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Martin Diehl
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@ -1347,16 +1347,13 @@ end subroutine plastic_nonlocal_dotState
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!---------------------------------------------------------------------------------------------------
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!> @brief calculates the rate of change of microstructure
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!---------------------------------------------------------------------------------------------------
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subroutine plastic_nonlocal_dotState2(Mp, F, Fp, Temperature,timestep, &
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instance,of,ip,el)
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subroutine plastic_nonlocal_dotState2(F, Fp,timestep, &
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instance,of,ip,el)
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real(pReal), dimension(3,3), intent(in) :: &
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Mp !< MandelStress
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real(pReal), dimension(3,3,homogenization_maxNgrains,discretization_nIP,discretization_nElem), intent(in) :: &
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F, & !< elastic deformation gradient
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Fp !< plastic deformation gradient
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real(pReal), intent(in) :: &
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Temperature, & !< temperature
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timestep !< substepped crystallite time increment
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integer, intent(in) :: &
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instance, &
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@ -1385,12 +1382,7 @@ subroutine plastic_nonlocal_dotState2(Mp, F, Fp, Temperature,timestep, &
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real(pReal), dimension(param(instance)%sum_N_sl,10) :: &
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rho, &
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rho0, & !< dislocation density at beginning of time step
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rhoDot, & !< density evolution
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rhoDotMultiplication, & !< density evolution by multiplication
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rhoDotFlux, & !< density evolution by flux
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rhoDotSingle2DipoleGlide, & !< density evolution by dipole formation (by glide)
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rhoDotAthermalAnnihilation, & !< density evolution by athermal annihilation
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rhoDotThermalAnnihilation !< density evolution by thermal annihilation
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rhoDotFlux !< density evolution by flux
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real(pReal), dimension(param(instance)%sum_N_sl,8) :: &
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rhoSgl, & !< current single dislocation densities (positive/negative screw and edge without dipoles)
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neighbor_rhoSgl0, & !< current single dislocation densities of neighboring ip (positive/negative screw and edge without dipoles)
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@ -1400,13 +1392,6 @@ subroutine plastic_nonlocal_dotState2(Mp, F, Fp, Temperature,timestep, &
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v0, &
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neighbor_v0, & !< dislocation glide velocity of enighboring ip
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gdot !< shear rates
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real(pReal), dimension(param(instance)%sum_N_sl) :: &
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tau, & !< current resolved shear stress
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vClimb !< climb velocity of edge dipoles
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real(pReal), dimension(param(instance)%sum_N_sl,2) :: &
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rhoDip, & !< current dipole dislocation densities (screw and edge dipoles)
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dLower, & !< minimum stable dipole distance for edges and screws
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dUpper !< current maximum stable dipole distance for edges and screws
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real(pReal), dimension(3,param(instance)%sum_N_sl,4) :: &
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m !< direction of dislocation motion
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real(pReal), dimension(3,3) :: &
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@ -1423,8 +1408,7 @@ subroutine plastic_nonlocal_dotState2(Mp, F, Fp, Temperature,timestep, &
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real(pReal) :: &
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area, & !< area of the current interface
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transmissivity, & !< overall transmissivity of dislocation flux to neighboring material point
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lineLength, & !< dislocation line length leaving the current interface
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selfDiffusion !< self diffusion
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lineLength !< dislocation line length leaving the current interface
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ph = material_phaseAt(1,el)
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if (timestep <= 0.0_pReal) then
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@ -1438,63 +1422,16 @@ subroutine plastic_nonlocal_dotState2(Mp, F, Fp, Temperature,timestep, &
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stt => state(instance))
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ns = prm%sum_N_sl
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tau = 0.0_pReal
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gdot = 0.0_pReal
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rho = getRho(instance,of,ip,el)
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rhoSgl = rho(:,sgl)
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rhoDip = rho(:,dip)
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rho0 = getRho0(instance,of,ip,el)
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my_rhoSgl0 = rho0(:,sgl)
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forall (s = 1:ns, t = 1:4) v(s,t) = plasticState(ph)%state(iV(s,t,instance),of)
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gdot = rhoSgl(:,1:4) * v * spread(prm%burgers,2,4)
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#ifdef DEBUG
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if (iand(debug_level(debug_constitutive),debug_levelBasic) /= 0 &
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.and. ((debug_e == el .and. debug_i == ip)&
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.or. .not. iand(debug_level(debug_constitutive),debug_levelSelective) /= 0 )) then
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write(6,'(a,/,10(12x,12(e12.5,1x),/))') '<< CONST >> rho / 1/m^2', rhoSgl, rhoDip
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write(6,'(a,/,4(12x,12(e12.5,1x),/))') '<< CONST >> gdot / 1/s',gdot
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endif
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#endif
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!****************************************************************************
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!*** limits for stable dipole height
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do s = 1,ns
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tau(s) = math_tensordot(Mp, prm%Schmid(1:3,1:3,s)) + dst%tau_back(s,of)
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if (abs(tau(s)) < 1.0e-15_pReal) tau(s) = 1.0e-15_pReal
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enddo
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dLower = prm%minDipoleHeight
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dUpper(:,1) = prm%mu * prm%burgers/(8.0_pReal * PI * (1.0_pReal - prm%nu) * abs(tau))
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dUpper(:,2) = prm%mu * prm%burgers/(4.0_pReal * PI * abs(tau))
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where(dNeq0(sqrt(sum(abs(rho(:,edg)),2)))) &
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dUpper(:,1) = min(1.0_pReal/sqrt(sum(abs(rho(:,edg)),2)),dUpper(:,1))
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where(dNeq0(sqrt(sum(abs(rho(:,scr)),2)))) &
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dUpper(:,2) = min(1.0_pReal/sqrt(sum(abs(rho(:,scr)),2)),dUpper(:,2))
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dUpper = max(dUpper,dLower)
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!****************************************************************************
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!*** dislocation multiplication
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rhoDotMultiplication = 0.0_pReal
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isBCC: if (lattice_structure(ph) == LATTICE_bcc_ID) then
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forall (s = 1:ns, sum(abs(v(s,1:4))) > 0.0_pReal)
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rhoDotMultiplication(s,1:2) = sum(abs(gdot(s,3:4))) / prm%burgers(s) & ! assuming double-cross-slip of screws to be decisive for multiplication
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* sqrt(stt%rho_forest(s,of)) / prm%lambda0(s) ! & ! mean free path
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! * 2.0_pReal * sum(abs(v(s,3:4))) / sum(abs(v(s,1:4))) ! ratio of screw to overall velocity determines edge generation
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rhoDotMultiplication(s,3:4) = sum(abs(gdot(s,3:4))) /prm%burgers(s) & ! assuming double-cross-slip of screws to be decisive for multiplication
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* sqrt(stt%rho_forest(s,of)) / prm%lambda0(s) ! & ! mean free path
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! * 2.0_pReal * sum(abs(v(s,1:2))) / sum(abs(v(s,1:4))) ! ratio of edge to overall velocity determines screw generation
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endforall
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else isBCC
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rhoDotMultiplication(:,1:4) = spread( &
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(sum(abs(gdot(:,1:2)),2) * prm%fEdgeMultiplication + sum(abs(gdot(:,3:4)),2)) &
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* sqrt(stt%rho_forest(:,of)) / prm%lambda0 / prm%burgers, 2, 4)
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endif isBCC
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forall (s = 1:ns, t = 1:4) v0(s,t) = plasticState(ph)%state0(iV(s,t,instance),of)
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@ -1644,105 +1581,6 @@ subroutine plastic_nonlocal_dotState2(Mp, F, Fp, Temperature,timestep, &
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enddo neighbors
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endif
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!****************************************************************************
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!*** calculate dipole formation and annihilation
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!*** formation by glide
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do c = 1,2
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rhoDotSingle2DipoleGlide(:,2*c-1) = -2.0_pReal * dUpper(:,c) / prm%burgers &
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* ( rhoSgl(:,2*c-1) * abs(gdot(:,2*c)) & ! negative mobile --> positive mobile
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+ rhoSgl(:,2*c) * abs(gdot(:,2*c-1)) & ! positive mobile --> negative mobile
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+ abs(rhoSgl(:,2*c+4)) * abs(gdot(:,2*c-1))) ! positive mobile --> negative immobile
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rhoDotSingle2DipoleGlide(:,2*c) = -2.0_pReal * dUpper(:,c) / prm%burgers &
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* ( rhoSgl(:,2*c-1) * abs(gdot(:,2*c)) & ! negative mobile --> positive mobile
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+ rhoSgl(:,2*c) * abs(gdot(:,2*c-1)) & ! positive mobile --> negative mobile
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+ abs(rhoSgl(:,2*c+3)) * abs(gdot(:,2*c))) ! negative mobile --> positive immobile
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rhoDotSingle2DipoleGlide(:,2*c+3) = -2.0_pReal * dUpper(:,c) / prm%burgers &
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* rhoSgl(:,2*c+3) * abs(gdot(:,2*c)) ! negative mobile --> positive immobile
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rhoDotSingle2DipoleGlide(:,2*c+4) = -2.0_pReal * dUpper(:,c) / prm%burgers &
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* rhoSgl(:,2*c+4) * abs(gdot(:,2*c-1)) ! positive mobile --> negative immobile
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rhoDotSingle2DipoleGlide(:,c+8) = abs(rhoDotSingle2DipoleGlide(:,2*c+3)) &
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+ abs(rhoDotSingle2DipoleGlide(:,2*c+4)) &
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- rhoDotSingle2DipoleGlide(:,2*c-1) &
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- rhoDotSingle2DipoleGlide(:,2*c)
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enddo
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!*** athermal annihilation
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rhoDotAthermalAnnihilation = 0.0_pReal
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forall (c=1:2) &
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rhoDotAthermalAnnihilation(:,c+8) = -2.0_pReal * dLower(:,c) / prm%burgers &
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* ( 2.0_pReal * (rhoSgl(:,2*c-1) * abs(gdot(:,2*c)) + rhoSgl(:,2*c) * abs(gdot(:,2*c-1))) & ! was single hitting single
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+ 2.0_pReal * (abs(rhoSgl(:,2*c+3)) * abs(gdot(:,2*c)) + abs(rhoSgl(:,2*c+4)) * abs(gdot(:,2*c-1))) & ! was single hitting immobile single or was immobile single hit by single
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+ rhoDip(:,c) * (abs(gdot(:,2*c-1)) + abs(gdot(:,2*c)))) ! single knocks dipole constituent
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! annihilated screw dipoles leave edge jogs behind on the colinear system
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if (lattice_structure(ph) == LATTICE_fcc_ID) &
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forall (s = 1:ns, prm%colinearSystem(s) > 0) &
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rhoDotAthermalAnnihilation(prm%colinearSystem(s),1:2) = - rhoDotAthermalAnnihilation(s,10) &
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* 0.25_pReal * sqrt(stt%rho_forest(s,of)) * (dUpper(s,2) + dLower(s,2)) * prm%edgeJogFactor
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!*** thermally activated annihilation of edge dipoles by climb
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rhoDotThermalAnnihilation = 0.0_pReal
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selfDiffusion = prm%Dsd0 * exp(-prm%selfDiffusionEnergy / (kB * Temperature))
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vClimb = prm%atomicVolume * selfDiffusion * prm%mu &
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/ ( kB * Temperature * PI * (1.0_pReal-prm%nu) * (dUpper(:,1) + dLower(:,1)))
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forall (s = 1:ns, dUpper(s,1) > dLower(s,1)) &
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rhoDotThermalAnnihilation(s,9) = max(- 4.0_pReal * rhoDip(s,1) * vClimb(s) / (dUpper(s,1) - dLower(s,1)), &
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- rhoDip(s,1) / timestep - rhoDotAthermalAnnihilation(s,9) &
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- rhoDotSingle2DipoleGlide(s,9)) ! make sure that we do not annihilate more dipoles than we have
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rhoDot = rhoDotFlux &
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+ rhoDotMultiplication &
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+ rhoDotSingle2DipoleGlide &
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+ rhoDotAthermalAnnihilation &
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+ rhoDotThermalAnnihilation
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#ifdef DEBUG
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if (iand(debug_level(debug_constitutive),debug_levelExtensive) /= 0 &
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.and. ((debug_e == el .and. debug_i == ip)&
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.or. .not. iand(debug_level(debug_constitutive),debug_levelSelective) /= 0 )) then
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write(6,'(a,/,4(12x,12(e12.5,1x),/))') '<< CONST >> dislocation multiplication', &
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rhoDotMultiplication(:,1:4) * timestep
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write(6,'(a,/,8(12x,12(e12.5,1x),/))') '<< CONST >> dislocation flux', &
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rhoDotFlux(:,1:8) * timestep
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write(6,'(a,/,10(12x,12(e12.5,1x),/))') '<< CONST >> dipole formation by glide', &
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rhoDotSingle2DipoleGlide * timestep
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write(6,'(a,/,10(12x,12(e12.5,1x),/))') '<< CONST >> athermal dipole annihilation', &
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rhoDotAthermalAnnihilation * timestep
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write(6,'(a,/,2(12x,12(e12.5,1x),/))') '<< CONST >> thermally activated dipole annihilation', &
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rhoDotThermalAnnihilation(:,9:10) * timestep
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write(6,'(a,/,10(12x,12(e12.5,1x),/))') '<< CONST >> total density change', &
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rhoDot * timestep
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write(6,'(a,/,10(12x,12(f12.5,1x),/))') '<< CONST >> relative density change', &
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rhoDot(:,1:8) * timestep / (abs(stt%rho(:,sgl))+1.0e-10), &
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rhoDot(:,9:10) * timestep / (stt%rho(:,dip)+1.0e-10)
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write(6,*)
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endif
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#endif
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if ( any(rho(:,mob) + rhoDot(:,1:4) * timestep < -prm%atol_rho) &
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.or. any(rho(:,dip) + rhoDot(:,9:10) * timestep < -prm%atol_rho)) then
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#ifdef DEBUG
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if (iand(debug_level(debug_constitutive),debug_levelExtensive) /= 0) then
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write(6,'(a,i5,a,i2)') '<< CONST >> evolution rate leads to negative density at el ',el,' ip ',ip
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write(6,'(a)') '<< CONST >> enforcing cutback !!!'
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endif
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#endif
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plasticState(ph)%dotState = IEEE_value(1.0_pReal,IEEE_quiet_NaN)
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else
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dot%rho(:,of) = pack(rhoDot,.true.)
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dot%gamma(:,of) = sum(gdot,2)
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endif
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end associate
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end subroutine plastic_nonlocal_dotState2
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