DAMASK_EICMD/src/phase_mechanical_elastic.f90

198 lines
6.4 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
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')
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%asDict(),'C_11','T')
prm%C_12 = polynomial(elastic%asDict(),'C_12','T')
prm%C_44 = polynomial(elastic%asDict(),'C_44','T')
if (any(phase_lattice(ph) == ['hP','tI'])) then
prm%C_13 = polynomial(elastic%asDict(),'C_13','T')
prm%C_33 = polynomial(elastic%asDict(),'C_33','T')
end if
if (phase_lattice(ph) == 'tI') &
prm%C_66 = polynomial(elastic%asDict(),'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) result(mu)
integer, intent(in) :: &
ph, &
en
real(pReal) :: &
mu
mu = lattice_equivalent_mu(elastic_C66(ph,en),'voigt')
end function elastic_mu
!--------------------------------------------------------------------------------------------------
!> @brief return Poisson ratio
!--------------------------------------------------------------------------------------------------
pure module function elastic_nu(ph,en) result(nu)
integer, intent(in) :: &
ph, &
en
real(pReal) :: &
nu
nu = lattice_equivalent_nu(elastic_C66(ph,en),'voigt')
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