stress iteration loop now uses generalized elasticity by calling TandItsTangent
the anlalytical tangent calculation should now be adopted to also use TandItsTangent
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Franz Roters
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@ -531,10 +531,8 @@ integer(pInt) NiterationCrystallite, & ! number of ite
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g, & ! grain index
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k, &
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l, &
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h, &
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o, &
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p, &
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j, &
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perturbation , & ! loop counter for forward,backward perturbation mode
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myNgrains, &
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mySizeState, &
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@ -552,7 +550,6 @@ real(pReal), dimension(3,3,3,3) :: C, &
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dSdFdot, &
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dFp_invdFdot
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real(pReal) :: counter
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logical :: error
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! --+>> INITIALIZE TO STARTING CONDITION <<+--
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@ -2691,6 +2688,7 @@ use debug, only: debug_what, &
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debug_StressLoopDistribution, &
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debug_LeapfrogBreakDistribution
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use constitutive, only: constitutive_LpAndItsTangent, &
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constitutive_TandItsTangent, &
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constitutive_homogenizedC
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use math, only: math_mul33x33, &
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math_mul33xx33, &
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@ -2706,7 +2704,8 @@ use math, only: math_mul33x33, &
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math_identity2nd, &
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math_Mandel66to3333, &
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math_Mandel6to33, &
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math_mandel33to6
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math_Mandel33to6, &
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math_Plain3333to99
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implicit none
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@ -2733,18 +2732,18 @@ real(pReal), dimension(3,3):: Fg_new, & ! deformation
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residuum_old, & ! last residuum of plastic velocity gradient
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deltaLp, & ! direction of next guess
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gradientR, & ! derivative of the residuum norm
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A, &
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Tstar,& ! 2nd Piola-Kirchhoff Stress
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A,&
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B, &
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BT, &
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AB, &
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BTA
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Fe ! elastic deformation gradient
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real(pReal), dimension(6):: Tstar_v ! 2nd Piola-Kirchhoff Stress in Mandel-Notation
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real(pReal), dimension(9,9):: dLp_dT_constitutive, & ! partial derivative of plastic velocity gradient calculated by constitutive law
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dT_dLp, & ! partial derivative of 2nd Piola-Kirchhoff stress
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dR_dLp, & ! partial derivative of residuum (Jacobian for NEwton-Raphson scheme)
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inv_dR_dLp ! inverse of dRdLp
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real(pReal), dimension(3,3,3,3):: C ! 4th rank elasticity tensor
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real(pReal), dimension(6,6):: C_66 ! simplified 2nd rank elasticity tensor
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real(pReal), dimension(9,9):: dLp_dT_constitutive, & ! partial derivative of plastic velocity gradient calculated by constitutive law
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dT_dFe_constitutive, & ! partial derivative of 2nd Piola-Kirchhoff stress calculated by constitutive law
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dFe_dLp, & ! partial derivative of elastic deformation gradient
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dR_dLp, & ! partial derivative of residuum (Jacobian for NEwton-Raphson scheme)
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inv_dR_dLp ! inverse of dRdLp
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real(pReal), dimension(3,3,3,3):: dT_dFe3333, & ! partial derivative of 2nd Piola-Kirchhoff stress
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dFe_dLp3333 ! partial derivative of elastic deformation gradient
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real(pReal) p_hydro, & ! volumetric part of 2nd Piola-Kirchhoff Stress
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det, & ! determinant
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expectedImprovement, &
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@ -2755,12 +2754,12 @@ real(pReal) p_hydro, & ! volumetric p
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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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dummy, &
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h, &
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j, &
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k, &
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l, &
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m, &
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n, &
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o, &
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p, &
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jacoCounter ! counter to check for Jacobian update
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integer(pLongInt) tick, &
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tock, &
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@ -2818,12 +2817,6 @@ endif
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A = math_mul33x33(transpose(invFp_current), math_mul33x33(transpose(Fg_new),math_mul33x33(Fg_new,invFp_current)))
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!* get elasticity tensor
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C_66 = constitutive_homogenizedC(g,i,e)
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C = math_Mandel66to3333(C_66)
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!* start LpLoop with normal step length
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NiterationStress = 0_pInt
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@ -2848,15 +2841,13 @@ LpLoop: do
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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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B = math_I3 - dt*Lpguess
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BT = math_transpose33(B)
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AB = math_mul33x33(A,B)
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BTA = math_mul33x33(BT,A)
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Fe = math_mul33x33(A,B) ! current elastic deformation tensor
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!* calculate 2nd Piola-Kirchhoff stress tensor
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Tstar_v = 0.5_pReal * math_mul66x6(C_66,math_mandel33to6(math_mul33x33(BT,AB) - math_I3))
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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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Tstar_v = math_Mandel33to6(Tstar)
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p_hydro = sum(Tstar_v(1:3)) / 3.0_pReal
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forall(n=1_pInt:3_pInt) Tstar_v(n) = Tstar_v(n) - p_hydro ! get deviatoric stress tensor
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@ -2982,12 +2973,15 @@ LpLoop: do
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!* calculate Jacobian for correction term and remember current residuum and Lpguess
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if (mod(jacoCounter, iJacoLpresiduum) == 0_pInt) then
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dT_dLp = 0.0_pReal
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do h=1_pInt,3_pInt; do j=1_pInt,3_pInt; do k=1_pInt,3_pInt; do l=1_pInt,3_pInt; do m=1_pInt,3_pInt
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dT_dLp(3*(h-1)+j,3*(k-1)+l) = dT_dLp(3*(h-1)+j,3*(k-1)+l) + C(h,j,l,m) * AB(k,m) + C(h,j,m,l) * BTA(m,k)
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enddo; enddo; enddo; enddo; enddo
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dT_dLp = -0.5_pReal * dt * dT_dLp
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dR_dLp = math_identity2nd(9_pInt) - math_mul99x99(dLp_dT_constitutive, dT_dLp)
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dFe_dLp3333 = 0.0_pReal
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do o=1_pInt,3_pInt; do p=1_pInt,3_pInt
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dFe_dLp3333(p,o,1:3,p) = A(o,1:3) ! dFe_dLp(i,j,k,l) = -dt * A(i,k) delta(j,l)
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enddo; enddo
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dFe_dLp3333 = -dt * dFe_dLp3333
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dFe_dLp = math_Plain3333to99(dFe_dLp3333)
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dT_dFe_constitutive = math_Plain3333to99(dT_dFe3333)
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dR_dLp = math_identity2nd(9_pInt) - &
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math_mul99x99(dLp_dT_constitutive, math_mul99x99(dT_dFe_constitutive , dFe_dLp))
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inv_dR_dLp = 0.0_pReal
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call math_invert(9_pInt,dR_dLp,inv_dR_dLp,dummy,error) ! invert dR/dLp --> dLp/dR
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if (error) then
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@ -2999,10 +2993,11 @@ LpLoop: do
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.or. .not. iand(debug_what(debug_crystallite), debug_levelSelective) /= 0_pInt)) then
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write(6,*)
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write(6,'(a,/,9(12x,9(e15.3,1x)/))') '<< CRYST >> dR_dLp',transpose(dR_dLp)
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write(6,'(a,/,9(12x,9(e15.3,1x)/))') '<< CRYST >> dT_dLp',transpose(dT_dLp)
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write(6,'(a,/,9(12x,9(e15.3,1x)/))') '<< CRYST >> dFe_dLp',transpose(dFe_dLp)
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write(6,'(a,/,9(12x,9(e15.3,1x)/))') '<< CRYST >> dT_dFe_constitutive',transpose(dT_dFe_constitutive)
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write(6,'(a,/,9(12x,9(e15.3,1x)/))') '<< CRYST >> dLp_dT_constitutive',transpose(dLp_dT_constitutive)
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write(6,'(a,/,3(12x,3(e20.7,1x)/))') '<< CRYST >> AB',math_transpose33(AB)
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write(6,'(a,/,3(12x,3(e20.7,1x)/))') '<< CRYST >> BTA',math_transpose33(BTA)
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write(6,'(a,/,3(12x,3(e20.7,1x)/))') '<< CRYST >> A',math_transpose33(A)
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write(6,'(a,/,3(12x,3(e20.7,1x)/))') '<< CRYST >> B',math_transpose33(B)
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write(6,'(a,/,3(12x,3(e20.7,1x)/))') '<< CRYST >> Lp_constitutive',math_transpose33(Lp_constitutive)
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write(6,'(a,/,3(12x,3(e20.7,1x)/))') '<< CRYST >> Lpguess',math_transpose33(Lpguess)
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endif
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