local stress correction of gradient in dead dislocations and neighboring excess density is additive
This commit is contained in:
Christoph Kords
parent
06c93435f2
commit
6bca2150f2
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@ -951,7 +951,6 @@ integer(pInt) neighboring_el, & ! element number o
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s, & ! slip system index
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t, & ! index of dilsocation type (e+, e-, s+, s-, used e+, used e-, used s+, used s-)
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dir, &
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side, &
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n
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integer(pInt), dimension(2) :: neighbor
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real(pReal) nu, & ! poisson's ratio
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@ -959,28 +958,20 @@ real(pReal) nu, & ! poisson's ratio
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b, &
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detFe, &
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detFp, &
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FVsize, &
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rhoExcessGradient
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real(pReal), dimension(2) :: rhoExcessGradient_over_rho, &
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gradient, &
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gradientDeads, &
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gradientInter, &
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gradientDistance, &
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gradientDistanceDeads, &
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gradientDistanceInter, &
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rhoExcessAtSampledPoint
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FVsize
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real(pReal), dimension(2) :: rhoExcessGradient, &
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rhoExcessGradient_over_rho, &
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rhoTotal
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real(pReal), dimension(3) :: ipCoords, &
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neighboring_ipCoords
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real(pReal), dimension(FE_maxNipNeighbors) :: &
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distance ! length of connection vector
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neighboring_ipCoords, &
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rhoExcessDifferences
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real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el)))) :: &
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rhoForest, & ! forest dislocation density
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tauBack, & ! back stress from pileup on same slip system
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tauThreshold ! threshold shear stress
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real(pReal), dimension(3,2) :: rhoExcessDifferences, &
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sampledPoint
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real(pReal), dimension(3,3) :: invFe, & ! inverse of elastic deformation gradient
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invFp ! inverse of plastic deformation gradient
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invFp, & ! inverse of plastic deformation gradient
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connections
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real(pReal), dimension(3,FE_maxNipNeighbors) :: &
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connection_latticeConf, &
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areaNormal_latticeConf
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@ -990,7 +981,6 @@ real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance
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rhoDip ! dipole dislocation density (edge, screw)
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real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),8) :: &
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rhoSgl ! single dislocation density (edge+, edge-, screw+, screw-, used edge+, used edge-, used screw+, used screw-)
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real(pReal), dimension(3,3,2) :: connections
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real(pReal), dimension(2,maxval(constitutive_nonlocal_totalNslip),FE_maxNipNeighbors) :: &
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neighboring_rhoExcess ! excess density at neighboring material point
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real(pReal), dimension(3,constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),2) :: &
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@ -1075,7 +1065,7 @@ if (.not. phase_localPlasticity(phase)) then
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- state(g,neighboring_ip,neighboring_el)%p((2_pInt*c-1_pInt)*ns+s) ! negative mobiles
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else
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! thats myself! probably using periodic images
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connection_latticeConf(1:3,n) = areaNormal_latticeConf(1:3,n) * FVsize
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connection_latticeConf(1:3,n) = 0.0_pReal
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neighboring_rhoExcess(1:2,1:ns,n) = rhoExcess
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endif
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else
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@ -1084,100 +1074,55 @@ if (.not. phase_localPlasticity(phase)) then
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endif
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else
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! local neighbor or different lattice structure or different plasticity instance
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connection_latticeConf(1:3,n) = math_mul33x3(invFe, neighboring_ipCoords - ipCoords)
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connection_latticeConf(1:3,n) = 0.0_pReal ! use central values instead
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neighboring_rhoExcess(1:2,1:ns,n) = rhoExcess
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endif
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else
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! free surface
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connection_latticeConf(1:3,n) = areaNormal_latticeConf(1:3,n) * FVsize
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connection_latticeConf(1:3,n) = 0.0_pReal ! use central values instead
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neighboring_rhoExcess(1:2,1:ns,n) = rhoExcess
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endif
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distance(n) = math_norm3(connection_latticeConf(1:3,n))
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enddo
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!* loop through the slip systems
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!* calculate the dislocation gradient in both directions of m with two different methods:
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!* 1. gradient between central excess density and dead dislocations in central ip
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!* 2. interpolate gradient from excess density in three neighboring ips
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!* take the heigher gradient in both directions and do a weighted sum with weights according to the distance
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!* loop through the slip systems and calculate the dislocation gradient by
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!* 1. interpolation of the excess density in the neighorhood
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!* 2. interpolation of the dead dislocation density in the central volume
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m(1:3,1:ns,1) = lattice_sd(1:3, constitutive_nonlocal_slipSystemLattice(1:ns,instance), latticeStruct)
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m(1:3,1:ns,2) = -lattice_st(1:3, constitutive_nonlocal_slipSystemLattice(1:ns,instance), latticeStruct)
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do s = 1_pInt,ns
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rhoExcessGradient_over_rho = 0.0_pReal
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!* gradient from interpolation of neighboring excess density
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do c = 1_pInt,2_pInt
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if (rhoSgl(s,2_pInt*c-1_pInt) + rhoSgl(s,2_pInt*c) < 1.0_pReal) then
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cycle ! no siginificant density
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endif
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!* gradient from dead dislocations
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gradientDeads = 0.0_pReal
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if (rhoSgl(s,2_pInt*c+3_pInt) > 0.0_pReal) then ! positive deads
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gradientDeads(1) = + 2.0_pReal * rhoSgl(s,2_pInt*c+3_pInt) / FVsize ! on positive side
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else
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gradientDeads(2) = - 2.0_pReal * rhoSgl(s,2_pInt*c+3_pInt) / FVsize ! on negative side
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endif
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if (rhoSgl(s,2_pInt*c+4_pInt) > 0.0_pReal) then ! negative deads
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gradientDeads(2) = gradientDeads(2) + 2.0_pReal * rhoSgl(s,2_pInt*c+4_pInt) / FVsize ! on negative side
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else
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gradientDeads(1) = gradientDeads(1) - 2.0_pReal * rhoSgl(s,2_pInt*c+4_pInt) / FVsize ! on positive side
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endif
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gradientDistanceDeads(1:2) = 0.5_pReal * FVsize
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!* gradient from interpolation
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gradientInter = 0.0_pReal
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rhoExcessDifferences = 0.0_pReal
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connections = 0.0_pReal
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gradientDistanceInter = 0.0_pReal
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do dir = 1_pInt,3_pInt
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if (math_mul3x3(areaNormal_latticeConf(1:3,2_pInt*dir-1_pInt),m(1:3,s,c)) > 0.0_pReal) then ! on positive side
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neighbor(1) = 2_pInt * dir - 1_pInt
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neighbor(2) = 2_pInt * dir
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else ! on negative side
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neighbor(1) = 2_pInt * dir
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neighbor(2) = 2_pInt * dir - 1_pInt
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endif
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do side = 1_pInt,2_pInt
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n = neighbor(side)
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rhoExcessDifferences(dir,side) = neighboring_rhoExcess(c,s,n) - rhoExcess(c,s)
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connections(dir,1:3,side) = connection_latticeConf(1:3,n)
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gradientDistanceInter(side) = gradientDistanceInter(side) &
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+ (math_mul3x3(connection_latticeConf(1:3,n),m(1:3,s,c))) ** 2.0_pReal / distance(n)
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enddo
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neighbor(1) = 2_pInt * dir - 1_pInt
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neighbor(2) = 2_pInt * dir
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connections(dir,1:3) = connection_latticeConf(1:3,neighbor(1)) - connection_latticeConf(1:3,neighbor(2))
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rhoExcessDifferences(dir) = neighboring_rhoExcess(c,s,neighbor(1)) - neighboring_rhoExcess(c,s,neighbor(2))
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enddo
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sampledPoint(1:3,1) = + gradientDistanceInter(1) * m(1:3,s,c)
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sampledPoint(1:3,2) = - gradientDistanceInter(2) * m(1:3,s,c)
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do side = 1_pInt,2_pInt
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rhoExcessAtSampledPoint(side) = math_mul3x3(math_mul33x3(math_inv33(connections(1:3,1:3,side)), &
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rhoExcessDifferences(1:3,side)), &
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sampledPoint(1:3,side)) &
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+ rhoExcess(c,s)
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enddo
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gradientInter(1) = (rhoExcessAtSampledPoint(1) - rhoExcess(c,s)) / gradientDistanceInter(1)
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gradientInter(2) = (rhoExcess(c,s) - rhoExcessAtSampledPoint(2)) / gradientDistanceInter(2)
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!* take maximum of both gradients and mix contributions from both sides according to weighted distances
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do dir = 1_pInt,2_pInt
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if (abs(gradientDeads(dir)) > abs(gradientInter(dir))) then
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gradient(dir) = gradientDeads(dir)
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gradientDistance(dir) = gradientDistanceDeads(dir)
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else
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gradient(dir) = gradientInter(dir)
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gradientDistance(dir) = gradientDistanceInter(dir)
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endif
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enddo
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rhoExcessGradient = (gradient(1) * gradientDistance(2) + gradient(2) * gradientDistance(1)) &
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/ (gradientDistance(1) + gradientDistance(2))
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!* excess gradient over density: in case of vanishing central total density we take the distance squared instead!!!
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rhoExcessGradient_over_rho(c) = rhoExcessGradient / (rhoSgl(s,2_pInt*c-1_pInt) + rhoSgl(s,2_pInt*c))
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rhoExcessGradient(c) = math_mul3x3(math_mul33x3(math_inv33(connections), rhoExcessDifferences), m(1:3,s,c))
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enddo
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!* plus gradient from deads
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do t = 1_pInt,4_pInt
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c = (t - 1_pInt) / 2_pInt + 1_pInt
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rhoExcessGradient(c) = rhoExcessGradient(c) + rhoSgl(s,t+4_pInt) / FVsize
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enddo
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!* normalized with the total density
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rhoExcessGradient_over_rho = 0.0_pReal
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rhoTotal(1_pInt) = sum(abs(rhoSgl(s,[1_pInt,2_pInt,5_pInt,6_pInt]))) + rhoDip(s,1_pInt)
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rhoTotal(2_pInt) = sum(abs(rhoSgl(s,[3_pInt,4_pInt,7_pInt,8_pInt]))) + rhoDip(s,2_pInt)
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forall (c = 1_pInt:2_pInt, rhoTotal(c) > 0.0_pReal) &
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rhoExcessGradient_over_rho(c) = rhoExcessGradient(c) / rhoTotal(c)
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!* gives the local stress correction when multiplied with a factor
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b = constitutive_nonlocal_burgers(s,instance)
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tauBack(s) = - mu * b / (2.0_pReal * pi) * (rhoExcessGradient_over_rho(1) / (1.0_pReal - nu) + rhoExcessGradient_over_rho(2))
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