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in kinetics: non schmid stresses only influence peierls mechanism, but not solid solution hardening; as a result the derivative of the velocity with respect to the resolved stress has to be split into a Schmid and a non-Schmid part

This commit is contained in:
Christoph Kords 2013-08-21 12:21:52 +00:00
parent ec377a6e8e
commit 4f8664baa3
1 changed files with 70 additions and 54 deletions
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124
code/constitutive_nonlocal.f90
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@ -1545,7 +1545,8 @@ endsubroutine
!********************************************************************* !*********************************************************************
!* calculates kinetics * !* calculates kinetics *
!********************************************************************* !*********************************************************************
subroutine constitutive_nonlocal_kinetics(v, dv_dtau, tau, tauThreshold, c, Temperature, g, ip, el) subroutine constitutive_nonlocal_kinetics(v, dv_dtau, dv_dtauNS, tau, tauNS, &
tauThreshold, c, Temperature, g, ip, el)
use debug, only: debug_level, & use debug, only: debug_level, &
debug_constitutive, & debug_constitutive, &
@ -1567,23 +1568,23 @@ integer(pInt), intent(in) :: g, & !< curre
c !< dislocation character (1:edge, 2:screw) c !< dislocation character (1:edge, 2:screw)
real(pReal), intent(in) :: Temperature !< temperature real(pReal), intent(in) :: Temperature !< temperature
real(pReal), dimension(totalNslip(phase_plasticityInstance(material_phase(g,ip,el)))), & real(pReal), dimension(totalNslip(phase_plasticityInstance(material_phase(g,ip,el)))), &
intent(in) :: tau, & !< resolved external shear stress (for bcc this already contains non Schmid effects) intent(in) :: tau, & !< resolved external shear stress (without non Schmid effects)
tauNS, & !< resolved external shear stress (including non Schmid effects)
tauThreshold !< threshold shear stress tauThreshold !< threshold shear stress
!*** output variables !*** output variables
real(pReal), dimension(totalNslip(phase_plasticityInstance(material_phase(g,ip,el)))), & real(pReal), dimension(totalNslip(phase_plasticityInstance(material_phase(g,ip,el)))), &
intent(out) :: v !< velocity intent(out) :: v, & !< velocity
real(pReal), dimension(totalNslip(phase_plasticityInstance(material_phase(g,ip,el)))), & dv_dtau, & !< velocity derivative with respect to resolved shear stress (without non Schmid contributions)
intent(out) :: dv_dtau !< velocity derivative with respect to resolved shear stress dv_dtauNS !< velocity derivative with respect to resolved shear stress (including non Schmid contributions)
!*** local variables !*** local variables
integer(pInt) :: instance, & !< current instance of this plasticity integer(pInt) :: instance, & !< current instance of this plasticity
ns, & !< short notation for the total number of active slip systems ns, & !< short notation for the total number of active slip systems
s !< index of my current slip system s !< index of my current slip system
real(pReal), dimension(totalNslip(phase_plasticityInstance(material_phase(g,ip,el)))) :: &
tauEff !< effective shear stress
real(pReal) tauRel_P, & real(pReal) tauRel_P, &
tauRel_S, & tauRel_S, &
tauEff, & !< effective shear stress
tPeierls, & !< waiting time in front of a peierls barriers tPeierls, & !< waiting time in front of a peierls barriers
tSolidSolution, & !< waiting time in front of a solid solution obstacle tSolidSolution, & !< waiting time in front of a solid solution obstacle
vViscous, & !< viscous glide velocity vViscous, & !< viscous glide velocity
@ -1607,30 +1608,31 @@ real(pReal) tauRel_P, &
instance = phase_plasticityInstance(material_phase(g,ip,el)) instance = phase_plasticityInstance(material_phase(g,ip,el))
ns = totalNslip(instance) ns = totalNslip(instance)
tauEff = abs(tau) - tauThreshold
v = 0.0_pReal v = 0.0_pReal
dv_dtau = 0.0_pReal dv_dtau = 0.0_pReal
dv_dtauNS = 0.0_pReal
if (Temperature > 0.0_pReal) then if (Temperature > 0.0_pReal) then
do s = 1_pInt,ns do s = 1_pInt,ns
if (tauEff(s) > 0.0_pReal) then if (abs(tau(s)) > tauThreshold(s)) then
!* Peierls contribution !* Peierls contribution
!* Effective stress includes non Schmid constributions
!* The derivative only gives absolute values; the correct sign is taken care of in the formula for the derivative of the velocity !* The derivative only gives absolute values; the correct sign is taken care of in the formula for the derivative of the velocity
tauEff = max(0.0_pReal, abs(tauNS(s)) - tauThreshold(s)) ! ensure that the effective stress is positive
meanfreepath_P = burgers(s,instance) meanfreepath_P = burgers(s,instance)
jumpWidth_P = burgers(s,instance) jumpWidth_P = burgers(s,instance)
activationLength_P = doublekinkwidth(instance) * burgers(s,instance) activationLength_P = doublekinkwidth(instance) * burgers(s,instance)
activationVolume_P = activationLength_P * jumpWidth_P * burgers(s,instance) activationVolume_P = activationLength_P * jumpWidth_P * burgers(s,instance)
criticalStress_P = peierlsStress(s,c,instance) criticalStress_P = peierlsStress(s,c,instance)
activationEnergy_P = criticalStress_P * activationVolume_P activationEnergy_P = criticalStress_P * activationVolume_P
tauRel_P = min(1.0_pReal, tauEff(s) / criticalStress_P) ! ensure that the activation probability cannot become greater than one tauRel_P = min(1.0_pReal, tauEff / criticalStress_P) ! ensure that the activation probability cannot become greater than one
tPeierls = 1.0_pReal / fattack(instance) & tPeierls = 1.0_pReal / fattack(instance) &
* exp(activationEnergy_P / (KB * Temperature) & * exp(activationEnergy_P / (KB * Temperature) &
* (1.0_pReal - tauRel_P**pParam(instance))**qParam(instance)) * (1.0_pReal - tauRel_P**pParam(instance))**qParam(instance))
if (tauEff(s) < criticalStress_P) then if (tauEff < criticalStress_P) then
dtPeierls_dtau = tPeierls * pParam(instance) * qParam(instance) * activationVolume_P / (KB * Temperature) & dtPeierls_dtau = tPeierls * pParam(instance) * qParam(instance) * activationVolume_P / (KB * Temperature) &
* (1.0_pReal - tauRel_P**pParam(instance))**(qParam(instance)-1.0_pReal) & * (1.0_pReal - tauRel_P**pParam(instance))**(qParam(instance)-1.0_pReal) &
* tauRel_P**(pParam(instance)-1.0_pReal) * tauRel_P**(pParam(instance)-1.0_pReal)
@ -1642,17 +1644,18 @@ if (Temperature > 0.0_pReal) then
!* Contribution from solid solution strengthening !* Contribution from solid solution strengthening
!* The derivative only gives absolute values; the correct sign is taken care of in the formula for the derivative of the velocity !* The derivative only gives absolute values; the correct sign is taken care of in the formula for the derivative of the velocity
tauEff = abs(tau(s)) - tauThreshold(s)
meanfreepath_S = burgers(s,instance) / sqrt(solidSolutionConcentration(instance)) meanfreepath_S = burgers(s,instance) / sqrt(solidSolutionConcentration(instance))
jumpWidth_S = solidSolutionSize(instance) * burgers(s,instance) jumpWidth_S = solidSolutionSize(instance) * burgers(s,instance)
activationLength_S = burgers(s,instance) / sqrt(solidSolutionConcentration(instance)) activationLength_S = burgers(s,instance) / sqrt(solidSolutionConcentration(instance))
activationVolume_S = activationLength_S * jumpWidth_S * burgers(s,instance) activationVolume_S = activationLength_S * jumpWidth_S * burgers(s,instance)
activationEnergy_S = solidSolutionEnergy(instance) activationEnergy_S = solidSolutionEnergy(instance)
criticalStress_S = activationEnergy_S / activationVolume_S criticalStress_S = activationEnergy_S / activationVolume_S
tauRel_S = min(1.0_pReal, tauEff(s) / criticalStress_S) ! ensure that the activation probability cannot become greater than one tauRel_S = min(1.0_pReal, tauEff / criticalStress_S) ! ensure that the activation probability cannot become greater than one
tSolidSolution = 1.0_pReal / fattack(instance) & tSolidSolution = 1.0_pReal / fattack(instance) &
* exp(activationEnergy_S / (KB * Temperature) & * exp(activationEnergy_S / (KB * Temperature) &
* (1.0_pReal - tauRel_S**pParam(instance))**qParam(instance)) * (1.0_pReal - tauRel_S**pParam(instance))**qParam(instance))
if (tauEff(s) < criticalStress_S) then if (tauEff < criticalStress_S) then
dtSolidSolution_dtau = tSolidSolution * pParam(instance) * qParam(instance) & dtSolidSolution_dtau = tSolidSolution * pParam(instance) * qParam(instance) &
* activationVolume_S / (KB * Temperature) & * activationVolume_S / (KB * Temperature) &
* (1.0_pReal - tauRel_S**pParam(instance))**(qParam(instance)-1.0_pReal) & * (1.0_pReal - tauRel_S**pParam(instance))**(qParam(instance)-1.0_pReal) &
@ -1664,8 +1667,9 @@ if (Temperature > 0.0_pReal) then
!* viscous glide velocity !* viscous glide velocity
tauEff = abs(tau(s)) - tauThreshold(s)
mobility = burgers(s,instance) / viscosity(instance) mobility = burgers(s,instance) / viscosity(instance)
vViscous = mobility * tauEff(s) vViscous = mobility * tauEff
!* Mean velocity results from waiting time at peierls barriers and solid solution obstacles with respective meanfreepath of !* Mean velocity results from waiting time at peierls barriers and solid solution obstacles with respective meanfreepath of
@ -1674,11 +1678,9 @@ if (Temperature > 0.0_pReal) then
v(s) = sign(1.0_pReal,tau(s)) & v(s) = sign(1.0_pReal,tau(s)) &
/ (tPeierls / meanfreepath_P + tSolidSolution / meanfreepath_S + 1.0_pReal / vViscous) / (tPeierls / meanfreepath_P + tSolidSolution / meanfreepath_S + 1.0_pReal / vViscous)
dv_dtau(s) = v(s) * v(s) & dv_dtau(s) = v(s) * v(s) * (dtSolidSolution_dtau / meanfreepath_S &
* (dtPeierls_dtau / meanfreepath_P & + mobility / (vViscous * vViscous))
+ dtSolidSolution_dtau / meanfreepath_S & dv_dtauNS(s) = v(s) * v(s) * dtPeierls_dtau / meanfreepath_P
+ 1.0_pReal / (mobility * tauEff(s)*tauEff(s)))
endif endif
enddo enddo
endif endif
@ -1691,10 +1693,12 @@ endif
write(6,*) write(6,*)
write(6,'(a,i8,1x,i2,1x,i1)') '<< CONST >> nonlocal_kinetics at el ip g',el,ip,g write(6,'(a,i8,1x,i2,1x,i1)') '<< CONST >> nonlocal_kinetics at el ip g',el,ip,g
write(6,*) write(6,*)
write(6,'(a,/,12x,12(f12.5,1x))') '<< CONST >> tauThreshold / MPa', tauThreshold / 1e6_pReal
write(6,'(a,/,12x,12(f12.5,1x))') '<< CONST >> tau / MPa', tau / 1e6_pReal write(6,'(a,/,12x,12(f12.5,1x))') '<< CONST >> tau / MPa', tau / 1e6_pReal
write(6,'(a,/,12x,12(f12.5,1x))') '<< CONST >> tauEff / MPa', tauEff / 1e6_pReal write(6,'(a,/,12x,12(f12.5,1x))') '<< CONST >> tauNS / MPa', tauNS / 1e6_pReal
write(6,'(a,/,12x,12(f12.5,1x))') '<< CONST >> v / 1e-3m/s', v * 1e3 write(6,'(a,/,12x,12(f12.5,1x))') '<< CONST >> v / 1e-3m/s', v * 1e3
write(6,'(a,/,12x,12(e12.5,1x))') '<< CONST >> dv_dtau', dv_dtau write(6,'(a,/,12x,12(e12.5,1x))') '<< CONST >> dv_dtau', dv_dtau
write(6,'(a,/,12x,12(e12.5,1x))') '<< CONST >> dv_dtauNS', dv_dtauNS
endif endif
#endif #endif
@ -1760,10 +1764,11 @@ real(pReal), dimension(totalNslip(phase_plasticityInstance(material_phase(g,ip,e
rhoSgl !< single dislocation densities (including blocked) rhoSgl !< single dislocation densities (including blocked)
real(pReal), dimension(totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),4) :: & real(pReal), dimension(totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),4) :: &
v, & !< velocity v, & !< velocity
tau, & !< resolved shear stress including non Schmid and backstress terms tauNS, & !< resolved shear stress including non Schmid and backstress terms
dgdot_dtau, & !< derivative of the shear rate with respect to the shear stress dv_dtau, & !< velocity derivative with respect to the shear stress
dv_dtau !< velocity derivative with respect to the shear stress dv_dtauNS !< velocity derivative with respect to the shear stress
real(pReal), dimension(totalNslip(phase_plasticityInstance(material_phase(g,ip,el)))) :: & real(pReal), dimension(totalNslip(phase_plasticityInstance(material_phase(g,ip,el)))) :: &
tau, & !< resolved shear stress including backstress terms
gdotTotal, & !< shear rate gdotTotal, & !< shear rate
tauBack, & !< back stress from dislocation gradients on same slip system tauBack, & !< back stress from dislocation gradients on same slip system
tauThreshold !< threshold shear stress tauThreshold !< threshold shear stress
@ -1799,26 +1804,31 @@ tauThreshold = state%p(iTauF(1:ns,myInstance))
do s = 1_pInt,ns do s = 1_pInt,ns
sLattice = slipSystemLattice(s,myInstance) sLattice = slipSystemLattice(s,myInstance)
tau(s,1:2) = math_mul6x6(Tstar_v, lattice_Sslip_v(1:6,1,sLattice,myStructure)) tau(s) = math_mul6x6(Tstar_v, lattice_Sslip_v(1:6,1,sLattice,myStructure))
if (tau(s,1) > 0.0_pReal) then tauNS(s,1) = tau(s)
tau(s,3) = math_mul33xx33(math_Mandel6to33(Tstar_v), nonSchmidProjection(1:3,1:3,1,s,myInstance)) tauNS(s,2) = tau(s)
tau(s,4) = math_mul33xx33(math_Mandel6to33(Tstar_v), nonSchmidProjection(1:3,1:3,3,s,myInstance)) if (tau(s) > 0.0_pReal) then
tauNS(s,3) = math_mul33xx33(math_Mandel6to33(Tstar_v), nonSchmidProjection(1:3,1:3,1,s,myInstance))
tauNS(s,4) = math_mul33xx33(math_Mandel6to33(Tstar_v), nonSchmidProjection(1:3,1:3,3,s,myInstance))
else else
tau(s,3) = math_mul33xx33(math_Mandel6to33(Tstar_v), nonSchmidProjection(1:3,1:3,2,s,myInstance)) tauNS(s,3) = math_mul33xx33(math_Mandel6to33(Tstar_v), nonSchmidProjection(1:3,1:3,2,s,myInstance))
tau(s,4) = math_mul33xx33(math_Mandel6to33(Tstar_v), nonSchmidProjection(1:3,1:3,4,s,myInstance)) tauNS(s,4) = math_mul33xx33(math_Mandel6to33(Tstar_v), nonSchmidProjection(1:3,1:3,4,s,myInstance))
endif endif
forall (t = 1_pInt:4_pInt) &
tau(s,t) = tau(s,t) + tauBack(s) ! add backstress
enddo enddo
forall (t = 1_pInt:4_pInt) &
tauNS(1:ns,t) = tauNS(1:ns,t) + tauBack ! add backstress
tau = tau + tauBack ! add backstress
!*** get dislocation velocity and its tangent and store the velocity in the state array !*** get dislocation velocity and its tangent and store the velocity in the state array
! edges ! edges
call constitutive_nonlocal_kinetics(v(1:ns,1), dv_dtau(1:ns,1), tau(1:ns,1), tauThreshold(1:ns), & call constitutive_nonlocal_kinetics(v(1:ns,1), dv_dtau(1:ns,1), dv_dtauNS(1:ns,1), &
tau(1:ns), tauNS(1:ns,1), tauThreshold(1:ns), &
1_pInt, Temperature, g, ip, el) 1_pInt, Temperature, g, ip, el)
v(1:ns,2) = v(1:ns,1) v(1:ns,2) = v(1:ns,1)
dv_dtau(1:ns,2) = dv_dtau(1:ns,1) dv_dtau(1:ns,2) = dv_dtau(1:ns,1)
dv_dtauNS(1:ns,2) = dv_dtauNS(1:ns,1)
state%p(iV(1:ns,2,myInstance)) = v(1:ns,1) state%p(iV(1:ns,2,myInstance)) = v(1:ns,1)
!screws !screws
@ -1826,11 +1836,13 @@ if (lattice_NnonSchmid(myStructure) == 0_pInt) then
forall(t = 3_pInt:4_pInt) forall(t = 3_pInt:4_pInt)
v(1:ns,t) = v(1:ns,1) v(1:ns,t) = v(1:ns,1)
dv_dtau(1:ns,t) = dv_dtau(1:ns,1) dv_dtau(1:ns,t) = dv_dtau(1:ns,1)
dv_dtauNS(1:ns,t) = dv_dtauNS(1:ns,1)
state%p(iV(1:ns,t,myInstance)) = v(1:ns,1) state%p(iV(1:ns,t,myInstance)) = v(1:ns,1)
endforall endforall
else ! take non-Schmid contributions into account else ! take non-Schmid contributions into account
do t = 3_pInt,4_pInt do t = 3_pInt,4_pInt
call constitutive_nonlocal_kinetics(v(1:ns,t), dv_dtau(1:ns,t), tau(1:ns,t), tauThreshold(1:ns), & call constitutive_nonlocal_kinetics(v(1:ns,t), dv_dtau(1:ns,t), dv_dtauNS(1:ns,t), &
tau(1:ns), tauNS(1:ns,t), tauThreshold(1:ns), &
2_pInt , Temperature, g, ip, el) 2_pInt , Temperature, g, ip, el)
state%p(iV(1:ns,t,myInstance)) = v(1:ns,t) state%p(iV(1:ns,t,myInstance)) = v(1:ns,t)
enddo enddo
@ -1843,32 +1855,36 @@ forall (s = 1_pInt:ns, t = 5_pInt:8_pInt, rhoSgl(s,t) * v(s,t-4_pInt) < 0.0_pRea
rhoSgl(s,t-4_pInt) = rhoSgl(s,t-4_pInt) + abs(rhoSgl(s,t)) rhoSgl(s,t-4_pInt) = rhoSgl(s,t-4_pInt) + abs(rhoSgl(s,t))
!*** Calculation of gdot and its tangent
gdotTotal = sum(rhoSgl(1:ns,1:4) * v, 2) * burgers(1:ns,myInstance)
forall (t = 1_pInt:4_pInt) &
dgdot_dtau(1:ns,t) = rhoSgl(1:ns,t) * dv_dtau(1:ns,t) * burgers(1:ns,myInstance)
!*** Calculation of Lp and its tangent !*** Calculation of Lp and its tangent
gdotTotal = sum(rhoSgl(1:ns,1:4) * v, 2) * burgers(1:ns,myInstance)
do s = 1_pInt,ns do s = 1_pInt,ns
sLattice = slipSystemLattice(s,myInstance) sLattice = slipSystemLattice(s,myInstance)
Lp = Lp + gdotTotal(s) * lattice_Sslip(1:3,1:3,1,sLattice,myStructure) Lp = Lp + gdotTotal(s) * lattice_Sslip(1:3,1:3,1,sLattice,myStructure)
if (tau(s,1) > 0.0_pReal) then
! Schmid contributions to tangent
forall (i=1_pInt:3_pInt,j=1_pInt:3_pInt,k=1_pInt:3_pInt,l=1_pInt:3_pInt) &
dLp_dTstar3333(i,j,k,l) = dLp_dTstar3333(i,j,k,l) &
+ lattice_Sslip(i,j,1,sLattice,myStructure) * lattice_Sslip(k,l,1,sLattice,myStructure) &
* sum(rhoSgl(s,1:4) * dv_dtau(s,1:4)) * burgers(s,myInstance)
! non Schmid contributions to tangent
if (tau(s) > 0.0_pReal) then
forall (i=1_pInt:3_pInt,j=1_pInt:3_pInt,k=1_pInt:3_pInt,l=1_pInt:3_pInt) & forall (i=1_pInt:3_pInt,j=1_pInt:3_pInt,k=1_pInt:3_pInt,l=1_pInt:3_pInt) &
dLp_dTstar3333(i,j,k,l) = dLp_dTstar3333(i,j,k,l) & dLp_dTstar3333(i,j,k,l) = dLp_dTstar3333(i,j,k,l) &
+ dgdot_dtau(s,1) * lattice_Sslip(i,j,1,sLattice,myStructure) * lattice_Sslip(k,l,1,sLattice,myStructure) & + lattice_Sslip(i,j,1,sLattice,myStructure) &
+ dgdot_dtau(s,2) * lattice_Sslip(i,j,1,sLattice,myStructure) * lattice_Sslip(k,l,1,sLattice,myStructure) & * ( nonSchmidProjection(k,l,1,s,myInstance) * rhoSgl(s,3) * dv_dtauNS(s,3) &
+ dgdot_dtau(s,3) * lattice_Sslip(i,j,1,sLattice,myStructure) * nonSchmidProjection(k,l,1,s,myInstance) & + nonSchmidProjection(k,l,3,s,myInstance) * rhoSgl(s,4) * dv_dtauNS(s,4) ) &
+ dgdot_dtau(s,4) * lattice_Sslip(i,j,1,sLattice,myStructure) * nonSchmidProjection(k,l,3,s,myInstance) * burgers(s,myInstance)
else else
forall (i=1_pInt:3_pInt,j=1_pInt:3_pInt,k=1_pInt:3_pInt,l=1_pInt:3_pInt) & forall (i=1_pInt:3_pInt,j=1_pInt:3_pInt,k=1_pInt:3_pInt,l=1_pInt:3_pInt) &
dLp_dTstar3333(i,j,k,l) = dLp_dTstar3333(i,j,k,l) & dLp_dTstar3333(i,j,k,l) = dLp_dTstar3333(i,j,k,l) &
+ dgdot_dtau(s,1) * lattice_Sslip(i,j,1,sLattice,myStructure) * lattice_Sslip(k,l,1,sLattice,myStructure) & + lattice_Sslip(i,j,1,sLattice,myStructure) &
+ dgdot_dtau(s,2) * lattice_Sslip(i,j,1,sLattice,myStructure) * lattice_Sslip(k,l,1,sLattice,myStructure) & * ( nonSchmidProjection(k,l,2,s,myInstance) * rhoSgl(s,3) * dv_dtauNS(s,3) &
+ dgdot_dtau(s,3) * lattice_Sslip(i,j,1,sLattice,myStructure) * nonSchmidProjection(k,l,2,s,myInstance) & + nonSchmidProjection(k,l,4,s,myInstance) * rhoSgl(s,4) * dv_dtauNS(s,4) ) &
+ dgdot_dtau(s,4) * lattice_Sslip(i,j,1,sLattice,myStructure) * nonSchmidProjection(k,l,4,s,myInstance) * burgers(s,myInstance)
endif endif
enddo enddo
dLp_dTstar99 = math_Plain3333to99(dLp_dTstar3333) dLp_dTstar99 = math_Plain3333to99(dLp_dTstar3333)
@ -2331,11 +2347,11 @@ rhoDotMultiplication = 0.0_pReal
if (myStructure == 2_pInt) then ! BCC if (myStructure == 2_pInt) then ! BCC
forall (s = 1:ns, sum(abs(v(s,1:4))) > 0.0_pReal) forall (s = 1:ns, sum(abs(v(s,1:4))) > 0.0_pReal)
rhoDotMultiplication(s,1:2) = sum(abs(gdot(s,3:4))) / burgers(s,myInstance) & ! assuming double-cross-slip of screws to be decisive for multiplication rhoDotMultiplication(s,1:2) = sum(abs(gdot(s,3:4))) / burgers(s,myInstance) & ! assuming double-cross-slip of screws to be decisive for multiplication
* sqrt(rhoForest(s)) / lambda0(s,myInstance) !& ! mean free path * sqrt(rhoForest(s)) / lambda0(s,myInstance) ! & ! mean free path
!* sum(abs(v(s,3:4))) / sum(abs(v(s,1:4))) ! ratio of screw to overall velocity determines edge generation ! * 2.0_pReal * sum(abs(v(s,3:4))) / sum(abs(v(s,1:4))) ! ratio of screw to overall velocity determines edge generation
rhoDotMultiplication(s,3:4) = sum(abs(gdot(s,3:4))) / burgers(s,myInstance) & ! assuming double-cross-slip of screws to be decisive for multiplication rhoDotMultiplication(s,3:4) = sum(abs(gdot(s,3:4))) / burgers(s,myInstance) & ! assuming double-cross-slip of screws to be decisive for multiplication
* sqrt(rhoForest(s)) / lambda0(s,myInstance) !& ! mean free path * sqrt(rhoForest(s)) / lambda0(s,myInstance) ! & ! mean free path
!* sum(abs(v(s,1:2))) / sum(abs(v(s,1:4))) ! ratio of edge to overall velocity determines screw generation ! * 2.0_pReal * sum(abs(v(s,1:2))) / sum(abs(v(s,1:4))) ! ratio of edge to overall velocity determines screw generation
endforall endforall
else ! ALL OTHER STRUCTURES else ! ALL OTHER STRUCTURES