changed internal representation of orientation and misorientation from euler angles to quaternions (this should also fix some bugs in the math_misorientation subroutine). includes a couple of new functions in math.f90 and some changes in crystallite.f90.
beware that crystallite output "orientation" now by default returns the orientation as quaternion. if you want euler angles instead, you have to add "eulerangles" as a crystallite output in your material.config file (see material.config template). for input of orientations in the texture block of the material.config you still have to specify the rotation in terms of euler angles, quaternions are not yet supported for input.
This commit is contained in:
Christoph Kords
parent
e6fdfdfc36
commit
948c119ee9
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@ -1451,7 +1451,7 @@ do n = 1,FE_NipNeighbors(mesh_element(2,el))
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area = mesh_ipArea(n,ip,el) * math_norm3(surfaceNormal)
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surfaceNormal = surfaceNormal / math_norm3(surfaceNormal) ! normalize the surface normal to unit length
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transmissivity = constitutive_nonlocal_transmissivity(misorientation(4,n), misorientation(1:3,n))
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transmissivity = constitutive_nonlocal_transmissivity(misorientation(:,n))
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highOrderScheme = .false.
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if ( neighboring_el > 0 .and. neighboring_ip > 0 ) then ! if neighbor exists...
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@ -1637,24 +1637,34 @@ endsubroutine
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!*********************************************************************
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!* transmissivity of IP interface *
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!*********************************************************************
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function constitutive_nonlocal_transmissivity(misorientationAngle, misorientationAxis)
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function constitutive_nonlocal_transmissivity(misorientation)
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use prec, only: pReal, &
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pInt
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use math, only: inDeg, &
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math_norm3
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implicit none
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!* input variables
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real(pReal), dimension(3), intent(in) :: misorientationAxis ! misorientation axis
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real(pReal), intent(in) :: misorientationAngle ! misorientation angle
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real(pReal), dimension(4), intent(in) :: misorientation ! misorientation as quaternion
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!* output variables
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real(pReal) constitutive_nonlocal_transmissivity ! transmissivity of an IP interface for dislocations
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!* local variables
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real(pReal) misorientationAngle, &
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axisNorm
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real(pReal), dimension(3) :: misorientationAxis
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! transmissivity depends on misorientation angle
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misorientationAngle = 2.0_pReal * dacos(min(1.0_pReal, max(-1.0_pReal, misorientation(1)))) * inDeg
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misorientationAxis = misorientation(2:4)
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axisNorm = math_norm3(misorientationAxis)
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if (axisNorm > tiny(axisNorm)) &
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misorientationAxis = misorientationAxis / axisNorm
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if (misorientationAngle < 3.0_pReal) then
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constitutive_nonlocal_transmissivity = 1.0_pReal
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elseif (misorientationAngle < 10.0_pReal) then
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@ -38,7 +38,7 @@ real(pReal), dimension (:,:,:,:), allocatable :: &
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crystallite_Tstar0_v, & ! 2nd Piola-Kirchhoff stress vector at start of FE inc
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crystallite_partionedTstar0_v, & ! 2nd Piola-Kirchhoff stress vector at start of homog inc
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crystallite_subTstar0_v, & ! 2nd Piola-Kirchhoff stress vector at start of crystallite inc
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crystallite_eulerangles ! euler angles phi1 Phi phi2
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crystallite_orientation ! orientation as quaternion
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real(pReal), dimension (:,:,:,:,:), allocatable :: &
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crystallite_Fe, & ! current "elastic" def grad (end of converged time step)
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crystallite_Fp, & ! current plastic def grad (end of converged time step)
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@ -56,7 +56,6 @@ real(pReal), dimension (:,:,:,:,:), allocatable :: &
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crystallite_partionedLp0,& ! plastic velocity grad at start of homog inc
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crystallite_subLp0,& ! plastic velocity grad at start of crystallite inc
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crystallite_P, & ! 1st Piola-Kirchhoff stress per grain
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crystallite_R, & ! crystal orientation (rotation matrix current -> lattice conf)
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crystallite_misorientation ! misorientation between two neighboring ips (only calculated for single grain IPs)
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real(pReal), dimension (:,:,:,:,:,:,:), allocatable :: &
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crystallite_dPdF, & ! individual dPdF per grain
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@ -145,8 +144,7 @@ subroutine crystallite_init(Temperature)
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allocate(crystallite_subF0(3,3,gMax,iMax,eMax)); crystallite_subF0 = 0.0_pReal
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allocate(crystallite_subFp0(3,3,gMax,iMax,eMax)); crystallite_subFp0 = 0.0_pReal
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allocate(crystallite_subLp0(3,3,gMax,iMax,eMax)); crystallite_subLp0 = 0.0_pReal
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allocate(crystallite_R(3,3,gMax,iMax,eMax)); crystallite_R = 0.0_pReal
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allocate(crystallite_eulerangles(3,gMax,iMax,eMax)); crystallite_eulerangles = 0.0_pReal
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allocate(crystallite_orientation(4,gMax,iMax,eMax)); crystallite_orientation = 0.0_pReal
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allocate(crystallite_misorientation(4,nMax,gMax,iMax,eMax)); crystallite_misorientation = 0.0_pReal
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allocate(crystallite_subTstar0_v(6,gMax,iMax,eMax)); crystallite_subTstar0_v = 0.0_pReal
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allocate(crystallite_dPdF(3,3,3,3,gMax,iMax,eMax)); crystallite_dPdF = 0.0_pReal
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@ -207,6 +205,8 @@ subroutine crystallite_init(Temperature)
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case('volume')
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mySize = 1
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case('orientation')
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mySize = 4
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case('eulerangles')
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mySize = 3
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case('defgrad')
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mySize = 9
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@ -291,8 +291,7 @@ subroutine crystallite_init(Temperature)
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write(6,'(a35,x,7(i5,x))') 'crystallite_subTstar0_v: ', shape(crystallite_subTstar0_v)
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write(6,'(a35,x,7(i5,x))') 'crystallite_dPdF: ', shape(crystallite_dPdF)
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write(6,'(a35,x,7(i5,x))') 'crystallite_fallbackdPdF: ', shape(crystallite_fallbackdPdF)
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write(6,'(a35,x,7(i5,x))') 'crystallite_R: ', shape(crystallite_R)
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write(6,'(a35,x,7(i5,x))') 'crystallite_eulerangles: ', shape(crystallite_eulerangles)
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write(6,'(a35,x,7(i5,x))') 'crystallite_orientation: ', shape(crystallite_orientation)
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write(6,'(a35,x,7(i5,x))') 'crystallite_misorientation: ', shape(crystallite_misorientation)
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write(6,'(a35,x,7(i5,x))') 'crystallite_dt: ', shape(crystallite_dt)
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write(6,'(a35,x,7(i5,x))') 'crystallite_subdt: ', shape(crystallite_subdt)
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@ -1499,7 +1498,7 @@ subroutine crystallite_orientations()
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use prec, only: pInt, &
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pReal
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use math, only: math_pDecomposition, &
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math_RtoEuler, &
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math_RtoQuaternion, &
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math_misorientation, &
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inDeg
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use FEsolving, only: FEsolving_execElem, &
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@ -1537,8 +1536,7 @@ integer(pInt) e, & ! element index
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neighboringPhase, & ! phase of my neighbor
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neighboringStructure, & ! lattice structure of my neighbor
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symmetryType ! type of crystal symmetry
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real(pReal), dimension(3,3) :: U, R, & ! polar decomposition of Fe
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netRotation ! net rotation between two orientations
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real(pReal), dimension(3,3) :: U, R
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logical error
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@ -1551,11 +1549,9 @@ logical error
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call math_pDecomposition(crystallite_Fe(:,:,g,i,e), U, R, error) ! polar decomposition of Fe
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if (error) then
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call IO_warning(650, e, i, g)
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crystallite_R(:,:,g,i,e) = 0.0_pReal
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crystallite_eulerangles(:,g,i,e) = (/400.0, 400.0, 400.0/) ! fake orientation
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crystallite_orientation(:,g,i,e) = (/1.0_pReal, 0.0_pReal, 0.0_pReal, 0.0_pReal/) ! fake orientation
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else
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crystallite_R(:,:,g,i,e) = transpose(R)
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crystallite_eulerangles(:,g,i,e) = math_RtoEuler(crystallite_R(:,:,g,i,e)) * inDeg
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crystallite_orientation(:,g,i,e) = math_RtoQuaternion(R)
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endif
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enddo
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@ -1599,19 +1595,17 @@ logical error
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symmetryType = 0_pInt
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end select
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call math_misorientation( crystallite_misorientation(1:3,n,1,i,e), &
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crystallite_misorientation(4,n,1,i,e), &
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netRotation, &
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crystallite_R(:,:,1,i,e), &
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crystallite_R(:,:,1,neighboring_i,neighboring_e), &
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symmetryType) ! calculate misorientation
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call math_misorientation( crystallite_misorientation(:,n,1,i,e), &
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crystallite_orientation(:,1,i,e), &
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crystallite_orientation(:,1,neighboring_i,neighboring_e), &
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symmetryType) ! calculate misorientation
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else ! for neighbor with different phase
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crystallite_misorientation(4,n,1,i,e) = 400.0_pReal ! set misorientation angle to 400
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crystallite_misorientation(:,n,1,i,e) = (/-1.0_pReal, 0.0_pReal, 0.0_pReal, 0.0_pReal/) ! set misorientation to maximum
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endif
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else ! no existing neighbor
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crystallite_misorientation(4,n,1,i,e) = 0.0_pReal ! set misorientation angle to zero
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crystallite_misorientation(:,n,1,i,e) = (/1.0_pReal, 0.0_pReal, 0.0_pReal, 0.0_pReal/) ! set misorientation to zero
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endif
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enddo
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endif
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@ -1636,6 +1630,7 @@ function crystallite_postResults(&
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!*** variables and functions from other modules ***!
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use prec, only: pInt, &
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pReal
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use math, only: math_QuaternionToEuler
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use mesh, only: mesh_element
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use material, only: microstructure_crystallite, &
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crystallite_Noutput, &
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@ -1676,7 +1671,10 @@ function crystallite_postResults(&
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crystallite_postResults(c+1) = material_volume(g,i,e) ! grain volume (not fraction but absolute, right?)
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c = c + 1_pInt
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case ('orientation')
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crystallite_postResults(c+1:c+3) = crystallite_eulerangles(:,g,i,e) ! grain orientation
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crystallite_postResults(c+1:c+4) = crystallite_orientation(:,g,i,e) ! grain orientation
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c = c + 4_pInt
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case ('eulerangles')
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crystallite_postResults(c+1:c+3) = math_QuaternionToEuler(crystallite_orientation(:,g,i,e)) ! grain orientation
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c = c + 3_pInt
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case ('defgrad')
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forall (k=0:2,l=0:2) crystallite_postResults(c+1+k*3+l) = crystallite_partionedF(k+1,l+1,g,i,e)
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@ -56,6 +56,7 @@ crystallite 1
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(output) phase
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(output) volume
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(output) orientation
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(output) eulerangles
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(output) defgrad
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#-------------------#
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559
code/math.f90
559
code/math.f90
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@ -65,143 +65,47 @@
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! Symmetry Operations for 3 different materials
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! 24 for cubic, 12 for hexagonal, 8 for tetragonal (24+12+8)x3=132
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real(pReal), dimension(3,3,44), parameter :: symOperations = &
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! Symmetry operations as quaternions
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! 24 for cubic, 12 for hexagonal = 36
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real(pReal), dimension(4,36), parameter :: symOperations = &
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reshape((/&
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1.0_pReal, 0.0_pReal, 0.0_pReal, &
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0.0_pReal, 1.0_pReal, 0.0_pReal, &
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0.0_pReal, 0.0_pReal, 1.0_pReal, &
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0.0_pReal, 0.0_pReal, 1.0_pReal, &
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1.0_pReal, 0.0_pReal, 0.0_pReal, &
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0.0_pReal, 1.0_pReal, 0.0_pReal, &
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0.0_pReal, 1.0_pReal, 0.0_pReal, &
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0.0_pReal, 0.0_pReal, 1.0_pReal, &
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1.0_pReal, 0.0_pReal, 0.0_pReal, &
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0.0_pReal, -1.0_pReal, 0.0_pReal, &
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0.0_pReal, 0.0_pReal, 1.0_pReal, &
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-1.0_pReal, 0.0_pReal, 0.0_pReal, &
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0.0_pReal, -1.0_pReal, 0.0_pReal, &
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0.0_pReal, 0.0_pReal, -1.0_pReal, &
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1.0_pReal, 0.0_pReal, 0.0_pReal, &
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0.0_pReal, 1.0_pReal, 0.0_pReal, &
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0.0_pReal, 0.0_pReal, -1.0_pReal, &
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-1.0_pReal, 0.0_pReal, 0.0_pReal, &
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0.0_pReal, 0.0_pReal, -1.0_pReal, &
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1.0_pReal, 0.0_pReal, 0.0_pReal, &
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0.0_pReal, -1.0_pReal, 0.0_pReal, &
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0.0_pReal, 0.0_pReal, -1.0_pReal, &
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-1.0_pReal, 0.0_pReal, 0.0_pReal, &
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0.0_pReal, 1.0_pReal, 0.0_pReal, &
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0.0_pReal, 0.0_pReal, 1.0_pReal, &
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-1.0_pReal, 0.0_pReal, 0.0_pReal, &
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0.0_pReal, -1.0_pReal, 0.0_pReal, &
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-1.0_pReal, 0.0_pReal, 0.0_pReal, &
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0.0_pReal, 1.0_pReal, 0.0_pReal, &
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0.0_pReal, 0.0_pReal, -1.0_pReal, &
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-1.0_pReal, 0.0_pReal, 0.0_pReal, &
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0.0_pReal, -1.0_pReal, 0.0_pReal, &
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0.0_pReal, 0.0_pReal, 1.0_pReal, &
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1.0_pReal, 0.0_pReal, 0.0_pReal, &
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0.0_pReal, -1.0_pReal, 0.0_pReal, &
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0.0_pReal, 0.0_pReal, -1.0_pReal, &
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0.0_pReal, 0.0_pReal, -1.0_pReal, &
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0.0_pReal, -1.0_pReal, 0.0_pReal, &
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-1.0_pReal, 0.0_pReal, 0.0_pReal, &
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0.0_pReal, 0.0_pReal, 1.0_pReal, &
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0.0_pReal, -1.0_pReal, 0.0_pReal, &
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1.0_pReal, 0.0_pReal, 0.0_pReal, &
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0.0_pReal, 0.0_pReal, 1.0_pReal, &
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0.0_pReal, 1.0_pReal, 0.0_pReal, &
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-1.0_pReal, 0.0_pReal, 0.0_pReal, &
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0.0_pReal, 0.0_pReal, -1.0_pReal, &
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0.0_pReal, 1.0_pReal, 0.0_pReal, &
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1.0_pReal, 0.0_pReal, 0.0_pReal, &
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-1.0_pReal, 0.0_pReal, 0.0_pReal, &
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0.0_pReal, 0.0_pReal, -1.0_pReal, &
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0.0_pReal, -1.0_pReal, 0.0_pReal, &
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1.0_pReal, 0.0_pReal, 0.0_pReal, &
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0.0_pReal, 0.0_pReal, -1.0_pReal, &
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0.0_pReal, 1.0_pReal, 0.0_pReal, &
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1.0_pReal, 0.0_pReal, 0.0_pReal, &
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0.0_pReal, 0.0_pReal, 1.0_pReal, &
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0.0_pReal, -1.0_pReal, 0.0_pReal, &
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-1.0_pReal, 0.0_pReal, 0.0_pReal, &
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0.0_pReal, 0.0_pReal, 1.0_pReal, &
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0.0_pReal, 1.0_pReal, 0.0_pReal, &
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0.0_pReal, -1.0_pReal, 0.0_pReal, &
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-1.0_pReal, 0.0_pReal, 0.0_pReal, &
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0.0_pReal, 0.0_pReal, -1.0_pReal, &
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0.0_pReal, 1.0_pReal, 0.0_pReal, &
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-1.0_pReal, 0.0_pReal, 0.0_pReal, &
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0.0_pReal, 0.0_pReal, 1.0_pReal, &
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0.0_pReal, 1.0_pReal, 0.0_pReal, &
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1.0_pReal, 0.0_pReal, 0.0_pReal, &
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0.0_pReal, 0.0_pReal, -1.0_pReal, &
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0.0_pReal, -1.0_pReal, 0.0_pReal, &
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1.0_pReal, 0.0_pReal, 0.0_pReal, &
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0.0_pReal, 0.0_pReal, 1.0_pReal, &
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1.0_pReal, 0.0_pReal, 0.0_pReal, &
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0.0_pReal, 1.0_pReal, 0.0_pReal, &
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0.0_pReal, 0.0_pReal, 1.0_pReal, &
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-0.5_pReal, 0.866025403_pReal, 0.0_pReal, &
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-0.866025403_pReal, -0.5_pReal, 0.0_pReal, &
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0.0_pReal, 0.0_pReal, 1.0_pReal, &
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-0.5_pReal, -0.866025403_pReal, 0.0_pReal, &
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0.866025403_pReal, -0.5_pReal, 0.0_pReal, &
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0.0_pReal, 0.0_pReal, 1.0_pReal, &
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0.5_pReal, 0.866025403_pReal, 0.0_pReal, &
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-0.866025403_pReal, 0.5_pReal, 0.0_pReal, &
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0.0_pReal, 0.0_pReal, 1.0_pReal, &
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-1.0_pReal, 0.0_pReal, 0.0_pReal, &
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0.0_pReal, -1.0_pReal, 0.0_pReal, &
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0.0_pReal, 0.0_pReal, 1.0_pReal, &
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0.5_pReal, -0.866025403_pReal, 0.0_pReal, &
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0.866025403_pReal, 0.5_pReal, 0.0_pReal, &
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0.0_pReal, 0.0_pReal, 1.0_pReal, &
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-0.5_pReal, -0.866025403_pReal, 0.0_pReal, &
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-0.866025403_pReal, 0.5_pReal, 0.0_pReal, &
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0.0_pReal, 0.0_pReal, -1.0_pReal, &
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1.0_pReal, 0.0_pReal, 0.0_pReal, &
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0.0_pReal, -1.0_pReal, 0.0_pReal, &
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0.0_pReal, 0.0_pReal, -1.0_pReal, &
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-0.5_pReal, 0.866025403_pReal, 0.0_pReal, &
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0.866025403_pReal, 0.5_pReal, 0.0_pReal, &
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0.0_pReal, 0.0_pReal, -1.0_pReal, &
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0.5_pReal, 0.866025403_pReal, 0.0_pReal, &
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0.866025403_pReal, -0.5_pReal, 0.0_pReal, &
|
||||
0.0_pReal, 0.0_pReal, -1.0_pReal, &
|
||||
-1.0_pReal, 0.0_pReal, 0.0_pReal, &
|
||||
0.0_pReal, 1.0_pReal, 0.0_pReal, &
|
||||
0.0_pReal, 0.0_pReal, -1.0_pReal, &
|
||||
0.5_pReal, -0.866025403_pReal, 0.0_pReal, &
|
||||
-0.866025403_pReal, -0.5_pReal, 0.0_pReal, &
|
||||
0.0_pReal, 0.0_pReal, -1.0_pReal, &
|
||||
1.0_pReal, 0.0_pReal, 0.0_pReal, &
|
||||
0.0_pReal, 1.0_pReal, 0.0_pReal, &
|
||||
0.0_pReal, 0.0_pReal, 1.0_pReal, &
|
||||
-1.0_pReal, 0.0_pReal, 0.0_pReal, &
|
||||
0.0_pReal, 1.0_pReal, 0.0_pReal, &
|
||||
0.0_pReal, 0.0_pReal, -1.0_pReal, &
|
||||
1.0_pReal, 0.0_pReal, 0.0_pReal, &
|
||||
0.0_pReal, -1.0_pReal, 0.0_pReal, &
|
||||
0.0_pReal, 0.0_pReal, -1.0_pReal, &
|
||||
-1.0_pReal, 0.0_pReal, 0.0_pReal, &
|
||||
0.0_pReal, -1.0_pReal, 0.0_pReal, &
|
||||
0.0_pReal, 0.0_pReal, 1.0_pReal, &
|
||||
0.0_pReal, 1.0_pReal, 0.0_pReal, &
|
||||
-1.0_pReal, 0.0_pReal, 0.0_pReal, &
|
||||
0.0_pReal, 0.0_pReal, 1.0_pReal, &
|
||||
0.0_pReal, -1.0_pReal, 0.0_pReal, &
|
||||
1.0_pReal, 0.0_pReal, 0.0_pReal, &
|
||||
0.0_pReal, 0.0_pReal, 1.0_pReal, &
|
||||
0.0_pReal, 1.0_pReal, 0.0_pReal, &
|
||||
1.0_pReal, 0.0_pReal, 0.0_pReal, &
|
||||
0.0_pReal, 0.0_pReal, -1.0_pReal, &
|
||||
0.0_pReal, -1.0_pReal, 0.0_pReal, &
|
||||
-1.0_pReal, 0.0_pReal, 0.0_pReal, &
|
||||
0.0_pReal, 0.0_pReal, -1.0_pReal &
|
||||
/),(/3,3,44/))
|
||||
1.0_pReal, 0.0_pReal, 0.0_pReal, 0.0_pReal, & ! cubic symmetry operations
|
||||
0.0_pReal, 0.0_pReal, 0.7071067811865476_pReal, 0.7071067811865476_pReal, & ! 2-fold symmetry
|
||||
0.0_pReal, 0.7071067811865476_pReal, 0.0_pReal, 0.7071067811865476_pReal, &
|
||||
0.0_pReal, 0.7071067811865476_pReal, 0.7071067811865476_pReal, 0.0_pReal, &
|
||||
0.0_pReal, 0.0_pReal, 0.7071067811865476_pReal, -0.7071067811865476_pReal, &
|
||||
0.0_pReal, -0.7071067811865476_pReal, 0.0_pReal, 0.7071067811865476_pReal, &
|
||||
0.0_pReal, 0.7071067811865476_pReal, -0.7071067811865476_pReal, 0.0_pReal, &
|
||||
0.5_pReal, 0.5_pReal, 0.5_pReal, 0.5_pReal, & ! 3-fold symmetry
|
||||
-0.5_pReal, 0.5_pReal, 0.5_pReal, 0.5_pReal, &
|
||||
0.5_pReal, -0.5_pReal, 0.5_pReal, 0.5_pReal, &
|
||||
-0.5_pReal, -0.5_pReal, 0.5_pReal, 0.5_pReal, &
|
||||
0.5_pReal, 0.5_pReal, -0.5_pReal, 0.5_pReal, &
|
||||
-0.5_pReal, 0.5_pReal, -0.5_pReal, 0.5_pReal, &
|
||||
0.5_pReal, 0.5_pReal, 0.5_pReal, -0.5_pReal, &
|
||||
-0.5_pReal, 0.5_pReal, 0.5_pReal, -0.5_pReal, &
|
||||
0.7071067811865476_pReal, 0.7071067811865476_pReal, 0.0_pReal, 0.0_pReal, & ! 4-fold symmetry
|
||||
0.0_pReal, 1.0_pReal, 0.0_pReal, 0.0_pReal, &
|
||||
-0.7071067811865476_pReal, 0.7071067811865476_pReal, 0.0_pReal, 0.0_pReal, &
|
||||
0.7071067811865476_pReal, 0.0_pReal, 0.7071067811865476_pReal, 0.0_pReal, &
|
||||
0.0_pReal, 0.0_pReal, 1.0_pReal, 0.0_pReal, &
|
||||
-0.7071067811865476_pReal, 0.0_pReal, 0.7071067811865476_pReal, 0.0_pReal, &
|
||||
0.7071067811865476_pReal, 0.0_pReal, 0.0_pReal, 0.7071067811865476_pReal, &
|
||||
0.0_pReal, 0.0_pReal, 0.0_pReal, 1.0_pReal, &
|
||||
-0.7071067811865476_pReal, 0.0_pReal, 0.0_pReal, 0.7071067811865476_pReal, &
|
||||
1.0_pReal, 0.0_pReal, 0.0_pReal, 0.0_pReal, & ! hexagonal symmetry operations
|
||||
0.0_pReal, 1.0_pReal, 0.0_pReal, 0.0_pReal, & ! 2-fold symmetry
|
||||
0.0_pReal, 0.0_pReal, 1.0_pReal, 0.0_pReal, &
|
||||
0.0_pReal, 0.5773502691896259_pReal, 1.154700538379252_pReal, 0.0_pReal, &
|
||||
0.0_pReal, -0.5773502691896259_pReal, 1.154700538379252_pReal, 0.0_pReal, &
|
||||
0.0_pReal, 1.154700538379252_pReal, 0.5773502691896259_pReal, 0.0_pReal, &
|
||||
0.0_pReal, -1.154700538379252_pReal, 0.5773502691896259_pReal, 0.0_pReal, &
|
||||
0.866025403784439_pReal, 0.0_pReal, 0.0_pReal, 0.5_pReal, & ! 6-fold symmetry
|
||||
-0.866025403784439_pReal, 0.0_pReal, 0.0_pReal, 0.5_pReal, &
|
||||
0.5_pReal, 0.0_pReal, 0.0_pReal, 0.866025403784439_pReal, &
|
||||
-0.5_pReal, 0.0_pReal, 0.0_pReal, 0.866025403784439_pReal, &
|
||||
0.0_pReal, 0.0_pReal, 0.0_pReal, 1.0_pReal &
|
||||
/),(/4,36/))
|
||||
|
||||
|
||||
|
||||
|
|
@ -242,92 +146,45 @@ real(pReal), dimension(3,3,44), parameter :: symOperations = &
|
|||
|
||||
|
||||
!**************************************************************************
|
||||
! calculates the misorientation for 2 orientations C1 and C2
|
||||
! calculates the misorientation for 2 orientations Q1 and Q2 (needs quaternions)
|
||||
!**************************************************************************
|
||||
subroutine math_misorientation(axis, angle, rot, ori1, ori2, symmetryType)
|
||||
subroutine math_misorientation(dQ, Q1, Q2, symmetryType)
|
||||
|
||||
use prec, only: pReal, pInt
|
||||
use IO, only: IO_warning
|
||||
implicit none
|
||||
|
||||
!*** input variables
|
||||
real(pReal), dimension(3,3), intent(in) :: ori1, & ! 1st orientation
|
||||
ori2 ! 2nd orientation
|
||||
integer(pInt), intent(in) :: symmetryType ! Type of crystal symmetry; 1:cubic, 2:hexagonal, 3:tetragonal
|
||||
real(pReal), dimension(4), intent(in) :: Q1, & ! 1st orientation
|
||||
Q2 ! 2nd orientation
|
||||
integer(pInt), intent(in) :: symmetryType ! Type of crystal symmetry; 1:cubic, 2:hexagonal
|
||||
|
||||
!*** output variables
|
||||
real(pReal), intent(out) :: angle ! misorientation angle in degrees
|
||||
real(pReal), dimension(3), intent(out) :: axis ! rotation axis of misorientation
|
||||
real(pReal), dimension(3,3), intent(out) :: rot ! net rotation of the misorientation
|
||||
real(pReal), dimension(4), intent(out) :: dQ ! misorientation
|
||||
|
||||
!*** local variables
|
||||
real(pReal) this_angle ! candidate for misorientation angle
|
||||
real(pReal), dimension(3) :: this_axis ! candidate for rotation axis
|
||||
real(pReal), dimension(3,3) :: this_rot ! candidate for net rotation
|
||||
real(pReal), dimension(3,3) :: ori1sym, ori2sym ! symmetrical counterpart of 1st and 2nd orientation respectively
|
||||
real(pReal) invNorm
|
||||
integer(pInt) NsymOperations, & ! number of possible symmetry operations
|
||||
startindex, endindex, &
|
||||
s1, s2, &
|
||||
i
|
||||
real(pReal), dimension(:,:,:), allocatable :: mySymOperations ! symmetry Operations for my crystal symmetry
|
||||
real(pReal), dimension(4) :: this_dQ ! candidate for misorientation
|
||||
integer(pInt) s
|
||||
integer(pInt), dimension(2), parameter :: NsymOperations = (/24,12/) ! number of possible symmetry operations
|
||||
real(pReal), dimension(:,:), allocatable :: mySymOperations ! symmetry Operations for my crystal symmetry
|
||||
|
||||
|
||||
axis = 0.0_pReal
|
||||
angle = 0.0_pReal
|
||||
rot = 0.0_pReal
|
||||
|
||||
! choose my symmetry operations according to my crystal symetry
|
||||
if (symmetryType == 1_pInt) then
|
||||
NsymOperations = 24_pInt
|
||||
startindex = 1_pInt
|
||||
elseif (symmetryType == 2_pInt) then
|
||||
NsymOperations = 12_pInt
|
||||
startindex = 25_pInt
|
||||
elseif (symmetryType == 3_pInt) then
|
||||
NsymOperations = 8_pInt
|
||||
startindex = 37_pInt
|
||||
else
|
||||
dQ = 0.0_pReal
|
||||
|
||||
if (symmetryType < 1_pInt .or. symmetryType > 2_pInt) then
|
||||
call IO_warning(700)
|
||||
return
|
||||
endif
|
||||
allocate(mySymOperations(3,3,NsymOperations))
|
||||
endindex = startindex + NsymOperations - 1_pInt
|
||||
mySymOperations = symOperations(:,:,startindex:endindex)
|
||||
|
||||
allocate(mySymOperations(4,NsymOperations(symmetryType)))
|
||||
mySymOperations = symOperations(:,sum(NsymOperations(1:symmetryType-1))+1:sum(NsymOperations(1:symmetryType))) ! choose symmetry operations according to crystal symmetry
|
||||
|
||||
! Initially set the orientation angle to maximum
|
||||
angle = 2.0_pReal * pi
|
||||
|
||||
! apply symmetry operation to 1st orientation
|
||||
do s1 = 1,NsymOperations
|
||||
ori1sym = math_mul33x33(mySymOperations(:,:,s1), ori1)
|
||||
|
||||
! calculate possible net rotation
|
||||
this_rot = math_mul33x33(ori1sym, transpose(ori2))
|
||||
|
||||
! store smallest misorientation for an axis inside standard orientation triangle
|
||||
! calculate rotation axis
|
||||
invNorm = ( (this_rot(1,2) - this_rot(2,1))**2.0_pReal &
|
||||
+ (this_rot(2,3) - this_rot(3,2))**2.0_pReal &
|
||||
+ (this_rot(3,1) - this_rot(1,3))**2.0_pReal ) ** (-0.5_pReal)
|
||||
this_axis(1) = (this_rot(2,3) - this_rot(3,2)) * invNorm
|
||||
this_axis(2) = (this_rot(3,1) - this_rot(1,3)) * invNorm
|
||||
this_axis(3) = (this_rot(1,2) - this_rot(2,1)) * invNorm
|
||||
|
||||
! calculate rotation angle
|
||||
this_angle = abs(0.5_pReal * pi - asin(0.4999999_pReal * (this_rot(1,1) + this_rot(2,2) + this_rot(3,3) - 1.0_pReal)))
|
||||
|
||||
if (abs(this_angle) < angle) then
|
||||
angle = this_angle
|
||||
rot = this_rot
|
||||
axis = this_axis
|
||||
endif
|
||||
dQ(1) = -1.0_pReal ! start with maximum misorientation angle
|
||||
do s = 1,NsymOperations(symmetryType) ! loop ver symmetry operations
|
||||
this_dQ = math_qMul( math_qConj(Q1), math_qMul(mySymOperations(:,s),Q2) ) ! misorientation candidate from Q1^-1*(sym*Q2)
|
||||
if (this_dQ(1) > dQ(1)) dQ = this_dQ ! store if misorientation angle is smaller (cos is larger) than previous one
|
||||
enddo
|
||||
|
||||
! convert angle to degrees
|
||||
angle = angle * inDeg
|
||||
|
||||
endsubroutine
|
||||
|
||||
|
||||
|
|
@ -681,6 +538,124 @@ endsubroutine
|
|||
ENDFUNCTION
|
||||
|
||||
|
||||
!**************************************************************************
|
||||
! quaternion multiplication q1xq2 = q12
|
||||
!**************************************************************************
|
||||
PURE FUNCTION math_qMul(A,B)
|
||||
|
||||
use prec, only: pReal, pInt
|
||||
implicit none
|
||||
|
||||
real(pReal), dimension(4), intent(in) :: A, B
|
||||
real(pReal), dimension(4) :: math_qMul
|
||||
|
||||
math_qMul(1) = A(1)*B(1) - A(2)*B(2) - A(3)*B(3) - A(4)*B(4)
|
||||
math_qMul(2) = A(1)*B(2) + A(2)*B(1) + A(3)*B(4) - A(4)*B(3)
|
||||
math_qMul(3) = A(1)*B(3) - A(2)*B(4) + A(3)*B(1) + A(4)*B(2)
|
||||
math_qMul(4) = A(1)*B(4) + A(2)*B(3) - A(3)*B(2) + A(4)*B(1)
|
||||
|
||||
ENDFUNCTION
|
||||
|
||||
|
||||
!**************************************************************************
|
||||
! quaternion dotproduct
|
||||
!**************************************************************************
|
||||
PURE FUNCTION math_qDot(A,B)
|
||||
|
||||
use prec, only: pReal, pInt
|
||||
implicit none
|
||||
|
||||
real(pReal), dimension(4), intent(in) :: A, B
|
||||
real(pReal) math_qDot
|
||||
|
||||
math_qDot = A(1)*B(1) + A(2)*B(2) + A(3)*B(3) + A(4)*B(4)
|
||||
|
||||
ENDFUNCTION
|
||||
|
||||
|
||||
!**************************************************************************
|
||||
! quaternion conjugation
|
||||
!**************************************************************************
|
||||
PURE FUNCTION math_qConj(Q)
|
||||
|
||||
use prec, only: pReal, pInt
|
||||
implicit none
|
||||
|
||||
real(pReal), dimension(4), intent(in) :: Q
|
||||
real(pReal), dimension(4) :: math_qConj
|
||||
|
||||
math_qConj(1) = Q(1)
|
||||
math_qConj(2:4) = -Q(2:4)
|
||||
|
||||
ENDFUNCTION
|
||||
|
||||
|
||||
!**************************************************************************
|
||||
! quaternion norm
|
||||
!**************************************************************************
|
||||
PURE FUNCTION math_qNorm(Q)
|
||||
|
||||
use prec, only: pReal, pInt
|
||||
implicit none
|
||||
|
||||
real(pReal), dimension(4), intent(in) :: Q
|
||||
real(pReal) math_qNorm
|
||||
|
||||
math_qNorm = dsqrt(max(0.0_pReal, Q(1)*Q(1) + Q(2)*Q(2) + Q(3)*Q(3) + Q(4)*Q(4)))
|
||||
|
||||
ENDFUNCTION
|
||||
|
||||
|
||||
!**************************************************************************
|
||||
! quaternion inversion
|
||||
!**************************************************************************
|
||||
PURE FUNCTION math_qInv(Q)
|
||||
|
||||
use prec, only: pReal, pInt
|
||||
implicit none
|
||||
|
||||
real(pReal), dimension(4), intent(in) :: Q
|
||||
real(pReal), dimension(4) :: math_qInv
|
||||
real(pReal) squareNorm
|
||||
|
||||
math_qInv = 0.0_pReal
|
||||
|
||||
squareNorm = math_qDot(Q,Q)
|
||||
if (squareNorm > tiny(squareNorm)) &
|
||||
math_qInv = math_qConj(Q) / squareNorm
|
||||
|
||||
ENDFUNCTION
|
||||
|
||||
|
||||
!**************************************************************************
|
||||
! quaternion inversion
|
||||
!**************************************************************************
|
||||
PURE FUNCTION math_qRot(Q,v)
|
||||
|
||||
use prec, only: pReal, pInt
|
||||
implicit none
|
||||
|
||||
real(pReal), dimension(4), intent(in) :: Q
|
||||
real(pReal), dimension(3), intent(in) :: v
|
||||
real(pReal), dimension(3) :: math_qRot
|
||||
real(pReal), dimension(4,4) :: T
|
||||
integer(pInt) i, j
|
||||
|
||||
do i = 1,4
|
||||
do j = 1,i
|
||||
T(i,j) = Q(i) * Q(j)
|
||||
enddo
|
||||
enddo
|
||||
|
||||
math_qRot(1) = -v(1)*(T(3,3)+T(4,4)) + v(2)*(T(3,2)-T(4,1)) + v(3)*(T(4,2)+T(3,1))
|
||||
math_qRot(2) = v(1)*(T(3,2)+T(4,1)) - v(2)*(T(2,2)+T(4,4)) + v(3)*(T(4,3)-T(2,1))
|
||||
math_qRot(3) = v(1)*(T(4,2)-T(3,1)) + v(2)*(T(4,3)+T(2,1)) - v(3)*(T(2,2)+T(3,3))
|
||||
|
||||
math_qRot = 2.0_pReal * math_qRot + v
|
||||
|
||||
ENDFUNCTION
|
||||
|
||||
|
||||
!**************************************************************************
|
||||
! transposition of a 3x3 matrix
|
||||
!**************************************************************************
|
||||
|
|
@ -1046,15 +1021,15 @@ pure function math_transpose3x3(A)
|
|||
!********************************************************************
|
||||
! euclidic norm of a 3x1 vector
|
||||
!********************************************************************
|
||||
pure function math_norm3(v3)
|
||||
pure function math_norm3(v)
|
||||
|
||||
use prec, only: pReal,pInt
|
||||
implicit none
|
||||
|
||||
real(pReal), dimension(3), intent(in) :: v3
|
||||
real(pReal), dimension(3), intent(in) :: v
|
||||
real(pReal) math_norm3
|
||||
|
||||
math_norm3 = sqrt(v3(1)*v3(1)+v3(2)*v3(2)+v3(3)*v3(3))
|
||||
math_norm3 = dsqrt(v(1)*v(1) + v(2)*v(2) + v(3)*v(3))
|
||||
return
|
||||
|
||||
endfunction
|
||||
|
|
@ -1275,6 +1250,138 @@ pure function math_transpose3x3(A)
|
|||
ENDFUNCTION
|
||||
|
||||
|
||||
!****************************************************************
|
||||
! rotation matrix from Euler angles
|
||||
!****************************************************************
|
||||
PURE FUNCTION math_EulerToR (Euler)
|
||||
|
||||
use prec, only: pReal, pInt
|
||||
implicit none
|
||||
|
||||
real(pReal), dimension(3), intent(in) :: Euler
|
||||
real(pReal), dimension(3,3) :: math_EulerToR
|
||||
real(pReal) c1, c, c2, s1, s, s2
|
||||
|
||||
C1=COS(Euler(1))
|
||||
C=COS(Euler(2))
|
||||
C2=COS(Euler(3))
|
||||
S1=SIN(Euler(1))
|
||||
S=SIN(Euler(2))
|
||||
S2=SIN(Euler(3))
|
||||
math_EulerToR(1,1)=C1*C2-S1*S2*C
|
||||
math_EulerToR(1,2)=S1*C2+C1*S2*C
|
||||
math_EulerToR(1,3)=S2*S
|
||||
math_EulerToR(2,1)=-C1*S2-S1*C2*C
|
||||
math_EulerToR(2,2)=-S1*S2+C1*C2*C
|
||||
math_EulerToR(2,3)=C2*S
|
||||
math_EulerToR(3,1)=S1*S
|
||||
math_EulerToR(3,2)=-C1*S
|
||||
math_EulerToR(3,3)=C
|
||||
return
|
||||
|
||||
ENDFUNCTION
|
||||
|
||||
|
||||
!********************************************************************
|
||||
! quaternion (w+ix+jy+kz) from orientation matrix
|
||||
!********************************************************************
|
||||
PURE FUNCTION math_RtoQuaternion(R)
|
||||
|
||||
use prec, only: pReal, pInt
|
||||
implicit none
|
||||
|
||||
real(pReal), dimension (3,3), intent(in) :: R
|
||||
real(pReal), dimension(4) :: math_RtoQuaternion, T
|
||||
|
||||
T(1) = max(0.0_pReal, 1.0_pReal + R(1,1) + R(2,2) + R(3,3))
|
||||
T(2) = max(0.0_pReal, 1.0_pReal + R(1,1) - R(2,2) - R(3,3))
|
||||
T(3) = max(0.0_pReal, 1.0_pReal - R(1,1) + R(2,2) - R(3,3))
|
||||
T(4) = max(0.0_pReal, 1.0_pReal - R(1,1) - R(2,2) + R(3,3))
|
||||
|
||||
math_RtoQuaternion = 0.5_pReal * dsqrt(T)
|
||||
|
||||
math_RtoQuaternion(2) = sign(math_RtoQuaternion(2), R(3,2) - R(2,3))
|
||||
math_RtoQuaternion(3) = sign(math_RtoQuaternion(3), R(1,3) - R(3,1))
|
||||
math_RtoQuaternion(4) = sign(math_RtoQuaternion(4), R(2,1) - R(1,2))
|
||||
|
||||
ENDFUNCTION
|
||||
|
||||
|
||||
!********************************************************************
|
||||
! orientation matrix from quaternion (w+ix+jy+kz)
|
||||
!********************************************************************
|
||||
PURE FUNCTION math_QuaternionToR(Q)
|
||||
|
||||
use prec, only: pReal, pInt
|
||||
implicit none
|
||||
|
||||
real(pReal), dimension(4), intent(in) :: Q
|
||||
real(pReal), dimension(3,3) :: math_QuaternionToR, T
|
||||
real(pReal) w2
|
||||
integer(pInt) i, j
|
||||
|
||||
forall (i = 1:3, j = 1:3) &
|
||||
T(i,j) = Q(i+1) * Q(j+1)
|
||||
|
||||
math_QuaternionToR = (2.0_pReal*Q(1)*Q(1) - 1.0_pReal) * math_I3 + 2.0_pReal * T ! symmetrical parts of R
|
||||
|
||||
w2 = 2.0_pReal * Q(1)
|
||||
math_QuaternionToR(2,1) = math_QuaternionToR(2,1) + w2 * Q(4) ! skew parts of R
|
||||
math_QuaternionToR(1,2) = math_QuaternionToR(1,2) - w2 * Q(4)
|
||||
math_QuaternionToR(3,1) = math_QuaternionToR(3,1) - w2 * Q(3)
|
||||
math_QuaternionToR(1,3) = math_QuaternionToR(1,3) + w2 * Q(3)
|
||||
math_QuaternionToR(3,2) = math_QuaternionToR(3,2) + w2 * Q(2)
|
||||
math_QuaternionToR(2,3) = math_QuaternionToR(2,3) - w2 * Q(2)
|
||||
|
||||
ENDFUNCTION
|
||||
|
||||
|
||||
!********************************************************************
|
||||
! orientation matrix from quaternion (w+ix+jy+kz)
|
||||
!********************************************************************
|
||||
PURE FUNCTION math_EulerToQuaternion(eulerangles)
|
||||
|
||||
use prec, only: pReal, pInt
|
||||
implicit none
|
||||
|
||||
real(pReal), dimension(3), intent(in) :: eulerangles
|
||||
real(pReal), dimension(4) :: math_EulerToQuaternion
|
||||
real(pReal), dimension(3) :: angles
|
||||
real(pReal) c, s
|
||||
|
||||
angles = 0.5_pReal * eulerangles * inRad
|
||||
|
||||
c = dcos(angles(2))
|
||||
s = dsin(angles(2))
|
||||
|
||||
math_EulerToQuaternion(1) = dcos(angles(1)+angles(3)) * c
|
||||
math_EulerToQuaternion(2) = dcos(angles(1)-angles(3)) * s
|
||||
math_EulerToQuaternion(3) = dsin(angles(1)-angles(3)) * s
|
||||
math_EulerToQuaternion(4) = dsin(angles(1)+angles(3)) * c
|
||||
|
||||
ENDFUNCTION
|
||||
|
||||
|
||||
!********************************************************************
|
||||
! orientation matrix from quaternion (w+ix+jy+kz)
|
||||
!********************************************************************
|
||||
PURE FUNCTION math_QuaternionToEuler(Q)
|
||||
|
||||
use prec, only: pReal, pInt
|
||||
implicit none
|
||||
|
||||
real(pReal), dimension(4), intent(in) :: Q
|
||||
real(pReal), dimension(3) :: math_QuaternionToEuler
|
||||
|
||||
math_QuaternionToEuler(1) = atan2(Q(1)*Q(3)+Q(2)*Q(4), Q(1)*Q(2)-Q(3)*Q(4))
|
||||
math_QuaternionToEuler(2) = acos(1.0_pReal-2.0_pReal*(Q(2)*Q(2)+Q(3)*Q(3)))
|
||||
math_QuaternionToEuler(3) = atan2(-Q(1)*Q(3)+Q(2)*Q(4), Q(1)*Q(2)+Q(3)*Q(4))
|
||||
|
||||
math_QuaternionToEuler = math_QuaternionToEuler * inDeg
|
||||
|
||||
ENDFUNCTION
|
||||
|
||||
|
||||
!****************************************************************
|
||||
! rotation matrix from axis and angle (in radians)
|
||||
!****************************************************************
|
||||
|
|
@ -1314,38 +1421,6 @@ pure function math_transpose3x3(A)
|
|||
ENDFUNCTION
|
||||
|
||||
|
||||
!****************************************************************
|
||||
! rotation matrix from Euler angles
|
||||
!****************************************************************
|
||||
PURE FUNCTION math_EulerToR (Euler)
|
||||
|
||||
use prec, only: pReal, pInt
|
||||
implicit none
|
||||
|
||||
real(pReal), dimension(3), intent(in) :: Euler
|
||||
real(pReal), dimension(3,3) :: math_EulerToR
|
||||
real(pReal) c1, c, c2, s1, s, s2
|
||||
|
||||
C1=COS(Euler(1))
|
||||
C=COS(Euler(2))
|
||||
C2=COS(Euler(3))
|
||||
S1=SIN(Euler(1))
|
||||
S=SIN(Euler(2))
|
||||
S2=SIN(Euler(3))
|
||||
math_EulerToR(1,1)=C1*C2-S1*S2*C
|
||||
math_EulerToR(1,2)=S1*C2+C1*S2*C
|
||||
math_EulerToR(1,3)=S2*S
|
||||
math_EulerToR(2,1)=-C1*S2-S1*C2*C
|
||||
math_EulerToR(2,2)=-S1*S2+C1*C2*C
|
||||
math_EulerToR(2,3)=C2*S
|
||||
math_EulerToR(3,1)=S1*S
|
||||
math_EulerToR(3,2)=-C1*S
|
||||
math_EulerToR(3,3)=C
|
||||
return
|
||||
|
||||
ENDFUNCTION
|
||||
|
||||
|
||||
!**************************************************************************
|
||||
! disorientation angle between two sets of Euler angles
|
||||
!**************************************************************************
|
||||
|
|
@ -1604,14 +1679,14 @@ math_sampleFiberOri = math_RtoEuler(math_mul33x33(pRot,math_mul33x33(fRot,oRot))
|
|||
EB2(2,2)=1.0_pReal
|
||||
EB3(3,3)=1.0_pReal
|
||||
ELSE
|
||||
RHO=SQRT(-3.0_pReal*P**3.0_pReal)/9.0_pReal
|
||||
RHO=DSQRT(-3.0_pReal*P**3.0_pReal)/9.0_pReal
|
||||
arg=-Q/RHO/2.0_pReal
|
||||
if(arg.GT.1) arg=1
|
||||
if(arg.LT.-1) arg=-1
|
||||
PHI=ACOS(arg)
|
||||
Y1=2*RHO**(1.0_pReal/3.0_pReal)*COS(PHI/3.0_pReal)
|
||||
Y2=2*RHO**(1.0_pReal/3.0_pReal)*COS(PHI/3.0_pReal+2.0_pReal/3.0_pReal*PI)
|
||||
Y3=2*RHO**(1.0_pReal/3.0_pReal)*COS(PHI/3.0_pReal+4.0_pReal/3.0_pReal*PI)
|
||||
PHI=DACOS(arg)
|
||||
Y1=2*RHO**(1.0_pReal/3.0_pReal)*DCOS(PHI/3.0_pReal)
|
||||
Y2=2*RHO**(1.0_pReal/3.0_pReal)*DCOS(PHI/3.0_pReal+2.0_pReal/3.0_pReal*PI)
|
||||
Y3=2*RHO**(1.0_pReal/3.0_pReal)*DCOS(PHI/3.0_pReal+4.0_pReal/3.0_pReal*PI)
|
||||
EW1=Y1-R/3.0_pReal
|
||||
EW2=Y2-R/3.0_pReal
|
||||
EW3=Y3-R/3.0_pReal
|
||||
|
|
|
|||
Loading…
Reference in New Issue