213 lines
6.8 KiB
Fortran
213 lines
6.8 KiB
Fortran
submodule(phase:mechanical) elastic
|
|
|
|
type :: tParameters
|
|
type(tPolynomial) :: &
|
|
C_11, &
|
|
C_12, &
|
|
C_13, &
|
|
C_33, &
|
|
C_44, &
|
|
C_66
|
|
end type tParameters
|
|
|
|
type(tParameters), allocatable, dimension(:) :: param
|
|
|
|
contains
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief initialize elasticity
|
|
!--------------------------------------------------------------------------------------------------
|
|
module subroutine elastic_init(phases)
|
|
|
|
type(tDict), pointer :: &
|
|
phases
|
|
|
|
integer :: &
|
|
ph
|
|
type(tDict), pointer :: &
|
|
phase, &
|
|
mech, &
|
|
elastic
|
|
character(len=:), allocatable :: refs
|
|
|
|
|
|
print'(/,1x,a)', '<<<+- phase:mechanical:elastic init -+>>>'
|
|
print'(/,1x,a)', '<<<+- phase:mechanical:elastic:Hooke init -+>>>'
|
|
|
|
print'(/,a,i0)', ' # phases: ',phases%length; flush(IO_STDOUT)
|
|
|
|
|
|
allocate(param(phases%length))
|
|
|
|
do ph = 1, phases%length
|
|
phase => phases%get_dict(ph)
|
|
mech => phase%get_dict('mechanical')
|
|
elastic => mech%get_dict('elastic')
|
|
print'(/,1x,a,i0,a)', 'phase ',ph,': '//phases%key(ph)
|
|
refs = config_listReferences(elastic,indent=3)
|
|
if (len(refs) > 0) print'(/,1x,a)', refs
|
|
if (elastic%get_asString('type') /= 'Hooke') call IO_error(200,ext_msg=elastic%get_asString('type'))
|
|
|
|
associate(prm => param(ph))
|
|
|
|
prm%C_11 = polynomial(elastic,'C_11','T')
|
|
prm%C_12 = polynomial(elastic,'C_12','T')
|
|
prm%C_44 = polynomial(elastic,'C_44','T')
|
|
|
|
if (any(phase_lattice(ph) == ['hP','tI'])) then
|
|
prm%C_13 = polynomial(elastic,'C_13','T')
|
|
prm%C_33 = polynomial(elastic,'C_33','T')
|
|
end if
|
|
|
|
if (phase_lattice(ph) == 'tI') &
|
|
prm%C_66 = polynomial(elastic,'C_66','T')
|
|
|
|
end associate
|
|
end do
|
|
|
|
end subroutine elastic_init
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief return 6x6 elasticity tensor
|
|
!--------------------------------------------------------------------------------------------------
|
|
pure module function elastic_C66(ph,en) result(C66)
|
|
|
|
integer, intent(in) :: &
|
|
ph, &
|
|
en
|
|
|
|
real(pReal), dimension(6,6) :: C66
|
|
real(pReal) :: T
|
|
|
|
|
|
associate(prm => param(ph))
|
|
|
|
C66 = 0.0_pReal
|
|
T = thermal_T(ph,en)
|
|
|
|
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
|
|
C66(1,3) = prm%C_13%at(T)
|
|
C66(3,3) = prm%C_33%at(T)
|
|
end if
|
|
|
|
if (phase_lattice(ph) == 'tI') C66(6,6) = prm%C_66%at(T)
|
|
|
|
C66 = lattice_symmetrize_C66(C66,phase_lattice(ph))
|
|
|
|
end associate
|
|
|
|
end function elastic_C66
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief return shear modulus
|
|
!--------------------------------------------------------------------------------------------------
|
|
pure module function elastic_mu(ph,en,isotropic_bound) result(mu)
|
|
|
|
integer, intent(in) :: &
|
|
ph, &
|
|
en
|
|
character(len=*), intent(in) :: isotropic_bound
|
|
real(pReal) :: &
|
|
mu
|
|
|
|
|
|
associate(prm => param(ph))
|
|
|
|
mu = lattice_isotropic_mu(elastic_C66(ph,en),isotropic_bound,phase_lattice(ph))
|
|
|
|
end associate
|
|
|
|
end function elastic_mu
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief return Poisson ratio
|
|
!--------------------------------------------------------------------------------------------------
|
|
pure module function elastic_nu(ph,en,isotropic_bound) result(nu)
|
|
|
|
integer, intent(in) :: &
|
|
ph, &
|
|
en
|
|
character(len=*), intent(in) :: isotropic_bound
|
|
real(pReal) :: &
|
|
nu
|
|
|
|
|
|
associate(prm => param(ph))
|
|
|
|
nu = lattice_isotropic_nu(elastic_C66(ph,en),isotropic_bound,phase_lattice(ph))
|
|
|
|
end associate
|
|
|
|
end function elastic_nu
|
|
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief return the 2nd Piola-Kirchhoff stress tensor and its tangent with respect to
|
|
!> the elastic and intermediate deformation gradients using Hooke's law
|
|
! ToDo: Use Voigt matrix directly
|
|
!--------------------------------------------------------------------------------------------------
|
|
module subroutine phase_hooke_SandItsTangents(S, dS_dFe, dS_dFi, &
|
|
Fe, Fi, ph, en)
|
|
|
|
integer, intent(in) :: &
|
|
ph, &
|
|
en
|
|
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
|
|
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)
|
|
|
|
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
|
|
|
|
do i =1,3; do j=1,3
|
|
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
|
|
|
|
end subroutine phase_hooke_SandItsTangents
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief Return the homogenized elasticity matrix.
|
|
!--------------------------------------------------------------------------------------------------
|
|
module function phase_homogenizedC66(ph,en) result(C)
|
|
|
|
real(pReal), dimension(6,6) :: C
|
|
integer, intent(in) :: ph, en
|
|
|
|
|
|
plasticType: select case (phase_plasticity(ph))
|
|
case (PLASTIC_DISLOTWIN_ID) plasticType
|
|
C = plastic_dislotwin_homogenizedC(ph,en)
|
|
case default plasticType
|
|
C = elastic_C66(ph,en)
|
|
end select plasticType
|
|
|
|
end function phase_homogenizedC66
|
|
|
|
|
|
end submodule elastic
|