt) :: iGrain,iGNghb,iFace,i,j,k,l
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real(pReal) :: muGrain,muGNghb,nDefNorm,bgGrain,bgGNghb
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|
||||
type(tParameters) :: prm
|
||||
integer(pInt), parameter :: nFace = 6_pInt
|
||||
real(pReal), parameter :: nDefToler = 1.0e-10_pReal
|
||||
|
||||
nGDim = param(instance)%Nconstituents
|
||||
rPen = 0.0_pReal
|
||||
nMis = 0.0_pReal
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
! get the correction factor the modulus of penalty stress representing the evolution of area of
|
||||
! the interfaces due to deformations
|
||||
surfCorr = surfaceCorrection(avgF,ip,el)
|
||||
|
||||
associate(prm => param(instance))
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
! debugging the surface correction factor
|
||||
if (iand(debug_level(debug_homogenization),debug_levelExtensive) /= 0_pInt &
|
||||
.and. debug_e == el .and. debug_i == ip) then
|
||||
!$OMP CRITICAL (write2out)
|
||||
write(6,'(1x,a20,2(1x,i3))')'Correction factor: ',ip,el
|
||||
write(6,'(1x,3(e11.4,1x))')(surfCorr(i), i = 1,3)
|
||||
!$OMP END CRITICAL (write2out)
|
||||
endif
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
! computing the mismatch and penalty stress tensor of all grains
|
||||
do iGrain = 1_pInt,homogenization_Ngrains(mesh_homogenizationAt(el))
|
||||
Gmoduli = equivalentModuli(iGrain,ip,el)
|
||||
muGrain = Gmoduli(1) ! collecting the equivalent shear modulus of grain
|
||||
bgGrain = Gmoduli(2) ! and the lengthh of Burgers vector
|
||||
iGrain3 = grain1to3(iGrain,instance) ! get the grain ID in local 3-dimensional index (x,y,z)-position
|
||||
|
||||
!* Looping over all six interfaces of each grain
|
||||
do iFace = 1_pInt,nFace
|
||||
intFace = getInterface(iFace,iGrain3) ! get the 4-dimensional index of the interface in local numbering system of the grain
|
||||
nVect = interfaceNormal(intFace,ip,el) ! get the interface normal
|
||||
iGNghb3 = iGrain3 ! identify the neighboring grain across the interface
|
||||
iGNghb3(abs(intFace(1))) = iGNghb3(abs(intFace(1))) + int(real(intFace(1),pReal)/real(abs(intFace(1)),pReal),pInt)
|
||||
if (iGNghb3(1) < 1) iGNghb3(1) = nGDim(1) ! with periodicity along e1 direction
|
||||
if (iGNghb3(1) > nGDim(1)) iGNghb3(1) = 1_pInt
|
||||
if (iGNghb3(2) < 1) iGNghb3(2) = nGDim(2) ! with periodicity along e2 direction
|
||||
if (iGNghb3(2) > nGDim(2)) iGNghb3(2) = 1_pInt
|
||||
if (iGNghb3(3) < 1) iGNghb3(3) = nGDim(3) ! with periodicity along e3 direction
|
||||
if (iGNghb3(3) > nGDim(3)) iGNghb3(3) = 1_pInt
|
||||
iGNghb = grain3to1(iGNghb3,instance) ! get the ID of the neighboring grain
|
||||
Gmoduli = equivalentModuli(iGNghb,ip,el) ! collecting the shear modulus and Burgers vector of the neighbor
|
||||
muGNghb = Gmoduli(1)
|
||||
bgGNghb = Gmoduli(2)
|
||||
gDef = 0.5_pReal*(fDef(1:3,1:3,iGNghb) - fDef(1:3,1:3,iGrain)) ! compute the difference/jump in deformation gradeint across the neighbor
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
! compute the mismatch tensor of all interfaces
|
||||
nDefNorm = 0.0_pReal
|
||||
nDef = 0.0_pReal
|
||||
do i = 1_pInt,3_pInt; do j = 1_pInt,3_pInt
|
||||
do k = 1_pInt,3_pInt; do l = 1_pInt,3_pInt
|
||||
nDef(i,j) = nDef(i,j) - nVect(k)*gDef(i,l)*math_civita(j,k,l) ! compute the interface mismatch tensor from the jump of deformation gradient
|
||||
enddo; enddo
|
||||
nDefNorm = nDefNorm + nDef(i,j)*nDef(i,j) ! compute the norm of the mismatch tensor
|
||||
enddo; enddo
|
||||
nDefNorm = max(nDefToler,sqrt(nDefNorm)) ! approximation to zero mismatch if mismatch is zero (singularity)
|
||||
nMis(abs(intFace(1)),iGrain) = nMis(abs(intFace(1)),iGrain) + nDefNorm ! total amount of mismatch experienced by the grain (at all six interfaces)
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
! debuggin the mismatch tensor
|
||||
if (iand(debug_level(debug_homogenization),debug_levelExtensive) /= 0_pInt &
|
||||
.and. debug_e == el .and. debug_i == ip) then
|
||||
!$OMP CRITICAL (write2out)
|
||||
write(6,'(1x,a20,i2,1x,a20,1x,i3)')'Mismatch to face: ',intFace(1),'neighbor grain: ',iGNghb
|
||||
do i = 1,3
|
||||
write(6,'(1x,3(e11.4,1x))')(nDef(i,j), j = 1,3)
|
||||
enddo
|
||||
write(6,'(1x,a20,e11.4)')'with magnitude: ',nDefNorm
|
||||
!$OMP END CRITICAL (write2out)
|
||||
endif
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
! compute the stress penalty of all interfaces
|
||||
do i = 1_pInt,3_pInt; do j = 1_pInt,3_pInt
|
||||
do k = 1_pInt,3_pInt; do l = 1_pInt,3_pInt
|
||||
rPen(i,j,iGrain) = rPen(i,j,iGrain) + 0.5_pReal*(muGrain*bgGrain + muGNghb*bgGNghb)*prm%xiAlpha &
|
||||
*surfCorr(abs(intFace(1)))/prm%dAlpha(abs(intFace(1))) &
|
||||
*cosh(prm%ciAlpha*nDefNorm) &
|
||||
*0.5_pReal*nVect(l)*nDef(i,k)/nDefNorm*math_civita(k,l,j) &
|
||||
*tanh(nDefNorm/xSmoo_RGC)
|
||||
enddo; enddo
|
||||
enddo; enddo
|
||||
enddo
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
! debugging the stress-like penalty
|
||||
if (iand(debug_level(debug_homogenization),debug_levelExtensive) /= 0_pInt &
|
||||
.and. debug_e == el .and. debug_i == ip) then
|
||||
!$OMP CRITICAL (write2out)
|
||||
write(6,'(1x,a20,i2)')'Penalty of grain: ',iGrain
|
||||
do i = 1,3
|
||||
write(6,'(1x,3(e11.4,1x))')(rPen(i,j,iGrain), j = 1,3)
|
||||
enddo
|
||||
!$OMP END CRITICAL (write2out)
|
||||
endif
|
||||
|
||||
enddo
|
||||
end associate
|
||||
|
||||
end subroutine stressPenalty
|
||||
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
!> @brief calculate stress-like penalty due to volume discrepancy
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
subroutine volumePenalty(vPen,vDiscrep,fDef,fAvg,ip,el)
|
||||
use debug, only: &
|
||||
debug_level, &
|
||||
debug_homogenization,&
|
||||
debug_levelExtensive, &
|
||||
debug_e, &
|
||||
debug_i
|
||||
use mesh, only: &
|
||||
mesh_homogenizationAt
|
||||
use math, only: &
|
||||
math_det33, &
|
||||
math_inv33
|
||||
use material, only: &
|
||||
homogenization_maxNgrains,&
|
||||
homogenization_Ngrains
|
||||
use numerics, only: &
|
||||
maxVolDiscr_RGC,&
|
||||
volDiscrMod_RGC,&
|
||||
volDiscrPow_RGC
|
||||
|
||||
implicit none
|
||||
real(pReal), dimension (3,3,homogenization_maxNgrains), intent(out) :: vPen ! stress-like penalty due to volume
|
||||
real(pReal), intent(out) :: vDiscrep ! total volume discrepancy
|
||||
real(pReal), dimension (3,3,homogenization_maxNgrains), intent(in) :: fDef ! deformation gradients
|
||||
real(pReal), dimension (3,3), intent(in) :: fAvg ! overall deformation gradient
|
||||
integer(pInt), intent(in) :: ip,& ! integration point
|
||||
el
|
||||
real(pReal), dimension (homogenization_maxNgrains) :: gVol
|
||||
integer(pInt) :: iGrain,nGrain,i,j
|
||||
|
||||
nGrain = homogenization_Ngrains(mesh_homogenizationAt(el))
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
! compute the volumes of grains and of cluster
|
||||
vDiscrep = math_det33(fAvg) ! compute the volume of the cluster
|
||||
do iGrain = 1_pInt,nGrain
|
||||
gVol(iGrain) = math_det33(fDef(1:3,1:3,iGrain)) ! compute the volume of individual grains
|
||||
vDiscrep = vDiscrep - gVol(iGrain)/real(nGrain,pReal) ! calculate the difference/dicrepancy between
|
||||
! the volume of the cluster and the the total volume of grains
|
||||
enddo
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
! calculate the stress and penalty due to volume discrepancy
|
||||
vPen = 0.0_pReal
|
||||
do iGrain = 1_pInt,nGrain
|
||||
vPen(:,:,iGrain) = -1.0_pReal/real(nGrain,pReal)*volDiscrMod_RGC*volDiscrPow_RGC/maxVolDiscr_RGC* &
|
||||
sign((abs(vDiscrep)/maxVolDiscr_RGC)**(volDiscrPow_RGC - 1.0),vDiscrep)* &
|
||||
gVol(iGrain)*transpose(math_inv33(fDef(:,:,iGrain)))
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
! debugging the stress-like penalty
|
||||
if (iand(debug_level(debug_homogenization),debug_levelExtensive) /= 0_pInt &
|
||||
.and. debug_e == el .and. debug_i == ip) then
|
||||
!$OMP CRITICAL (write2out)
|
||||
write(6,'(1x,a30,i2)')'Volume penalty of grain: ',iGrain
|
||||
do i = 1,3
|
||||
write(6,'(1x,3(e11.4,1x))')(vPen(i,j,iGrain), j = 1,3)
|
||||
enddo
|
||||
!$OMP END CRITICAL (write2out)
|
||||
endif
|
||||
enddo
|
||||
|
||||
end subroutine volumePenalty
|
||||
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
!> @brief compute the correction factor accouted for surface evolution (area change) due to
|
||||
! deformation
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
function surfaceCorrection(avgF,ip,el)
|
||||
use math, only: &
|
||||
math_invert33, &
|
||||
math_mul33x33
|
||||
|
||||
implicit none
|
||||
real(pReal), dimension(3) :: surfaceCorrection
|
||||
real(pReal), dimension(3,3), intent(in) :: avgF !< average F
|
||||
integer(pInt), intent(in) :: ip,& !< integration point number
|
||||
el !< element number
|
||||
real(pReal), dimension(3,3) :: invC
|
||||
real(pReal), dimension(3) :: nVect
|
||||
real(pReal) :: detF
|
||||
integer(pInt) :: i,j,iBase
|
||||
logical :: error
|
||||
|
||||
call math_invert33(math_mul33x33(transpose(avgF),avgF),invC,detF,error)
|
||||
|
||||
surfaceCorrection = 0.0_pReal
|
||||
do iBase = 1_pInt,3_pInt
|
||||
nVect = interfaceNormal([iBase,1_pInt,1_pInt,1_pInt],ip,el) ! get the normal of the interface
|
||||
do i = 1_pInt,3_pInt; do j = 1_pInt,3_pInt
|
||||
surfaceCorrection(iBase) = surfaceCorrection(iBase) + invC(i,j)*nVect(i)*nVect(j) ! compute the component of (the inverse of) the stretch in the direction of the normal
|
||||
enddo; enddo
|
||||
surfaceCorrection(iBase) = sqrt(surfaceCorrection(iBase))*detF ! get the surface correction factor (area contraction/enlargement)
|
||||
enddo
|
||||
|
||||
end function surfaceCorrection
|
||||
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
!> @brief compute the equivalent shear and bulk moduli from the elasticity tensor
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
function equivalentModuli(grainID,ip,el)
|
||||
use constitutive, only: &
|
||||
constitutive_homogenizedC
|
||||
|
||||
implicit none
|
||||
integer(pInt), intent(in) :: &
|
||||
grainID,&
|
||||
ip, & !< integration point number
|
||||
el !< element number
|
||||
real(pReal), dimension (6,6) :: elasTens
|
||||
real(pReal), dimension(2) :: equivalentModuli
|
||||
real(pReal) :: &
|
||||
cEquiv_11, &
|
||||
cEquiv_12, &
|
||||
cEquiv_44
|
||||
|
||||
elasTens = constitutive_homogenizedC(grainID,ip,el)
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
! compute the equivalent shear modulus after Turterltaub and Suiker, JMPS (2005)
|
||||
cEquiv_11 = (elasTens(1,1) + elasTens(2,2) + elasTens(3,3))/3.0_pReal
|
||||
cEquiv_12 = (elasTens(1,2) + elasTens(2,3) + elasTens(3,1) + &
|
||||
elasTens(1,3) + elasTens(2,1) + elasTens(3,2))/6.0_pReal
|
||||
cEquiv_44 = (elasTens(4,4) + elasTens(5,5) + elasTens(6,6))/3.0_pReal
|
||||
equivalentModuli(1) = 0.2_pReal*(cEquiv_11 - cEquiv_12) + 0.6_pReal*cEquiv_44
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
! obtain the length of Burgers vector (could be model dependend)
|
||||
equivalentModuli(2) = 2.5e-10_pReal
|
||||
|
||||
end function equivalentModuli
|
||||
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
|
|
@ -1394,44 +1433,4 @@ pure function interface1to4(iFace1D, instance)
|
|||
end function interface1to4
|
||||
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
!> @brief calculating the grain deformation gradient (the same with
|
||||
! homogenization_RGC_partionDeformation, but used only for perturbation scheme)
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
subroutine grainDeformation(F, avgF, ip, el)
|
||||
use mesh, only: &
|
||||
mesh_homogenizationAt
|
||||
use material, only: &
|
||||
homogenization_maxNgrains,&
|
||||
homogenization_typeInstance
|
||||
|
||||
implicit none
|
||||
real(pReal), dimension (3,3,homogenization_maxNgrains), intent(out) :: F !< partioned F per grain
|
||||
real(pReal), dimension (3,3), intent(in) :: avgF !<
|
||||
integer(pInt), intent(in) :: &
|
||||
el, & !< element number
|
||||
ip !< integration point number
|
||||
real(pReal), dimension (3) :: aVect,nVect
|
||||
integer(pInt), dimension (4) :: intFace
|
||||
integer(pInt), dimension (3) :: iGrain3
|
||||
integer(pInt) :: instance, iGrain,iFace,i,j
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
! compute the deformation gradient of individual grains due to relaxations
|
||||
instance = homogenization_typeInstance(mesh_homogenizationAt(el))
|
||||
F = 0.0_pReal
|
||||
do iGrain = 1_pInt,product(param(instance)%Nconstituents)
|
||||
iGrain3 = grain1to3(iGrain,instance)
|
||||
do iFace = 1_pInt,6_pInt
|
||||
intFace = getInterface(iFace,iGrain3)
|
||||
aVect = relaxationVector(intFace,instance, ip, el)
|
||||
nVect = interfaceNormal(intFace,ip,el)
|
||||
forall (i=1_pInt:3_pInt,j=1_pInt:3_pInt) &
|
||||
F(i,j,iGrain) = F(i,j,iGrain) + aVect(i)*nVect(j) ! effective relaxations
|
||||
enddo
|
||||
F(1:3,1:3,iGrain) = F(1:3,1:3,iGrain) + avgF ! relaxed deformation gradient
|
||||
enddo
|
||||
|
||||
end subroutine grainDeformation
|
||||
|
||||
end module homogenization_RGC
|
||||
|
|
|
|||
Loading…
Reference in New Issue