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
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!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
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!> @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
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real(pReal) :: &
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M, & !< Taylor factor
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dot_gamma_0, & !< reference strain rate
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n, & !< stress exponent
h_0, &
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h_ln, &
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xi_inf, & !< maximum critical stress
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a, &
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c_1, &
c_4, &
c_3, &
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c_2
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logical :: &
dilatation
character(len=pStringLen), allocatable, dimension(:) :: &
output
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end type tParameters
type :: tIsotropicState
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real(pReal), pointer, dimension(:) :: &
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xi, &
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gamma
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end type tIsotropicState
!--------------------------------------------------------------------------------------------------
! containers for parameters and state
type(tParameters), allocatable, dimension(:) :: param
type(tIsotropicState), allocatable, dimension(:) :: &
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dotState, &
state
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contains
!--------------------------------------------------------------------------------------------------
!> @brief Perform module initialization.
!> @details reads in material parameters, allocates arrays, and does sanity checks
!--------------------------------------------------------------------------------------------------
module function plastic_isotropic_init() result(myPlasticity)
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logical, dimension(:), allocatable :: myPlasticity
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integer :: &
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ph, &
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Nmembers, &
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sizeState, sizeDotState
real(pReal) :: &
xi_0 !< initial critical stress
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character(len=pStringLen) :: &
extmsg = ''
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class(tNode), pointer :: &
phases, &
phase, &
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mech, &
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pl
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myPlasticity = plastic_active('isotropic')
if(count(myPlasticity) == 0) return
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print'(/,a)', ' <<<+- phase:mechanical:plastic:isotropic init -+>>>'
print'(a,i0)', ' # phases: ',count(myPlasticity); flush(IO_STDOUT)
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print*, 'Maiti and Eisenlohr, Scripta Materialia 145:3740, 2018'
print*, '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))
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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__)
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prm%output = output_asStrings(pl)
#else
prm%output = pl%get_asStrings('output',defaultVal=emptyStringArray)
#endif
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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')
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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.)
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!--------------------------------------------------------------------------------------------------
! 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
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Nmembers = count(material_phaseAt2 == ph)
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sizeDotState = size(['xi ','gamma'])
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sizeState = sizeDotState
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call phase_allocateState(plasticState(ph),Nmembers,sizeState,sizeDotState,0)
!--------------------------------------------------------------------------------------------------
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! state aliases and initialization
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stt%xi => plasticState(ph)%state (1,:)
stt%xi = xi_0
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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'
stt%gamma => plasticState(ph)%state (2,:)
dot%gamma => plasticState(ph)%dotState(2,:)
plasticState(ph)%atol(2) = pl%get_asFloat('atol_gamma',defaultVal=1.0e-6_pReal)
if (plasticState(ph)%atol(2) < 0.0_pReal) extmsg = trim(extmsg)//' atol_gamma'
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! global alias
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plasticState(ph)%slipRate => plasticState(ph)%dotState(2:2,:)
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plasticState(ph)%state0 = plasticState(ph)%state ! ToDo: this could be done centrally
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end associate
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!--------------------------------------------------------------------------------------------------
! exit if any parameter is out of range
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if (extmsg /= '') call IO_error(211,ext_msg=trim(extmsg)//'(isotropic)')
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enddo
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end function plastic_isotropic_init
!--------------------------------------------------------------------------------------------------
!> @brief Calculate plastic velocity gradient and its tangent.
!--------------------------------------------------------------------------------------------------
module subroutine isotropic_LpAndItsTangent(Lp,dLp_dMp,Mp,ph,me)
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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
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real(pReal), dimension(3,3), intent(in) :: &
Mp !< Mandel stress
integer, intent(in) :: &
ph, &
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me
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real(pReal), dimension(3,3) :: &
Mp_dev !< deviatoric part of the Mandel stress
real(pReal) :: &
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dot_gamma, & !< strainrate
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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))
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Mp_dev = math_deviatoric33(Mp)
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squarenorm_Mp_dev = math_tensordot(Mp_dev,Mp_dev)
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norm_Mp_dev = sqrt(squarenorm_Mp_dev)
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if (norm_Mp_dev > 0.0_pReal) then
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dot_gamma = prm%dot_gamma_0 * (sqrt(1.5_pReal) * norm_Mp_dev/(prm%M*stt%xi(me))) **prm%n
Lp = dot_gamma/prm%M * Mp_dev/norm_Mp_dev
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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
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dLp_dMp = dot_gamma / prm%M * dLp_dMp / norm_Mp_dev
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else
Lp = 0.0_pReal
dLp_dMp = 0.0_pReal
end if
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end associate
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end subroutine isotropic_LpAndItsTangent
!--------------------------------------------------------------------------------------------------
!> @brief Calculate inelastic velocity gradient and its tangent.
!--------------------------------------------------------------------------------------------------
module subroutine plastic_isotropic_LiAndItsTangent(Li,dLi_dMi,Mi,ph,me)
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real(pReal), dimension(3,3), intent(out) :: &
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Li !< inleastic velocity gradient
real(pReal), dimension(3,3,3,3), intent(out) :: &
dLi_dMi !< derivative of Li with respect to Mandel stress
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real(pReal), dimension(3,3), intent(in) :: &
Mi !< Mandel stress
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integer, intent(in) :: &
ph, &
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me
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real(pReal) :: &
tr !< trace of spherical part of Mandel stress (= 3 x pressure)
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integer :: &
k, l, m, n
associate(prm => param(ph), stt => state(ph))
tr=math_trace33(math_spherical33(Mi))
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if (prm%dilatation .and. abs(tr) > 0.0_pReal) then ! no stress or J2 plasticity --> Li and its derivative are zero
Li = math_I3 &
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* prm%dot_gamma_0/prm%M * (3.0_pReal*prm%M*stt%xi(me))**(-prm%n) &
* tr * abs(tr)**(prm%n-1.0_pReal)
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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)
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else
Li = 0.0_pReal
dLi_dMi = 0.0_pReal
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endif
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end associate
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end subroutine plastic_isotropic_LiAndItsTangent
!--------------------------------------------------------------------------------------------------
!> @brief Calculate the rate of change of microstructure.
!--------------------------------------------------------------------------------------------------
module subroutine isotropic_dotState(Mp,ph,me)
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real(pReal), dimension(3,3), intent(in) :: &
Mp !< Mandel stress
integer, intent(in) :: &
ph, &
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me
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real(pReal) :: &
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dot_gamma, & !< strainrate
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xi_inf_star, & !< saturation xi
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norm_Mp !< norm of the (deviatoric) Mandel stress
associate(prm => param(ph), stt => state(ph), &
dot => dotState(ph))
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if (prm%dilatation) then
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norm_Mp = sqrt(math_tensordot(Mp,Mp))
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else
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norm_Mp = sqrt(math_tensordot(math_deviatoric33(Mp),math_deviatoric33(Mp)))
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endif
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dot_gamma = prm%dot_gamma_0 * (sqrt(1.5_pReal) * norm_Mp /(prm%M*stt%xi(me))) **prm%n
if (dot_gamma > 1e-12_pReal) then
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if (dEq0(prm%c_1)) then
xi_inf_star = prm%xi_inf
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else
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xi_inf_star = prm%xi_inf &
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+ 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)
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endif
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dot%xi(me) = dot_gamma &
* ( prm%h_0 + prm%h_ln * log(dot_gamma) ) &
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* abs( 1.0_pReal - stt%xi(me)/xi_inf_star )**prm%a &
* sign(1.0_pReal, 1.0_pReal - stt%xi(me)/xi_inf_star)
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else
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dot%xi(me) = 0.0_pReal
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endif
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dot%gamma(me) = dot_gamma ! ToDo: not really used
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end associate
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end subroutine isotropic_dotState
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!--------------------------------------------------------------------------------------------------
!> @brief Write results to HDF5 output file.
!--------------------------------------------------------------------------------------------------
module subroutine plastic_isotropic_results(ph,group)
integer, intent(in) :: ph
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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')
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call results_writeDataset(group,stt%xi,trim(prm%output(o)), &
'resistance against plastic flow','Pa')
end select
enddo outputsLoop
end associate
end subroutine plastic_isotropic_results
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end submodule isotropic