DAMASK_EICMD/src/phase_mechanical_elastic.f90

198 lines
6.4 KiB
Fortran
Raw Normal View History

2021-03-16 21:50:24 +05:30
submodule(phase:mechanical) elastic
type :: tParameters
2022-01-31 19:35:15 +05:30
type(tPolynomial) :: &
C_11, &
C_12, &
C_13, &
C_33, &
C_44, &
C_66
end type tParameters
type(tParameters), allocatable, dimension(:) :: param
2021-03-16 21:50:24 +05:30
contains
!--------------------------------------------------------------------------------------------------
2021-11-22 02:19:04 +05:30
!> @brief initialize elasticity
!--------------------------------------------------------------------------------------------------
2021-03-16 21:50:24 +05:30
module subroutine elastic_init(phases)
class(tNode), pointer :: &
phases
integer :: &
2021-05-20 02:07:36 +05:30
ph
2021-03-16 21:50:24 +05:30
class(tNode), pointer :: &
phase, &
mech, &
2021-05-20 02:07:36 +05:30
elastic
2022-01-10 22:33:32 +05:30
print'(/,1x,a)', '<<<+- phase:mechanical:elastic init -+>>>'
print'(/,1x,a)', '<<<+- phase:mechanical:elastic:Hooke init -+>>>'
2021-05-27 11:55:48 +05:30
print'(/,a,i0)', ' # phases: ',phases%length; flush(IO_STDOUT)
2021-03-16 21:50:24 +05:30
allocate(param(phases%length))
2021-03-16 21:50:24 +05:30
do ph = 1, phases%length
phase => phases%get(ph)
mech => phase%get('mechanical')
elastic => mech%get('elastic')
if (elastic%get_asString('type') /= 'Hooke') call IO_error(200,ext_msg=elastic%get_asString('type'))
associate(prm => param(ph))
2022-01-31 19:35:15 +05:30
prm%C_11 = polynomial(elastic%asDict(),'C_11','T')
prm%C_12 = polynomial(elastic%asDict(),'C_12','T')
prm%C_44 = polynomial(elastic%asDict(),'C_44','T')
2022-02-13 03:08:58 +05:30
2021-06-01 14:39:02 +05:30
if (any(phase_lattice(ph) == ['hP','tI'])) then
2022-01-31 19:35:15 +05:30
prm%C_13 = polynomial(elastic%asDict(),'C_13','T')
prm%C_33 = polynomial(elastic%asDict(),'C_33','T')
2021-11-25 03:21:14 +05:30
end if
2022-01-31 19:35:15 +05:30
if (phase_lattice(ph) == 'tI') &
prm%C_66 = polynomial(elastic%asDict(),'C_66','T')
end associate
end do
2021-03-16 21:50:24 +05:30
end subroutine elastic_init
2021-11-18 17:16:37 +05:30
!--------------------------------------------------------------------------------------------------
2021-11-22 02:19:04 +05:30
!> @brief return 6x6 elasticity tensor
!--------------------------------------------------------------------------------------------------
pure module function elastic_C66(ph,en) result(C66)
integer, intent(in) :: &
ph, &
en
2021-11-26 21:53:42 +05:30
real(pReal), dimension(6,6) :: C66
2021-11-25 03:21:14 +05:30
real(pReal) :: T
2021-11-18 17:16:37 +05:30
associate(prm => param(ph))
2022-02-02 22:15:13 +05:30
C66 = 0.0_pReal
2021-11-25 03:21:14 +05:30
T = thermal_T(ph,en)
2021-11-25 19:21:31 +05:30
2022-01-31 19:35:15 +05:30
C66(1,1) = prm%C_11%at(T)
C66(1,2) = prm%C_12%at(T)
C66(4,4) = prm%C_44%at(T)
if (any(phase_lattice(ph) == ['hP','tI'])) then
2022-01-31 19:35:15 +05:30
C66(1,3) = prm%C_13%at(T)
C66(3,3) = prm%C_33%at(T)
end if
2021-11-18 17:16:37 +05:30
2022-01-31 19:35:15 +05:30
if (phase_lattice(ph) == 'tI') C66(6,6) = prm%C_66%at(T)
2021-11-18 17:16:37 +05:30
C66 = lattice_symmetrize_C66(C66,phase_lattice(ph))
end associate
end function elastic_C66
2021-11-18 17:16:37 +05:30
!--------------------------------------------------------------------------------------------------
2021-11-22 02:19:04 +05:30
!> @brief return shear modulus
!--------------------------------------------------------------------------------------------------
pure module function elastic_mu(ph,en) result(mu)
integer, intent(in) :: &
ph, &
en
real(pReal) :: &
mu
2021-11-18 17:16:37 +05:30
mu = lattice_equivalent_mu(elastic_C66(ph,en),'voigt')
end function elastic_mu
!--------------------------------------------------------------------------------------------------
2021-11-22 02:19:04 +05:30
!> @brief return Poisson ratio
!--------------------------------------------------------------------------------------------------
pure module function elastic_nu(ph,en) result(nu)
integer, intent(in) :: &
ph, &
en
real(pReal) :: &
nu
2021-11-18 17:16:37 +05:30
nu = lattice_equivalent_nu(elastic_C66(ph,en),'voigt')
end function elastic_nu
2021-03-16 21:50:24 +05:30
!--------------------------------------------------------------------------------------------------
2021-11-22 02:19:04 +05:30
!> @brief return the 2nd Piola-Kirchhoff stress tensor and its tangent with respect to
2021-03-16 21:50:24 +05:30
!> the elastic and intermediate deformation gradients using Hooke's law
! ToDo: Use Voigt matrix directly
2021-03-16 21:50:24 +05:30
!--------------------------------------------------------------------------------------------------
module subroutine phase_hooke_SandItsTangents(S, dS_dFe, dS_dFi, &
2021-04-29 02:59:57 +05:30
Fe, Fi, ph, en)
2021-03-16 21:50:24 +05:30
integer, intent(in) :: &
ph, &
2021-04-29 02:59:57 +05:30
en
2021-03-16 21:50:24 +05:30
real(pReal), intent(in), dimension(3,3) :: &
Fe, & !< elastic deformation gradient
Fi !< intermediate deformation gradient
real(pReal), intent(out), dimension(3,3) :: &
S !< 2nd Piola-Kirchhoff stress tensor in lattice configuration
real(pReal), intent(out), dimension(3,3,3,3) :: &
dS_dFe, & !< derivative of 2nd P-K stress with respect to elastic deformation gradient
dS_dFi !< derivative of 2nd P-K stress with respect to intermediate deformation gradient
real(pReal), dimension(3,3) :: E
real(pReal), dimension(6,6) :: C66
2021-03-16 21:50:24 +05:30
real(pReal), dimension(3,3,3,3) :: C
integer :: &
i, j
C66 = phase_damage_C66(phase_homogenizedC66(ph,en),ph,en)
C = math_Voigt66to3333_stiffness(C66)
2021-03-16 21:50:24 +05:30
E = 0.5_pReal*(matmul(transpose(Fe),Fe)-math_I3) !< Green-Lagrange strain in unloaded configuration
S = math_Voigt6to33_stress(matmul(C66,math_33toVoigt6_strain(matmul(matmul(transpose(Fi),E),Fi))))!< 2PK stress in lattice configuration in work conjugate with GL strain pulled back to lattice configuration
2021-03-16 21:50:24 +05:30
2021-11-19 02:29:09 +05:30
do i =1,3; do j=1,3
2021-03-16 21:50:24 +05:30
dS_dFe(i,j,1:3,1:3) = matmul(Fe,matmul(matmul(Fi,C(i,j,1:3,1:3)),transpose(Fi))) !< dS_ij/dFe_kl = C_ijmn * Fi_lm * Fi_on * Fe_ko
dS_dFi(i,j,1:3,1:3) = 2.0_pReal*matmul(matmul(E,Fi),C(i,j,1:3,1:3)) !< dS_ij/dFi_kl = C_ijln * E_km * Fe_mn
end do; end do
2021-03-16 21:50:24 +05:30
end subroutine phase_hooke_SandItsTangents
2021-04-29 19:46:51 +05:30
!--------------------------------------------------------------------------------------------------
!> @brief Return the homogenized elasticity matrix.
2021-04-29 19:46:51 +05:30
!--------------------------------------------------------------------------------------------------
2021-11-18 21:07:34 +05:30
module function phase_homogenizedC66(ph,en) result(C)
2021-04-29 19:46:51 +05:30
real(pReal), dimension(6,6) :: C
integer, intent(in) :: ph, en
2021-11-18 17:16:37 +05:30
2021-04-29 19:46:51 +05:30
plasticType: select case (phase_plasticity(ph))
2021-12-11 14:24:46 +05:30
case (PLASTIC_DISLOTWIN_ID) plasticType
C = plastic_dislotwin_homogenizedC(ph,en)
2021-04-29 19:46:51 +05:30
case default plasticType
2021-11-19 02:29:09 +05:30
C = elastic_C66(ph,en)
2021-04-29 19:46:51 +05:30
end select plasticType
2021-11-18 21:07:34 +05:30
end function phase_homogenizedC66
2021-04-29 19:46:51 +05:30
2021-03-16 21:50:24 +05:30
end submodule elastic