Correspondence Matrix applied
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achalhp
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@ -404,6 +404,7 @@ module crystal
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crystal_slip_direction, &
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crystal_slip_transverse, &
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crystal_labels_slip, &
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crystal_CorrespondenceMatrix_twin, &
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crystal_labels_twin
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contains
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@ -2111,6 +2112,60 @@ function getlabels(active,potential,system) result(labels)
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end function getlabels
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!--------------------------------------------------------------------------------------------------
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!> @brief correspondence matrix for twinning
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!> details only active twin systems are considered
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!--------------------------------------------------------------------------------------------------
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function crystal_CorrespondenceMatrix_twin(Ntwin,lattice,cOverA) result(CorrespondenceMatrix)
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integer, dimension(:), intent(in) :: Ntwin !< number of active twin systems per family
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character(len=*), intent(in) :: lattice !< lattice structure
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real(pReal), intent(in) :: cOverA !< c/a ratio
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real(pReal), dimension(3,3,sum(Ntwin)) :: CorrespondenceMatrix
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real(pReal), dimension(3,3,sum(Ntwin)) :: coordinateSystem
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real(pReal), dimension(sum(Ntwin)) :: characteristicShearTwin
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real(pReal), dimension(3,3,sum(Ntwin)) :: SchmidMatrixTwin
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real(pReal), dimension(:,:), allocatable :: twinSystems
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integer, dimension(:), allocatable :: NtwinMax
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integer :: i
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select case(lattice)
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case('cF')
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NtwinMax = CF_NTWINSYSTEM
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twinSystems = CF_SYSTEMTWIN
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case('cI')
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NtwinMax = CI_NTWINSYSTEM
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twinSystems = CI_SYSTEMTWIN
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case('hP')
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NtwinMax = HP_NTWINSYSTEM
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twinSystems = HP_SYSTEMTWIN !< the twin system matrix is different from V2.0
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case default
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allocate(NtwinMax(0))
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call IO_error(137,ext_msg='crystal_CorrespondenceMatrix_twin: '//trim(lattice))
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end select
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if (any(NtwinMax(1:size(Ntwin)) - Ntwin < 0)) &
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call IO_error(145,ext_msg='Ntwin '//trim(lattice))
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if (any(Ntwin < 0)) &
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call IO_error(144,ext_msg='Ntwin '//trim(lattice))
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coordinateSystem = buildCoordinateSystem(Ntwin,NtwinMax,twinSystems,lattice,cOverA)
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! characteristicShearTwin = 0.0_pReal*lattice_characteristicShear_Twin(Ntwin,lattice,cOverA) ! for removing shear from CorrespondenceMatrix
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characteristicShearTwin = crystal_characteristicShear_Twin(Ntwin,lattice,cOverA)
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SchmidMatrixTwin = crystal_SchmidMatrix_twin(Ntwin,lattice,cOverA)
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!write(6,*)'coordinate system', coordinateSystem(1:3,2,1)
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!CorrespondenceMatrix(1:3,1:3,1) = math_axisAngleToR(coordinateSystem(1:3,2,6), 180.0_pReal*INRAD) ! delete this
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do i = 1, sum(Ntwin)
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CorrespondenceMatrix(1:3,1:3,i) = matmul(math_axisAngleToR(coordinateSystem(1:3,2,i), &
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180.0_pReal*INRAD), MATH_I3 + characteristicShearTwin(i)* &
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SchmidMatrixTwin(1:3,1:3,i))
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enddo
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end function crystal_CorrespondenceMatrix_twin
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!--------------------------------------------------------------------------------------------------
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!> @brief Equivalent Poisson's ratio (ν)
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@ -2307,4 +2362,7 @@ subroutine crystal_selfTest()
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end subroutine crystal_selfTest
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end module crystal
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42
src/math.f90
42
src/math.f90
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@ -1470,4 +1470,46 @@ subroutine math_selfTest()
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end subroutine math_selfTest
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!--------------------------------------------------------------------------------------------------
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!> @brief rotation matrix from axis and angle (in radians)
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!> @details rotation matrix is meant to represent a ACTIVE rotation
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!> @details (see http://en.wikipedia.org/wiki/Euler_angles for definitions)
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!> @details formula for active rotation taken from http://mathworld.wolfram.com/RodriguesRotationFormula.html
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!> @details equivalent to eu2om (P=-1) from "D Rowenhorst et al. Consistent representations of and
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!> @details conversions between 3D rotations, Model. Simul. Mater. Sci. Eng. 23-8 (2015)"
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!--------------------------------------------------------------------------------------------------
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pure function math_axisAngleToR(axis,omega)
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implicit none
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real(pReal), dimension(3,3) :: math_axisAngleToR
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real(pReal), dimension(3), intent(in) :: axis
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real(pReal), intent(in) :: omega
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real(pReal), dimension(3) :: n
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real(pReal) :: norm,s,c,c1
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norm = norm2(axis)
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wellDefined: if (norm > 1.0e-8_pReal) then
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n = axis/norm ! normalize axis to be sure
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s = sin(omega)
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c = cos(omega)
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c1 = 1.0_pReal - c
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math_axisAngleToR(1,1) = c + c1*n(1)**2.0_pReal
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math_axisAngleToR(1,2) = c1*n(1)*n(2) - s*n(3)
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math_axisAngleToR(1,3) = c1*n(1)*n(3) + s*n(2)
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math_axisAngleToR(2,1) = c1*n(1)*n(2) + s*n(3)
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math_axisAngleToR(2,2) = c + c1*n(2)**2.0_pReal
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math_axisAngleToR(2,3) = c1*n(2)*n(3) - s*n(1)
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math_axisAngleToR(3,1) = c1*n(1)*n(3) - s*n(2)
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math_axisAngleToR(3,2) = c1*n(2)*n(3) + s*n(1)
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math_axisAngleToR(3,3) = c + c1*n(3)**2.0_pReal
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else wellDefined
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math_axisAngleToR = math_I3
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endif wellDefined
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end function math_axisAngleToR
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end module math
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@ -32,7 +32,8 @@ submodule(phase:plastic) phenopowerlaw
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P_sl, &
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P_tw, &
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P_nS_pos, &
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P_nS_neg
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P_nS_neg, &
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CorrespondenceMatrix
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integer :: &
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sum_N_sl, & !< total number of active slip system
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sum_N_tw !< total number of active twin systems
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@ -203,12 +204,13 @@ module function plastic_phenopowerlaw_init() result(myPlasticity)
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prm%c_4 = math_expand(pl%get_as1dReal('c_4', requiredSize=size(N_tw), &
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defaultVal=misc_zeros(size(N_tw))), N_tw)
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prm%CorrespondenceMatrix = crystal_CorrespondenceMatrix_twin(N_tw,phase_lattice(ph),phase_cOverA(ph))
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prm%gamma_char = crystal_characteristicShear_twin(N_tw,phase_lattice(ph),phase_cOverA(ph))
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prm%h_tw_tw = crystal_interaction_TwinByTwin(N_tw,pl%get_as1dReal('h_tw-tw'),phase_lattice(ph))
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prm%P_tw = crystal_SchmidMatrix_twin(N_tw,phase_lattice(ph),phase_cOverA(ph))
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prm%systems_tw = crystal_labels_twin(N_tw,phase_lattice(ph))
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! sanity checks
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if (any(prm%dot_gamma_0_tw <= 0.0_pREAL)) extmsg = trim(extmsg)//' dot_gamma_0_tw'
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if (any(prm%n_tw <= 0.0_pREAL)) extmsg = trim(extmsg)//' n_tw'
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@ -225,6 +227,7 @@ module function plastic_phenopowerlaw_init() result(myPlasticity)
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prm%h_0_tw_tw, &
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source=emptyRealArray)
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allocate(prm%h_tw_tw(0,0))
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allocate(prm%CorrespondenceMatrix(0,0,0))
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end if twinActive
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!--------------------------------------------------------------------------------------------------
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@ -511,7 +514,7 @@ pure subroutine kinetics_tw(Mp,ph,en,&
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associate(prm => param(ph), stt => state(ph))
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tau_tw = [(math_tensordot(Mp,prm%P_tw(1:3,1:3,i)),i=1,prm%sum_N_tw)]
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tau_tw = [(math_tensordot(Mp,prm%CorrespondenceMatrix(1:3,1:3,i)),i=1,prm%sum_N_tw)]
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where(tau_tw > 0.0_pREAL)
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dot_gamma_tw = (1.0_pREAL-sum(stt%gamma_tw(:,en)/prm%gamma_char)) & ! only twin in untwinned volume fraction
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