updated analytic jacobian calculation to correctly take into account intermediate configuration Fi. improved convergence of Li loop in stress integration
This commit is contained in:
Pratheek Shanthraj
parent
0b59519a2a
commit
dd8458a775
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@ -586,17 +586,19 @@ subroutine crystallite_stressAndItsTangent(updateJaco)
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logical, dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: &
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convergenceFlag_backup
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! local variables used for calculating analytic Jacobian
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real(pReal) :: detInvFi
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real(pReal) :: detFi
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real(pReal), dimension(3,3) :: temp_33, &
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Fi, &
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invFi, &
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invFi0
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real(pReal), dimension(3,3,3,3) :: dSdFe, &
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dSdF, &
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dSdFiInv, &
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junk2, &
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dLidS, &
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dLpdS, &
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dFpinvdF, &
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dFiinvdF, &
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rhs_3333, &
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lhs_3333, &
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temp_3333
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@ -1111,23 +1113,35 @@ subroutine crystallite_stressAndItsTangent(updateJaco)
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! --- ANALYTIC JACOBIAN ---
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!$OMP PARALLEL DO PRIVATE(dSdF,dSdFe,dLpdS,dFpinvdF,rhs_3333,lhs_3333,temp_99,temp_33,dLidS,&
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!$OMP Fi,invFi,invFi0,detInvFi,temp_3333,myNgrains)
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!$OMP PARALLEL DO PRIVATE(dSdF,dSdFe,dSdFiInv,dLpdS,dFpinvdF,dFiinvdF,dLidS,rhs_3333,lhs_3333,&
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!$OMP Fi,invFi,invFi0,detFi,temp_99,temp_33,temp_3333,myNgrains)
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elementLooping6: do e = FEsolving_execElem(1),FEsolving_execElem(2)
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myNgrains = homogenization_Ngrains(mesh_element(3,e))
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do i = FEsolving_execIP(1,e),FEsolving_execIP(2,e) ! iterate over IPs of this element to be processed
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do g = 1_pInt,myNgrains
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Fi = constitutive_getFi(g,i,e)
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detFi = math_det33(Fi)
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invFi = math_inv33(Fi)
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invFi0 = math_inv33(constitutive_getFi0(g,i,e))
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call constitutive_TandItsTangent(temp_33,dSdFe,crystallite_Fe(1:3,1:3,g,i,e),g,i,e) ! call constitutive law to calculate 2nd Piola-Kirchhoff stress and its derivative
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forall(p=1_pInt:3_pInt, o=1_pInt:3_pInt) &
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dSdFe(1:3,1:3,o,p) = math_mul33x33(invFi,math_mul33x33(dSdFe(1:3,1:3,o,p), &
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math_transpose33(invFi)))*detFi
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dSdFiInv = 0.0_pReal
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temp_33 = math_mul33x33(temp_33,math_transpose33(invFi))*detFi
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forall(p=1_pInt:3_pInt, o=1_pInt:3_pInt) &
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dSdFiInv(o,1:3,p,1:3) = dSdFiInv(o,1:3,p,1:3) + math_I3(o,p)*temp_33
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forall(p=1_pInt:3_pInt, o=1_pInt:3_pInt) &
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dSdFiInv(1:3,o,p,1:3) = dSdFiInv(1:3,o,p,1:3) + math_I3(o,p)*math_transpose33(temp_33)
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forall(p=1_pInt:3_pInt, o=1_pInt:3_pInt) &
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dSdFiInv(1:3,1:3,o,p) = dSdFiInv(1:3,1:3,o,p) - math_Mandel6to33(crystallite_Tstar_v(1:6,g,i,e))*invFi(p,o)
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call constitutive_LpAndItsTangent(temp_33,temp_99,crystallite_Tstar_v(1:6,g,i,e), &
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g,i,e)
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dLpdS = reshape(temp_99,shape=[3,3,3,3])
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call constitutive_LiAndItsTangent(temp_33,temp_99,crystallite_Tstar_v(1:6,g,i,e), &
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crystallite_Lp(1:3,1:3,g,i,e), g,i,e)
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dLidS = reshape(temp_99,shape=[3,3,3,3])
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Fi = constitutive_getFi(g,i,e)
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invFi = math_inv33(Fi)
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invFi0 = math_inv33(constitutive_getFi0(g,i,e))
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detInvFi = math_det33(invFi)
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temp_33 = math_transpose33(math_mul33x33(crystallite_invFp(1:3,1:3,g,i,e),invFi))
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rhs_3333 = 0.0_pReal
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@ -1135,17 +1149,24 @@ subroutine crystallite_stressAndItsTangent(updateJaco)
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rhs_3333(p,o,1:3,1:3) = math_mul33x33(dSdFe(p,o,1:3,1:3),temp_33)
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temp_3333 = 0.0_pReal
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temp_33 = math_mul33x33(crystallite_partionedF(1:3,1:3,g,i,e), &
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math_inv33(crystallite_Fp0(1:3,1:3,g,i,e)))
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temp_33 = math_mul33x33(crystallite_subF(1:3,1:3,g,i,e), &
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math_inv33(crystallite_subFp0(1:3,1:3,g,i,e)))
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forall(p=1_pInt:3_pInt, o=1_pInt:3_pInt) &
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temp_3333(1:3,1:3,p,o) = math_mul33x33(math_mul33x33(temp_33,dLpdS(1:3,1:3,p,o)),invFi)
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temp_33 = math_mul33x33(math_mul33x33(crystallite_partionedF(1:3,1:3,g,i,e), &
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temp_33 = math_mul33x33(math_mul33x33(crystallite_subF(1:3,1:3,g,i,e), &
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crystallite_invFp(1:3,1:3,g,i,e)), invFi0)
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forall(p=1_pInt:3_pInt, o=1_pInt:3_pInt) &
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temp_3333(1:3,1:3,p,o) = temp_3333(1:3,1:3,p,o) + math_mul33x33(temp_33,dLidS(1:3,1:3,p,o))
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lhs_3333 = crystallite_dt(g,i,e)*math_mul3333xx3333(dSdFe,temp_3333)
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lhs_3333 = crystallite_subdt(g,i,e)*math_mul3333xx3333(dSdFe,temp_3333)
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temp_3333 = 0.0_pReal
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temp_33 = math_mul33x33(crystallite_invFp(1:3,1:3,g,i,e), invFi0)
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forall(p=1_pInt:3_pInt, o=1_pInt:3_pInt) &
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temp_3333(1:3,1:3,p,o) = math_mul33x33(temp_33,dLidS(1:3,1:3,p,o))
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lhs_3333 = lhs_3333 + crystallite_subdt(g,i,e)*math_mul3333xx3333(dSdFiInv,temp_3333)
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call math_invert(9_pInt,math_identity2nd(9_pInt)+reshape(lhs_3333,shape=[9,9]),temp_99,error)
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if (error) call IO_error(error_ID=400_pInt,ext_msg='analytic tangent inversion')
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@ -1154,25 +1175,32 @@ subroutine crystallite_stressAndItsTangent(updateJaco)
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dFpinvdF = 0.0_pReal
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temp_3333 = math_mul3333xx3333(dLpdS,dSdF)
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forall(p=1_pInt:3_pInt, o=1_pInt:3_pInt) &
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dFpinvdF(1:3,1:3,p,o) = -crystallite_dt(g,i,e)* &
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math_mul33x33(math_inv33(crystallite_Fp0(1:3,1:3,g,i,e)), &
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dFpinvdF(1:3,1:3,p,o) = -crystallite_subdt(g,i,e)* &
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math_mul33x33(math_inv33(crystallite_subFp0(1:3,1:3,g,i,e)), &
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math_mul33x33(temp_3333(1:3,1:3,p,o),invFi))
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dFiinvdF = 0.0_pReal
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temp_3333 = math_mul3333xx3333(dLidS,dSdF)
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forall(p=1_pInt:3_pInt, o=1_pInt:3_pInt) &
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dFiinvdF(1:3,1:3,p,o) = -crystallite_subdt(g,i,e)* &
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math_mul33x33(math_inv33(crystallite_Fp(1:3,1:3,g,i,e)), &
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math_mul33x33(invFi0,temp_3333(1:3,1:3,p,o)))
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crystallite_dPdF(1:3,1:3,1:3,1:3,g,i,e) = 0.0_pReal
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temp_33 = math_mul33x33(crystallite_invFp(1:3,1:3,g,i,e), &
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math_mul33x33(math_Mandel6to33(crystallite_Tstar_v(1:6,g,i,e)), &
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math_transpose33(crystallite_invFp(1:3,1:3,g,i,e))))/detInvFi
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math_transpose33(crystallite_invFp(1:3,1:3,g,i,e))))*detFi
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forall(p=1_pInt:3_pInt) &
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crystallite_dPdF(p,1:3,p,1:3,g,i,e) = math_transpose33(temp_33)
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temp_33 = math_mul33x33(math_Mandel6to33(crystallite_Tstar_v(1:6,g,i,e)), &
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math_transpose33(crystallite_invFp(1:3,1:3,g,i,e)))/detInvFi
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math_transpose33(crystallite_invFp(1:3,1:3,g,i,e)))*detFi
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forall(p=1_pInt:3_pInt, o=1_pInt:3_pInt) &
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crystallite_dPdF(1:3,1:3,p,o,g,i,e) = crystallite_dPdF(1:3,1:3,p,o,g,i,e) + &
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math_mul33x33(math_mul33x33(crystallite_subF(1:3,1:3,g,i,e),dFpinvdF(1:3,1:3,p,o)),temp_33)
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temp_33 = math_mul33x33(crystallite_subF(1:3,1:3,g,i,e), &
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crystallite_invFp(1:3,1:3,g,i,e))/detInvFi
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crystallite_invFp(1:3,1:3,g,i,e))*detFi
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forall(p=1_pInt:3_pInt, o=1_pInt:3_pInt) &
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crystallite_dPdF(1:3,1:3,p,o,g,i,e) = crystallite_dPdF(1:3,1:3,p,o,g,i,e) + &
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math_mul33x33(math_mul33x33(temp_33,dSdF(1:3,1:3,p,o)), &
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@ -1180,11 +1208,15 @@ subroutine crystallite_stressAndItsTangent(updateJaco)
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temp_33 = math_mul33x33(math_mul33x33(crystallite_subF(1:3,1:3,g,i,e), &
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crystallite_invFp(1:3,1:3,g,i,e)), &
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math_Mandel6to33(crystallite_Tstar_v(1:6,g,i,e)))/detInvFi
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math_Mandel6to33(crystallite_Tstar_v(1:6,g,i,e)))*detFi
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forall(p=1_pInt:3_pInt, o=1_pInt:3_pInt) &
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crystallite_dPdF(1:3,1:3,p,o,g,i,e) = crystallite_dPdF(1:3,1:3,p,o,g,i,e) + &
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math_mul33x33(temp_33,math_transpose33(dFpinvdF(1:3,1:3,p,o)))
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forall(p=1_pInt:3_pInt, o=1_pInt:3_pInt) &
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crystallite_dPdF(1:3,1:3,p,o,g,i,e) = crystallite_dPdF(1:3,1:3,p,o,g,i,e) - &
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crystallite_subF(1:3,1:3,g,i,e)*sum(math_transpose33(Fi)*dFiinvdF(1:3,1:3,p,o))
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enddo; enddo
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enddo elementLooping6
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!$OMP END PARALLEL DO
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@ -3585,13 +3617,17 @@ logical function crystallite_integrateStress(&
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dT_dFe99, & ! partial derivative of 2nd Piola-Kirchhoff stress calculated by constitutive law
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dFe_dLp99, & ! partial derivative of elastic deformation gradient
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dFe_dLi99, &
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dFiInv_dLi99, &
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dT_dFiInv99, &
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dRLp_dLp, & ! partial derivative of residuum (Jacobian for NEwton-Raphson scheme)
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dRLp_dLp2, & ! working copy of dRdLp
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dRLi_dLi ! partial derivative of residuumI (Jacobian for NEwton-Raphson scheme)
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real(pReal), dimension(3,3,3,3):: dT_dFe3333, & ! partial derivative of 2nd Piola-Kirchhoff stress
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dT_dFe3333_unloaded, &
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dFe_dLp3333, & ! partial derivative of elastic deformation gradient
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dFe_dLi3333
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dFe_dLi3333, &
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dFiInv_dLi3333, &
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dT_dFiInv3333
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real(pReal) det, & ! determinant
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detInvFi, &
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steplengthLp0, &
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@ -3736,9 +3772,16 @@ logical function crystallite_integrateStress(&
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call constitutive_TandItsTangent(Tstar_unloaded, dT_dFe3333_unloaded, 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(invFi, &
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math_mul33x33(Tstar_unloaded,math_transpose33(invFi)))/detInvFi ! push Tstar forward from unloaded to plastic (lattice) configuration
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dT_dFe3333 = 0.0_pReal
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dT_dFiInv3333 = 0.0_pReal
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temp_33 = math_mul33x33(Tstar_unloaded,math_transpose33(invFi))/detInvFi ! push Tstar forward from unloaded to plastic (lattice) configuration
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do o=1_pInt,3_pInt; do p=1_pInt,3_pInt
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dT_dFe3333(1:3,1:3,o,p) = math_mul33x33(invFi, &
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math_mul33x33(dT_dFe3333_unloaded(1:3,1:3,o,p),math_transpose33(invFi)))/detInvFi
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dT_dFe3333 (1:3,1:3,o,p) = &
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math_mul33x33(invFi,math_mul33x33(dT_dFe3333_unloaded(1:3,1:3,o,p), &
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math_transpose33(invFi)))/detInvFi
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dT_dFiInv3333(o,1:3,p,1:3) = dT_dFiInv3333(o,1:3,p,1:3) + math_I3(o,p)*temp_33
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dT_dFiInv3333(1:3,o,p,1:3) = dT_dFiInv3333(1:3,o,p,1:3) + math_I3(o,p)*math_transpose33(temp_33)
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dT_dFiInv3333(1:3,1:3,o,p) = dT_dFiInv3333(1:3,1:3,o,p) - Tstar*invFi(p,o)
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enddo; enddo
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Tstar_v = math_Mandel33to6(Tstar)
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@ -3881,13 +3924,17 @@ logical function crystallite_integrateStress(&
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if (mod(jacoCounterLi, iJacoLpresiduum) == 0_pInt) then
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temp_33 = math_mul33x33(math_mul33x33(A,B),invFi_current)
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dFe_dLi3333 = 0.0_pReal
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dFiInv_dLi3333 = 0.0_pReal
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do o=1_pInt,3_pInt; do p=1_pInt,3_pInt
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dFe_dLi3333(o,1:3,p,1:3) = temp_33 ! dFe_dLp(i,j,k,l) = -dt * A(i,k) invFi(l,j)
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dFe_dLi3333 (1:3,o,1:3,p) = -dt*math_I3(o,p)*temp_33 ! dFe_dLp(i,j,k,l) = -dt * A(i,k) invFi(l,j)
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dFiInv_dLi3333(1:3,o,1:3,p) = -dt*math_I3(o,p)*invFi_current
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enddo; enddo
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dFe_dLi3333 = - dt * dFe_dLi3333
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dT_dFiInv99 = math_Plain3333to99(dT_dFiInv3333)
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dFe_dLi99 = math_Plain3333to99(dFe_dLi3333)
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dFiInv_dLi99 = math_Plain3333to99(dFiInv_dLi3333)
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dRLi_dLi = math_identity2nd(9_pInt) &
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- math_mul99x99(dLi_dT_constitutive99, math_mul99x99(dT_dFe99, dFe_dLi99))
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- math_mul99x99(dLi_dT_constitutive99, math_mul99x99(dT_dFe99, dFe_dLi99) + &
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math_mul99x99(dT_dFiInv99, dFiInv_dLi99))
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work = math_plain33to9(residuumLi)
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#if(FLOAT==8)
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call dgesv(9,1,dRLi_dLi,9,ipiv,work,9,ierr) ! solve dRLi/dLp * delta Li = -res for delta Li
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@ -3926,7 +3973,7 @@ logical function crystallite_integrateStress(&
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!* calculate 1st Piola-Kirchhoff stress
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crystallite_P(1:3,1:3,g,i,e) = math_mul33x33(math_mul33x33(Fe_new,Fi), &
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crystallite_P(1:3,1:3,g,i,e) = math_mul33x33(math_mul33x33(Fg_new,invFp_new), &
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math_mul33x33(math_Mandel6to33(Tstar_v), &
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math_transpose33(invFp_new)))/detInvFi
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