added intermediate configuration to crystal plasticity kinematics intended handle intermediate deformation stages consistently in a finite strain framework
currently implemented for thermal strains, but will expand on this to add damage strains, phase transformation strains etc.
This commit is contained in:
Pratheek Shanthraj
parent
f9a1e71207
commit
9779127521
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@ -36,6 +36,7 @@ module constitutive
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constitutive_getAdiabaticTemperature, &
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constitutive_putAdiabaticTemperature, &
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constitutive_getTemperature, &
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constitutive_getThermalStrain, &
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constitutive_getLocalVacancyConcentration, &
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constitutive_putLocalVacancyConcentration, &
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constitutive_getVacancyConcentration, &
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@ -712,10 +713,7 @@ subroutine constitutive_hooke_TandItsTangent(T, dT_dFe, Fe, ipc, ip, el)
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damage = constitutive_getDamage(ipc,ip,el)
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C = damage*damage*math_Mandel66to3333(constitutive_homogenizedC(ipc,ip,el))
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T = math_mul3333xx33(C,0.5_pReal*(math_mul33x33(math_transpose33(Fe),Fe)-math_I3) - &
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lattice_thermalExpansion33(1:3,1:3,mappingConstitutive(2,ipc,ip,el))* &
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(constitutive_getTemperature(ipc,ip,el) - &
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lattice_referenceTemperature(mappingConstitutive(2,ipc,ip,el))))
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T = math_mul3333xx33(C,0.5_pReal*(math_mul33x33(math_transpose33(Fe),Fe)-math_I3))
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dT_dFe = 0.0_pReal
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forall (i=1_pInt:3_pInt, j=1_pInt:3_pInt, k=1_pInt:3_pInt, l=1_pInt:3_pInt) &
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@ -1169,8 +1167,6 @@ function constitutive_getTemperature(ipc, ip, el)
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FIELD_THERMAL_local_ID, &
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FIELD_THERMAL_nonlocal_ID, &
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material_homog
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use lattice, only: &
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lattice_referenceTemperature
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implicit none
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integer(pInt), intent(in) :: &
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ipc, & !< grain number
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@ -1191,6 +1187,35 @@ function constitutive_getTemperature(ipc, ip, el)
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end function constitutive_getTemperature
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!--------------------------------------------------------------------------------------------------
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!> @brief returns thermal deformation gradient
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!--------------------------------------------------------------------------------------------------
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function constitutive_getThermalStrain(ipc, ip, el)
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use prec, only: &
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pReal
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use math, only: &
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math_I3
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use lattice, only: &
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lattice_referenceTemperature, &
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lattice_thermalExpansion33
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use material, only: &
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mappingConstitutive
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implicit none
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integer(pInt), intent(in) :: &
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ipc, & !< grain number
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ip, & !< integration point number
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el !< element number
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real(pReal), dimension(3,3) :: &
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constitutive_getThermalStrain
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constitutive_getThermalStrain = math_I3 + &
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(constitutive_getTemperature(ipc, ip, el) - &
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lattice_referenceTemperature(mappingConstitutive(2,ipc,ip,el)))* &
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lattice_thermalExpansion33(1:3,1:3,mappingConstitutive(2,ipc,ip,el))
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end function constitutive_getThermalStrain
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!--------------------------------------------------------------------------------------------------
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!> @brief returns local vacancy concentration
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!--------------------------------------------------------------------------------------------------
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@ -3296,7 +3296,8 @@ logical function crystallite_integrateStress(&
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debug_cumLpTicks, &
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debug_StressLoopDistribution
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use constitutive, only: constitutive_LpAndItsTangent, &
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constitutive_TandItsTangent
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constitutive_TandItsTangent, &
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constitutive_getThermalStrain
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use math, only: math_mul33x33, &
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math_mul33xx33, &
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math_mul66x6, &
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@ -3339,7 +3340,10 @@ logical function crystallite_integrateStress(&
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Tstar,& ! 2nd Piola-Kirchhoff Stress
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A,&
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B, &
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Fe ! elastic deformation gradient
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Fe, & ! elastic deformation gradient
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Fi, & ! gradient of intermediate deformation stages
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Ci, & ! stretch of intermediate deformation stages
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invFi
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real(pReal), dimension(6):: Tstar_v ! 2nd Piola-Kirchhoff Stress in Mandel-Notation
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real(pReal), dimension(9):: work ! needed for matrix inversion by LAPACK
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integer(pInt), dimension(9) :: ipiv ! needed for matrix inversion by LAPACK
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@ -3354,7 +3358,8 @@ logical function crystallite_integrateStress(&
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steplength0, &
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steplength, &
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dt, & ! time increment
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aTol
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aTol, &
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detFi
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logical error ! flag indicating an error
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integer(pInt) NiterationStress, & ! number of stress integrations
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ierr, & ! error indicator for LAPACK
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@ -3418,6 +3423,11 @@ logical function crystallite_integrateStress(&
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return
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endif
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A = math_mul33x33(Fg_new,invFp_current) ! intermediate tensor needed later to calculate dFe_dLp
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Fi = math_I3 ! intermediate configuration, assume decomposition as F = Fe Fi Fp
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Fi = math_mul33x33(Fi,constitutive_getThermalStrain(g,i,e))
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Ci = math_mul33x33(math_transpose33(Fi),Fi) ! non-plastic stretch tensor (neglecting elastic contributions)
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invFi = math_inv33(Fi)
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detFi = math_det33(Fi)
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!* start LpLoop with normal step length
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@ -3443,8 +3453,10 @@ logical function crystallite_integrateStress(&
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!* calculate (elastic) 2nd Piola--Kirchhoff stress tensor and its tangent from constitutive law
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B = math_I3 - dt*Lpguess
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Fe = math_mul33x33(A,B) ! current elastic deformation tensor
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call constitutive_TandItsTangent(Tstar, dT_dFe3333, Fe, g,i,e) ! call constitutive law to calculate 2nd Piola-Kirchhoff stress and its derivative
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Fe = math_mul33x33(math_mul33x33(A,B),invFi) ! current elastic deformation tensor
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call constitutive_TandItsTangent(Tstar, dT_dFe3333, Fe, g,i,e) ! call constitutive law to calculate 2nd Piola-Kirchhoff stress and its derivative in unloaded configuration
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Tstar = math_mul33x33(Ci, math_mul33x33(invFi, &
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math_mul33x33(Tstar,math_transpose33(invFi))))/detFi ! push Tstar forward to plastic (lattice) configuration
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Tstar_v = math_Mandel33to6(Tstar)
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@ -3574,13 +3586,14 @@ logical function crystallite_integrateStress(&
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#endif
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return
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endif
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Fe_new = math_mul33x33(Fg_new,invFp_new) ! calc resulting Fe
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Fe_new = math_mul33x33(math_mul33x33(Fg_new,invFp_new),invFi) ! calc resulting Fe
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!* calculate 1st Piola-Kirchhoff stress
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crystallite_P(1:3,1:3,g,i,e) = math_mul33x33(Fe_new, math_mul33x33(math_Mandel6to33(Tstar_v), &
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math_transpose33(invFp_new)))
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crystallite_P(1:3,1:3,g,i,e) = math_mul33x33(math_mul33x33(Fe_new,Fi), &
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math_mul33x33(math_Mandel6to33(Tstar_v), &
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math_transpose33(invFp_new)))*detFi
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!* store local values in global variables
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