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polishing (partly redoing changes that got lost when going to rev 3000)

This commit is contained in:
Martin Diehl 2014-05-23 17:13:08 +00:00
parent 51e7f9eed9
commit fcb89f7e75
1 changed files with 339 additions and 385 deletions
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code/constitutive_nonlocal.f90
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@ -43,9 +43,6 @@ OTHERSTATES = ['velocityEdgePos ', &
real(pReal), parameter, private :: & real(pReal), parameter, private :: &
KB = 1.38e-23_pReal !< Physical parameter, Boltzmann constant in J/Kelvin KB = 1.38e-23_pReal !< Physical parameter, Boltzmann constant in J/Kelvin
!* Definition of global variables
integer(pInt), dimension(:), allocatable, public, protected :: & integer(pInt), dimension(:), allocatable, public, protected :: &
constitutive_nonlocal_sizeDotState, & !< number of dotStates = number of basic state variables constitutive_nonlocal_sizeDotState, & !< number of dotStates = number of basic state variables
constitutive_nonlocal_sizeDependentState, & !< number of dependent state variables constitutive_nonlocal_sizeDependentState, & !< number of dependent state variables
@ -1552,15 +1549,16 @@ if (.not. phase_localPlasticity(phase) .and. shortRangeStressCorrection(instance
rhoExcessGradient_over_rho = 0.0_pReal rhoExcessGradient_over_rho = 0.0_pReal
forall (c = 1_pInt:2_pInt) & forall (c = 1_pInt:2_pInt) &
rhoTotal(c) = (sum(abs(rhoSgl(s,[2*c-1,2*c,2*c+3,2*c+4]))) + rhoDip(s,c) + sum(neighbor_rhoTotal(c,s,:))) & rhoTotal(c) = (sum(abs(rhoSgl(s,[2*c-1,2*c,2*c+3,2*c+4]))) + rhoDip(s,c) &
/ real(1_pInt + nRealNeighbors,pReal) + sum(neighbor_rhoTotal(c,s,:))) / real(1_pInt + nRealNeighbors,pReal)
forall (c = 1_pInt:2_pInt, rhoTotal(c) > 0.0_pReal) & forall (c = 1_pInt:2_pInt, rhoTotal(c) > 0.0_pReal) &
rhoExcessGradient_over_rho(c) = rhoExcessGradient(c) / rhoTotal(c) rhoExcessGradient_over_rho(c) = rhoExcessGradient(c) / rhoTotal(c)
!* gives the local stress correction when multiplied with a factor !* gives the local stress correction when multiplied with a factor
tauBack(s) = - lattice_mu(phase) * burgers(s,instance) / (2.0_pReal * pi) & tauBack(s) = - lattice_mu(phase) * burgers(s,instance) / (2.0_pReal * pi) &
* (rhoExcessGradient_over_rho(1) / (1.0_pReal - lattice_nu(phase)) + rhoExcessGradient_over_rho(2)) * (rhoExcessGradient_over_rho(1) / (1.0_pReal - lattice_nu(phase)) &
+ rhoExcessGradient_over_rho(2))
enddo enddo
endif endif
@ -2036,7 +2034,6 @@ ns = totalNslip(instance)
!*** shortcut to state variables !*** shortcut to state variables
forall (s = 1_pInt:ns, t = 1_pInt:4_pInt) forall (s = 1_pInt:ns, t = 1_pInt:4_pInt)
rhoSgl(s,t) = max(state%p(iRhoU(s,t,instance)), 0.0_pReal) ! ensure positive single mobile densities rhoSgl(s,t) = max(state%p(iRhoU(s,t,instance)), 0.0_pReal) ! ensure positive single mobile densities
rhoSgl(s,t+4_pInt) = state%p(iRhoB(s,t,instance)) rhoSgl(s,t+4_pInt) = state%p(iRhoB(s,t,instance))
@ -2091,43 +2088,7 @@ dUpper(1:ns,1) = lattice_mu(phase) * burgers(1:ns,instance) &
dUpper(1:ns,2) = lattice_mu(phase) * burgers(1:ns,instance) / (4.0_pReal * pi * abs(tau)) dUpper(1:ns,2) = lattice_mu(phase) * burgers(1:ns,instance) / (4.0_pReal * pi * abs(tau))
!in the test there is an FPE exception. Division by zero?
!in the test there is an FPE exception. Divistion by zero?
forall (c = 1_pInt:2_pInt) & forall (c = 1_pInt:2_pInt) &
dUpper(1:ns,c) = min(1.0_pReal / sqrt(rhoSgl(1:ns,2*c-1) + rhoSgl(1:ns,2*c) & dUpper(1:ns,c) = min(1.0_pReal / sqrt(rhoSgl(1:ns,2*c-1) + rhoSgl(1:ns,2*c) &
+ abs(rhoSgl(1:ns,2*c+3)) + abs(rhoSgl(1:ns,2*c+4)) + rhoDip(1:ns,c)), & + abs(rhoSgl(1:ns,2*c+3)) + abs(rhoSgl(1:ns,2*c+4)) + rhoDip(1:ns,c)), &
@ -2140,10 +2101,12 @@ deltaDUpper = dUpper - dUpperOld
deltaRhoDipole2SingleStress = 0.0_pReal deltaRhoDipole2SingleStress = 0.0_pReal
forall (c=1_pInt:2_pInt, s=1_pInt:ns, deltaDUpper(s,c) < 0.0_pReal) & forall (c=1_pInt:2_pInt, s=1_pInt:ns, deltaDUpper(s,c) < 0.0_pReal) &
deltaRhoDipole2SingleStress(s,8_pInt+c) = rhoDip(s,c) * deltaDUpper(s,c) / (dUpperOld(s,c) - dLower(s,c)) deltaRhoDipole2SingleStress(s,8_pInt+c) = rhoDip(s,c) * deltaDUpper(s,c) &
/ (dUpperOld(s,c) - dLower(s,c))
forall (t=1_pInt:4_pInt) & forall (t=1_pInt:4_pInt) &
deltaRhoDipole2SingleStress(1_pInt:ns,t) = -0.5_pReal * deltaRhoDipole2SingleStress(1_pInt:ns,(t-1_pInt)/2_pInt+9_pInt) deltaRhoDipole2SingleStress(1_pInt:ns,t) = -0.5_pReal &
* deltaRhoDipole2SingleStress(1_pInt:ns,(t-1_pInt)/2_pInt+9_pInt)
@ -2674,7 +2637,6 @@ endif
!*** formation by glide !*** formation by glide
do c = 1_pInt,2_pInt do c = 1_pInt,2_pInt
rhoDotSingle2DipoleGlide(1:ns,2*c-1) = -2.0_pReal * dUpper(1:ns,c) / burgers(1:ns,instance) & rhoDotSingle2DipoleGlide(1:ns,2*c-1) = -2.0_pReal * dUpper(1:ns,c) / burgers(1:ns,instance) &
* (rhoSgl(1:ns,2*c-1) * abs(gdot(1:ns,2*c)) & ! negative mobile --> positive mobile * (rhoSgl(1:ns,2*c-1) * abs(gdot(1:ns,2*c)) & ! negative mobile --> positive mobile
+ rhoSgl(1:ns,2*c) * abs(gdot(1:ns,2*c-1)) & ! positive mobile --> negative mobile + rhoSgl(1:ns,2*c) * abs(gdot(1:ns,2*c-1)) & ! positive mobile --> negative mobile
@ -2724,7 +2686,8 @@ vClimb = atomicVolume(instance) * selfDiffusion / ( KB * Temperature ) &
* 2.0_pReal / ( dUpper(1:ns,1) + dLower(1:ns,1) ) * 2.0_pReal / ( dUpper(1:ns,1) + dLower(1:ns,1) )
forall (s = 1_pInt:ns, dUpper(s,1) > dLower(s,1)) & forall (s = 1_pInt:ns, dUpper(s,1) > dLower(s,1)) &
rhoDotThermalAnnihilation(s,9) = max(- 4.0_pReal * rhoDip(s,1) * vClimb(s) / (dUpper(s,1) - dLower(s,1)), & rhoDotThermalAnnihilation(s,9) = max(- 4.0_pReal * rhoDip(s,1) * vClimb(s) / (dUpper(s,1) - dLower(s,1)), &
- rhoDip(s,1) / timestep - rhoDotAthermalAnnihilation(s,9) - rhoDotSingle2DipoleGlide(s,9)) ! make sure that we do not annihilate more dipoles than we have - rhoDip(s,1) / timestep - rhoDotAthermalAnnihilation(s,9) &
- rhoDotSingle2DipoleGlide(s,9)) ! make sure that we do not annihilate more dipoles than we have
@ -2753,14 +2716,18 @@ endif
if (iand(debug_level(debug_constitutive),debug_levelExtensive) /= 0_pInt & if (iand(debug_level(debug_constitutive),debug_levelExtensive) /= 0_pInt &
.and. ((debug_e == el .and. debug_i == ip .and. debug_g == ipc)& .and. ((debug_e == el .and. debug_i == ip .and. debug_g == ipc)&
.or. .not. iand(debug_level(debug_constitutive),debug_levelSelective) /= 0_pInt )) then .or. .not. iand(debug_level(debug_constitutive),debug_levelSelective) /= 0_pInt )) then
write(6,'(a,/,4(12x,12(e12.5,1x),/))') '<< CONST >> dislocation multiplication', rhoDotMultiplication(1:ns,1:4) * timestep write(6,'(a,/,4(12x,12(e12.5,1x),/))') '<< CONST >> dislocation multiplication', &
write(6,'(a,/,8(12x,12(e12.5,1x),/))') '<< CONST >> dislocation flux', rhoDotFlux(1:ns,1:8) * timestep rhoDotMultiplication(1:ns,1:4) * timestep
write(6,'(a,/,10(12x,12(e12.5,1x),/))') '<< CONST >> dipole formation by glide', rhoDotSingle2DipoleGlide * timestep write(6,'(a,/,8(12x,12(e12.5,1x),/))') '<< CONST >> dislocation flux', &
rhoDotFlux(1:ns,1:8) * timestep
write(6,'(a,/,10(12x,12(e12.5,1x),/))') '<< CONST >> dipole formation by glide', &
rhoDotSingle2DipoleGlide * timestep
write(6,'(a,/,10(12x,12(e12.5,1x),/))') '<< CONST >> athermal dipole annihilation', & write(6,'(a,/,10(12x,12(e12.5,1x),/))') '<< CONST >> athermal dipole annihilation', &
rhoDotAthermalAnnihilation * timestep rhoDotAthermalAnnihilation * timestep
write(6,'(a,/,2(12x,12(e12.5,1x),/))') '<< CONST >> thermally activated dipole annihilation', & write(6,'(a,/,2(12x,12(e12.5,1x),/))') '<< CONST >> thermally activated dipole annihilation', &
rhoDotThermalAnnihilation(1:ns,9:10) * timestep rhoDotThermalAnnihilation(1:ns,9:10) * timestep
write(6,'(a,/,10(12x,12(e12.5,1x),/))') '<< CONST >> total density change', rhoDot * timestep write(6,'(a,/,10(12x,12(e12.5,1x),/))') '<< CONST >> total density change', &
rhoDot * timestep
write(6,'(a,/,10(12x,12(f12.5,1x),/))') '<< CONST >> relative density change', & write(6,'(a,/,10(12x,12(f12.5,1x),/))') '<< CONST >> relative density change', &
rhoDot(1:ns,1:8) * timestep / (abs(rhoSglOriginal)+1.0e-10), & rhoDot(1:ns,1:8) * timestep / (abs(rhoSglOriginal)+1.0e-10), &
rhoDot(1:ns,9:10) * timestep / (rhoDipOriginal+1.0e-10) rhoDot(1:ns,9:10) * timestep / (rhoDipOriginal+1.0e-10)
@ -2830,8 +2797,6 @@ integer(pInt), intent(in) :: i, & !
real(pReal), dimension(4,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: & real(pReal), dimension(4,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
orientation ! crystal orientation in quaternions orientation ! crystal orientation in quaternions
!* output variables
!* local variables !* local variables
integer(pInt) Nneighbors, & ! number of neighbors integer(pInt) Nneighbors, & ! number of neighbors
n, & ! neighbor index n, & ! neighbor index
@ -2997,62 +2962,59 @@ use lattice, only: lattice_mu, &
implicit none implicit none
!*** input variables !*** input variables
integer(pInt), intent(in) :: ipc, & ! current grain ID integer(pInt), intent(in) :: ipc, & !< current grain ID
ip, & ! current integration point ip, & !< current integration point
el ! current element el !< current element
real(pReal), dimension(3,3,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: & real(pReal), dimension(3,3,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
Fe ! elastic deformation gradient Fe !< elastic deformation gradient
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: & type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
state ! microstructural state state !< microstructural state
!*** input/output variables
!*** output variables !*** output variables
real(pReal), dimension(3,3) :: constitutive_nonlocal_dislocationstress real(pReal), dimension(3,3) :: constitutive_nonlocal_dislocationstress
!*** local variables !*** local variables
integer(pInt) neighbor_el, & ! element number of neighbor material point integer(pInt) neighbor_el, & !< element number of neighbor material point
neighbor_ip, & ! integration point of neighbor material point neighbor_ip, & !< integration point of neighbor material point
instance, & ! my instance of this plasticity instance, & !< my instance of this plasticity
neighbor_instance, & ! instance of this plasticity of neighbor material point neighbor_instance, & !< instance of this plasticity of neighbor material point
phase, & phase, &
neighbor_phase, & neighbor_phase, &
ns, & ! total number of active slip systems at my material point ns, & !< total number of active slip systems at my material point
neighbor_ns, & ! total number of active slip systems at neighbor material point neighbor_ns, & !< total number of active slip systems at neighbor material point
c, & ! index of dilsocation character (edge, screw) c, & !< index of dilsocation character (edge, screw)
s, & ! slip system index s, & !< slip system index
t, & ! index of dilsocation type (e+, e-, s+, s-, used e+, used e-, used s+, used s-) t, & !< index of dilsocation type (e+, e-, s+, s-, used e+, used e-, used s+, used s-)
dir, & dir, &
deltaX, deltaY, deltaZ, & deltaX, deltaY, deltaZ, &
side, & side, &
j j
integer(pInt), dimension(2,3) :: periodicImages integer(pInt), dimension(2,3) :: periodicImages
real(pReal) x, y, z, & ! coordinates of connection vector in neighbor lattice frame real(pReal) x, y, z, & !< coordinates of connection vector in neighbor lattice frame
xsquare, ysquare, zsquare, & ! squares of respective coordinates xsquare, ysquare, zsquare, & !< squares of respective coordinates
distance, & ! length of connection vector distance, & !< length of connection vector
segmentLength, & ! segment length of dislocations segmentLength, & !< segment length of dislocations
lambda, & lambda, &
R, Rsquare, Rcube, & R, Rsquare, Rcube, &
denominator, & denominator, &
flipSign, & flipSign, &
neighbor_ipVolumeSideLength, & neighbor_ipVolumeSideLength, &
detFe detFe
real(pReal), dimension(3) :: connection, & ! connection vector between me and my neighbor in the deformed configuration real(pReal), dimension(3) :: connection, & !< connection vector between me and my neighbor in the deformed configuration
connection_neighborLattice, & ! connection vector between me and my neighbor in the lattice configuration of my neighbor connection_neighborLattice, & !< connection vector between me and my neighbor in the lattice configuration of my neighbor
connection_neighborSlip, & ! connection vector between me and my neighbor in the slip system frame of my neighbor connection_neighborSlip, & !< connection vector between me and my neighbor in the slip system frame of my neighbor
maxCoord, minCoord, & maxCoord, minCoord, &
meshSize, & meshSize, &
coords, & ! x,y,z coordinates of cell center of ip volume coords, & !< x,y,z coordinates of cell center of ip volume
neighbor_coords ! x,y,z coordinates of cell center of neighbor ip volume neighbor_coords !< x,y,z coordinates of cell center of neighbor ip volume
real(pReal), dimension(3,3) :: sigma, & ! dislocation stress for one slip system in neighbor material point's slip system frame real(pReal), dimension(3,3) :: sigma, & !< dislocation stress for one slip system in neighbor material point's slip system frame
Tdislo_neighborLattice, & ! dislocation stress as 2nd Piola-Kirchhoff stress at neighbor material point Tdislo_neighborLattice, & !< dislocation stress as 2nd Piola-Kirchhoff stress at neighbor material point
invFe, & ! inverse of my elastic deformation gradient invFe, & !< inverse of my elastic deformation gradient
neighbor_invFe, & neighbor_invFe, &
neighborLattice2myLattice ! mapping from neighbor MPs lattice configuration to my lattice configuration neighborLattice2myLattice !< mapping from neighbor MPs lattice configuration to my lattice configuration
real(pReal), dimension(2,2,maxval(totalNslip)) :: & real(pReal), dimension(2,2,maxval(totalNslip)) :: &
neighbor_rhoExcess ! excess density at neighbor material point (edge/screw,mobile/dead,slipsystem) neighbor_rhoExcess !< excess density at neighbor material point (edge/screw,mobile/dead,slipsystem)
real(pReal), dimension(2,maxval(totalNslip)) :: & real(pReal), dimension(2,maxval(totalNslip)) :: &
rhoExcessDead rhoExcessDead
real(pReal), dimension(totalNslip(phase_plasticityInstance(material_phase(ipc,ip,el))),8) :: & real(pReal), dimension(totalNslip(phase_plasticityInstance(material_phase(ipc,ip,el))),8) :: &
@ -3149,9 +3111,7 @@ ipLoop: do neighbor_ip = 1_pInt,FE_Nips(FE_geomtype(mesh_element(2,neighbor_el))
!* and add up the stress contributions from egde and screw excess on these slip systems (if significant) !* and add up the stress contributions from egde and screw excess on these slip systems (if significant)
do s = 1_pInt,neighbor_ns do s = 1_pInt,neighbor_ns
if (all(abs(neighbor_rhoExcess(:,:,s)) < significantRho(instance))) then if (all(abs(neighbor_rhoExcess(:,:,s)) < significantRho(instance))) cycle ! not significant
cycle ! not significant
endif
!* map the connection vector from the lattice into the slip system frame !* map the connection vector from the lattice into the slip system frame
@ -3163,9 +3123,7 @@ ipLoop: do neighbor_ip = 1_pInt,FE_Nips(FE_geomtype(mesh_element(2,neighbor_el))
!* edge contribution to stress !* edge contribution to stress
sigma = 0.0_pReal sigma = 0.0_pReal
x = connection_neighborSlip(1) [x,y,z] = connection_neighborSlip
y = connection_neighborSlip(2)
z = connection_neighborSlip(3)
xsquare = x * x xsquare = x * x
ysquare = y * y ysquare = y * y
zsquare = z * z zsquare = z * z
@ -3174,7 +3132,8 @@ ipLoop: do neighbor_ip = 1_pInt,FE_Nips(FE_geomtype(mesh_element(2,neighbor_el))
if (abs(neighbor_rhoExcess(1,j,s)) < significantRho(instance)) then if (abs(neighbor_rhoExcess(1,j,s)) < significantRho(instance)) then
cycle cycle
elseif (j > 1_pInt) then elseif (j > 1_pInt) then
x = connection_neighborSlip(1) + sign(0.5_pReal * segmentLength, & x = connection_neighborSlip(1) &
+ sign(0.5_pReal * segmentLength, &
state(ipc,neighbor_ip,neighbor_el)%p(iRhoB(s,1,neighbor_instance)) & state(ipc,neighbor_ip,neighbor_el)%p(iRhoB(s,1,neighbor_instance)) &
- state(ipc,neighbor_ip,neighbor_el)%p(iRhoB(s,2,neighbor_instance))) - state(ipc,neighbor_ip,neighbor_el)%p(iRhoB(s,2,neighbor_instance)))
xsquare = x * x xsquare = x * x
@ -3187,9 +3146,7 @@ ipLoop: do neighbor_ip = 1_pInt,FE_Nips(FE_geomtype(mesh_element(2,neighbor_el))
Rsquare = R * R Rsquare = R * R
Rcube = Rsquare * R Rcube = Rsquare * R
denominator = R * (R + flipSign * lambda) denominator = R * (R + flipSign * lambda)
if (denominator == 0.0_pReal) then if (denominator == 0.0_pReal) exit ipLoop
exit ipLoop
endif
sigma(1,1) = sigma(1,1) - real(side,pReal) & sigma(1,1) = sigma(1,1) - real(side,pReal) &
* flipSign * z / denominator & * flipSign * z / denominator &
@ -3220,7 +3177,8 @@ ipLoop: do neighbor_ip = 1_pInt,FE_Nips(FE_geomtype(mesh_element(2,neighbor_el))
if (abs(neighbor_rhoExcess(2,j,s)) < significantRho(instance)) then if (abs(neighbor_rhoExcess(2,j,s)) < significantRho(instance)) then
cycle cycle
elseif (j > 1_pInt) then elseif (j > 1_pInt) then
y = connection_neighborSlip(2) + sign(0.5_pReal * segmentLength, & y = connection_neighborSlip(2)
+ sign(0.5_pReal * segmentLength, &
state(ipc,neighbor_ip,neighbor_el)%p(iRhoB(s,3,neighbor_instance)) & state(ipc,neighbor_ip,neighbor_el)%p(iRhoB(s,3,neighbor_instance)) &
- state(ipc,neighbor_ip,neighbor_el)%p(iRhoB(s,4,neighbor_instance))) - state(ipc,neighbor_ip,neighbor_el)%p(iRhoB(s,4,neighbor_instance)))
ysquare = y * y ysquare = y * y
@ -3233,20 +3191,18 @@ ipLoop: do neighbor_ip = 1_pInt,FE_Nips(FE_geomtype(mesh_element(2,neighbor_el))
Rsquare = R * R Rsquare = R * R
Rcube = Rsquare * R Rcube = Rsquare * R
denominator = R * (R + flipSign * lambda) denominator = R * (R + flipSign * lambda)
if (denominator == 0.0_pReal) then if (denominator == 0.0_pReal) exit ipLoop
exit ipLoop
endif
sigma(1,2) = sigma(1,2) - real(side,pReal) * flipSign * z * (1.0_pReal - lattice_nu(phase)) / denominator & sigma(1,2) = sigma(1,2) - real(side,pReal) * flipSign * z &
* (1.0_pReal - lattice_nu(phase)) / denominator &
* neighbor_rhoExcess(2,j,s) * neighbor_rhoExcess(2,j,s)
sigma(1,3) = sigma(1,3) + real(side,pReal) * flipSign * y * (1.0_pReal - lattice_nu(phase)) / denominator & sigma(1,3) = sigma(1,3) + real(side,pReal) * flipSign * y &
* (1.0_pReal - lattice_nu(phase)) / denominator &
* neighbor_rhoExcess(2,j,s) * neighbor_rhoExcess(2,j,s)
enddo enddo
enddo enddo
if (all(abs(sigma) < 1.0e-10_pReal)) then ! SIGMA IS NOT A REAL STRESS, THATS WHY WE NEED A REALLY SMALL VALUE HERE if (all(abs(sigma) < 1.0e-10_pReal)) cycle ! SIGMA IS NOT A REAL STRESS, THATS WHY WE NEED A REALLY SMALL VALUE HERE
cycle
endif
!* copy symmetric parts !* copy symmetric parts
@ -3279,9 +3235,7 @@ ipLoop: do neighbor_ip = 1_pInt,FE_Nips(FE_geomtype(mesh_element(2,neighbor_el))
+ state(ipc,ip,el)%p(iRhoB(s,2*c,instance)) ! negative deads (here we use symmetry: if this has negative sign it is treated as positive density at positive position instead of negative density at negative position) + state(ipc,ip,el)%p(iRhoB(s,2*c,instance)) ! negative deads (here we use symmetry: if this has negative sign it is treated as positive density at positive position instead of negative density at negative position)
do s = 1_pInt,ns do s = 1_pInt,ns
if (all(abs(rhoExcessDead(:,s)) < significantRho(instance))) then if (all(abs(rhoExcessDead(:,s)) < significantRho(instance))) cycle ! not significant
cycle ! not significant
endif
sigma = 0.0_pReal ! all components except for sigma13 are zero sigma = 0.0_pReal ! all components except for sigma13 are zero
sigma(1,3) = - (rhoExcessDead(1,s) + rhoExcessDead(2,s) * (1.0_pReal - lattice_nu(phase))) & sigma(1,3) = - (rhoExcessDead(1,s) + rhoExcessDead(2,s) * (1.0_pReal - lattice_nu(phase))) &
* neighbor_ipVolumeSideLength * lattice_mu(phase) * burgers(s,instance) & * neighbor_ipVolumeSideLength * lattice_mu(phase) * burgers(s,instance) &