DAMASK_EICMD/src/phase_mechanical_plastic_is...

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!--------------------------------------------------------------------------------------------------
!> @author Franz Roters, Max-Planck-Institut für Eisenforschung GmbH
!> @author Philip Eisenlohr, Max-Planck-Institut für Eisenforschung GmbH
!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
!> @brief material subroutine for isotropic plasticity
!> @details Isotropic Plasticity which resembles the phenopowerlaw plasticity without
!! resolving the stress on the slip systems. Will give the response of phenopowerlaw for an
!! untextured polycrystal
!--------------------------------------------------------------------------------------------------
submodule(phase:plastic) isotropic
type :: tParameters
real(pReal) :: &
M, & !< Taylor factor
dot_gamma_0, & !< reference strain rate
n, & !< stress exponent
h_0, &
h, & !< hardening pre-factor
h_ln, &
xi_inf, & !< maximum critical stress
a, &
c_1, &
c_4, &
c_3, &
c_2
logical :: &
dilatation
character(len=pStringLen), allocatable, dimension(:) :: &
output
end type tParameters
type :: tIsotropicState
real(pReal), pointer, dimension(:) :: &
xi
end type tIsotropicState
!--------------------------------------------------------------------------------------------------
! containers for parameters and state
type(tParameters), allocatable, dimension(:) :: param
type(tIsotropicState), allocatable, dimension(:) :: &
dotState, &
state
contains
!--------------------------------------------------------------------------------------------------
!> @brief Perform module initialization.
!> @details reads in material parameters, allocates arrays, and does sanity checks
!--------------------------------------------------------------------------------------------------
module function plastic_isotropic_init() result(myPlasticity)
logical, dimension(:), allocatable :: myPlasticity
integer :: &
ph, &
Nmembers, &
sizeState, sizeDotState
real(pReal) :: &
xi_0 !< initial critical stress
character(len=pStringLen) :: &
extmsg = ''
class(tNode), pointer :: &
phases, &
phase, &
mech, &
pl
myPlasticity = plastic_active('isotropic')
if(count(myPlasticity) == 0) return
print'(/,1x,a)', '<<<+- phase:mechanical:plastic:isotropic init -+>>>'
print'(/,a,i0)', ' # phases: ',count(myPlasticity); flush(IO_STDOUT)
print'(/,a)', 'T. Maiti and P. Eisenlohr, Scripta Materialia 145:3740, 2018'
print'(/,a)', 'https://doi.org/10.1016/j.scriptamat.2017.09.047'
phases => config_material%get('phase')
allocate(param(phases%length))
allocate(state(phases%length))
allocate(dotState(phases%length))
do ph = 1, phases%length
if(.not. myPlasticity(ph)) cycle
associate(prm => param(ph), dot => dotState(ph), stt => state(ph))
phase => phases%get(ph)
mech => phase%get('mechanical')
pl => mech%get('plastic')
#if defined (__GFORTRAN__)
prm%output = output_as1dString(pl)
#else
prm%output = pl%get_as1dString('output',defaultVal=emptyStringArray)
#endif
xi_0 = pl%get_asFloat('xi_0')
prm%xi_inf = pl%get_asFloat('xi_inf')
prm%dot_gamma_0 = pl%get_asFloat('dot_gamma_0')
prm%n = pl%get_asFloat('n')
prm%h_0 = pl%get_asFloat('h_0')
prm%h = pl%get_asFloat('h', defaultVal=3.0_pReal) ! match for fcc random polycrystal
prm%M = pl%get_asFloat('M')
prm%h_ln = pl%get_asFloat('h_ln', defaultVal=0.0_pReal)
prm%c_1 = pl%get_asFloat('c_1', defaultVal=0.0_pReal)
prm%c_4 = pl%get_asFloat('c_4', defaultVal=0.0_pReal)
prm%c_3 = pl%get_asFloat('c_3', defaultVal=0.0_pReal)
prm%c_2 = pl%get_asFloat('c_2', defaultVal=0.0_pReal)
prm%a = pl%get_asFloat('a')
prm%dilatation = pl%get_AsBool('dilatation',defaultVal = .false.)
!--------------------------------------------------------------------------------------------------
! sanity checks
if (xi_0 < 0.0_pReal) extmsg = trim(extmsg)//' xi_0'
if (prm%dot_gamma_0 <= 0.0_pReal) extmsg = trim(extmsg)//' dot_gamma_0'
if (prm%n <= 0.0_pReal) extmsg = trim(extmsg)//' n'
if (prm%a <= 0.0_pReal) extmsg = trim(extmsg)//' a'
if (prm%M <= 0.0_pReal) extmsg = trim(extmsg)//' M'
!--------------------------------------------------------------------------------------------------
! allocate state arrays
Nmembers = count(material_phaseID == ph)
sizeDotState = size(['xi'])
sizeState = sizeDotState
call phase_allocateState(plasticState(ph),Nmembers,sizeState,sizeDotState,0)
!--------------------------------------------------------------------------------------------------
! state aliases and initialization
stt%xi => plasticState(ph)%state (1,:)
stt%xi = xi_0
dot%xi => plasticState(ph)%dotState(1,:)
plasticState(ph)%atol(1) = pl%get_asFloat('atol_xi',defaultVal=1.0_pReal)
if (plasticState(ph)%atol(1) < 0.0_pReal) extmsg = trim(extmsg)//' atol_xi'
end associate
!--------------------------------------------------------------------------------------------------
! exit if any parameter is out of range
if (extmsg /= '') call IO_error(211,ext_msg=trim(extmsg)//'(isotropic)')
end do
end function plastic_isotropic_init
!--------------------------------------------------------------------------------------------------
!> @brief Calculate plastic velocity gradient and its tangent.
!--------------------------------------------------------------------------------------------------
module subroutine isotropic_LpAndItsTangent(Lp,dLp_dMp,Mp,ph,en)
real(pReal), dimension(3,3), intent(out) :: &
Lp !< plastic velocity gradient
real(pReal), dimension(3,3,3,3), intent(out) :: &
dLp_dMp !< derivative of Lp with respect to the Mandel stress
real(pReal), dimension(3,3), intent(in) :: &
Mp !< Mandel stress
integer, intent(in) :: &
ph, &
en
real(pReal), dimension(3,3) :: &
Mp_dev !< deviatoric part of the Mandel stress
real(pReal) :: &
dot_gamma, & !< strainrate
norm_Mp_dev, & !< norm of the deviatoric part of the Mandel stress
squarenorm_Mp_dev !< square of the norm of the deviatoric part of the Mandel stress
integer :: &
k, l, m, n
associate(prm => param(ph), stt => state(ph))
Mp_dev = math_deviatoric33(Mp)
squarenorm_Mp_dev = math_tensordot(Mp_dev,Mp_dev)
norm_Mp_dev = sqrt(squarenorm_Mp_dev)
if (norm_Mp_dev > 0.0_pReal) then
dot_gamma = prm%dot_gamma_0 * (sqrt(1.5_pReal) * norm_Mp_dev/(prm%M*stt%xi(en))) **prm%n
Lp = dot_gamma * Mp_dev/norm_Mp_dev
forall (k=1:3,l=1:3,m=1:3,n=1:3) &
dLp_dMp(k,l,m,n) = (prm%n-1.0_pReal) * Mp_dev(k,l)*Mp_dev(m,n) / squarenorm_Mp_dev
forall (k=1:3,l=1:3) &
dLp_dMp(k,l,k,l) = dLp_dMp(k,l,k,l) + 1.0_pReal
forall (k=1:3,m=1:3) &
dLp_dMp(k,k,m,m) = dLp_dMp(k,k,m,m) - 1.0_pReal/3.0_pReal
dLp_dMp = dot_gamma * dLp_dMp / norm_Mp_dev
else
Lp = 0.0_pReal
dLp_dMp = 0.0_pReal
end if
end associate
end subroutine isotropic_LpAndItsTangent
!--------------------------------------------------------------------------------------------------
!> @brief Calculate inelastic velocity gradient and its tangent.
!--------------------------------------------------------------------------------------------------
module subroutine plastic_isotropic_LiAndItsTangent(Li,dLi_dMi,Mi,ph,en)
real(pReal), dimension(3,3), intent(out) :: &
Li !< inleastic velocity gradient
real(pReal), dimension(3,3,3,3), intent(out) :: &
dLi_dMi !< derivative of Li with respect to Mandel stress
real(pReal), dimension(3,3), intent(in) :: &
Mi !< Mandel stress
integer, intent(in) :: &
ph, &
en
real(pReal) :: &
tr !< trace of spherical part of Mandel stress (= 3 x pressure)
integer :: &
k, l, m, n
associate(prm => param(ph), stt => state(ph))
tr=math_trace33(math_spherical33(Mi))
if (prm%dilatation .and. abs(tr) > 0.0_pReal) then ! no stress or J2 plasticity --> Li and its derivative are zero
Li = math_I3 &
* prm%dot_gamma_0 * (3.0_pReal*prm%M*stt%xi(en))**(-prm%n) &
* tr * abs(tr)**(prm%n-1.0_pReal)
forall (k=1:3,l=1:3,m=1:3,n=1:3) dLi_dMi(k,l,m,n) = prm%n / tr * Li(k,l) * math_I3(m,n)
else
Li = 0.0_pReal
dLi_dMi = 0.0_pReal
end if
end associate
end subroutine plastic_isotropic_LiAndItsTangent
!--------------------------------------------------------------------------------------------------
!> @brief Calculate the rate of change of microstructure.
!--------------------------------------------------------------------------------------------------
module subroutine isotropic_dotState(Mp,ph,en)
real(pReal), dimension(3,3), intent(in) :: &
Mp !< Mandel stress
integer, intent(in) :: &
ph, &
en
real(pReal) :: &
dot_gamma, & !< strainrate
xi_inf_star, & !< saturation xi
norm_Mp !< norm of the (deviatoric) Mandel stress
associate(prm => param(ph), stt => state(ph), &
dot => dotState(ph))
if (prm%dilatation) then
norm_Mp = sqrt(math_tensordot(Mp,Mp))
else
norm_Mp = sqrt(math_tensordot(math_deviatoric33(Mp),math_deviatoric33(Mp)))
end if
dot_gamma = prm%dot_gamma_0 * (sqrt(1.5_pReal) * norm_Mp /(prm%M*stt%xi(en))) **prm%n
if (dot_gamma > 1e-12_pReal) then
if (dEq0(prm%c_1)) then
xi_inf_star = prm%xi_inf
else
xi_inf_star = prm%xi_inf &
+ asinh( (dot_gamma / prm%c_1)**(1.0_pReal / prm%c_2))**(1.0_pReal / prm%c_3) &
/ prm%c_4 * (dot_gamma / prm%dot_gamma_0)**(1.0_pReal / prm%n)
end if
dot%xi(en) = dot_gamma &
* ( prm%h_0 + prm%h_ln * log(dot_gamma) ) &
* sign(abs(1.0_pReal - stt%xi(en)/xi_inf_star)**prm%a *prm%h, 1.0_pReal-stt%xi(en)/xi_inf_star)
else
dot%xi(en) = 0.0_pReal
end if
end associate
end subroutine isotropic_dotState
!--------------------------------------------------------------------------------------------------
!> @brief Write results to HDF5 output file.
!--------------------------------------------------------------------------------------------------
module subroutine plastic_isotropic_results(ph,group)
integer, intent(in) :: ph
character(len=*), intent(in) :: group
integer :: o
associate(prm => param(ph), stt => state(ph))
outputsLoop: do o = 1,size(prm%output)
select case(trim(prm%output(o)))
case ('xi')
call results_writeDataset(stt%xi,group,trim(prm%output(o)), &
'resistance against plastic flow','Pa')
end select
end do outputsLoop
end associate
end subroutine plastic_isotropic_results
end submodule isotropic