* now able to introduce some scatter in the initial single dislocation density (only for nonlocal model!) ; setting the parameter "rhoSglScatter" to a positive value generates a gauss distribution for the dislocation density with standard deviation equal to "rhoSglScatter"
* dislocation stress calculation is only done for nonlocal constitution ("/nonlocal/" keyword is present in material.config)
This commit is contained in:
Christoph Kords
parent
6511b4b5a2
commit
faba13f7fd
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@ -1227,6 +1227,8 @@ endfunction
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msg = 'Non-positive wall depth'
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case (237)
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msg = 'Non-positive obstacle strength'
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case (238)
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msg = 'Negative scatter for dislocation density'
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case (240)
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msg = 'Non-positive Taylor factor'
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case (241)
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@ -62,7 +62,8 @@ real(pReal), dimension(:), allocatable :: constitutive_nonlocal_
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constitutive_nonlocal_d0, & ! wall depth as multiple of b
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constitutive_nonlocal_tauObs, & ! obstacle strength in Pa
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constitutive_nonlocal_fattack, & ! attack frequency in Hz
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constitutive_nonlocal_vs ! maximum dislocation velocity = velocity of sound
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constitutive_nonlocal_vs, & ! maximum dislocation velocity = velocity of sound
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constitutive_nonlocal_rhoSglScatter ! standard deviation of scatter in initial dislocation density
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real(pReal), dimension(:,:,:), allocatable :: constitutive_nonlocal_Cslip_66 ! elasticity matrix in Mandel notation for each instance
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real(pReal), dimension(:,:,:,:,:), allocatable :: constitutive_nonlocal_Cslip_3333 ! elasticity matrix for each instance
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real(pReal), dimension(:,:), allocatable :: constitutive_nonlocal_rhoSglEdgePos0, & ! initial edge_pos dislocation density per slip system for each family and instance
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@ -222,6 +223,7 @@ allocate(constitutive_nonlocal_d0(maxNinstance))
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allocate(constitutive_nonlocal_tauObs(maxNinstance))
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allocate(constitutive_nonlocal_vs(maxNinstance))
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allocate(constitutive_nonlocal_fattack(maxNinstance))
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allocate(constitutive_nonlocal_rhoSglScatter(maxNinstance))
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constitutive_nonlocal_CoverA = 0.0_pReal
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constitutive_nonlocal_C11 = 0.0_pReal
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constitutive_nonlocal_C12 = 0.0_pReal
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@ -241,6 +243,7 @@ constitutive_nonlocal_d0 = 0.0_pReal
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constitutive_nonlocal_tauObs = 0.0_pReal
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constitutive_nonlocal_vs = 0.0_pReal
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constitutive_nonlocal_fattack = 0.0_pReal
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constitutive_nonlocal_rhoSglScatter = 0.0_pReal
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allocate(constitutive_nonlocal_rhoSglEdgePos0(lattice_maxNslipFamily, maxNinstance))
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allocate(constitutive_nonlocal_rhoSglEdgeNeg0(lattice_maxNslipFamily, maxNinstance))
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@ -349,6 +352,8 @@ do
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constitutive_nonlocal_vs(i) = IO_floatValue(line,positions,2)
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case('fattack')
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constitutive_nonlocal_fattack(i) = IO_floatValue(line,positions,2)
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case('rhosglscatter')
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constitutive_nonlocal_rhoSglScatter(i) = IO_floatValue(line,positions,2)
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end select
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endif
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enddo
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@ -392,6 +397,7 @@ enddo
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if (constitutive_nonlocal_tauObs(i) <= 0.0_pReal) call IO_error(237)
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if (constitutive_nonlocal_vs(i) <= 0.0_pReal) call IO_error(226)
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if (constitutive_nonlocal_fattack(i) <= 0.0_pReal) call IO_error(235)
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if (constitutive_nonlocal_rhoSglScatter(i) < 0.0_pReal) call IO_error(238)
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!*** determine total number of active slip systems
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@ -629,11 +635,13 @@ endsubroutine
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!*********************************************************************
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!* initial microstructural state (just the "basic" states) *
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!*********************************************************************
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pure function constitutive_nonlocal_stateInit(myInstance)
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function constitutive_nonlocal_stateInit(myInstance)
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use prec, only: pReal, &
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pInt
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use lattice, only: lattice_maxNslipFamily
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use math, only: math_sampleGaussVar
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implicit none
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!*** input variables
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@ -661,8 +669,9 @@ integer(pInt) ns, & ! short notation f
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f, & ! index of lattice family
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from, &
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upto, &
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s ! index of slip system
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s, & ! index of slip system
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i
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real(pReal), dimension(2) :: noise
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constitutive_nonlocal_stateInit = 0.0_pReal
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ns = constitutive_nonlocal_totalNslip(myInstance)
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@ -670,12 +679,17 @@ ns = constitutive_nonlocal_totalNslip(myInstance)
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!*** set the basic state variables
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do f = 1,lattice_maxNslipFamily
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from = 1+sum(constitutive_nonlocal_Nslip(1:f-1,myInstance))
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from = 1 + sum(constitutive_nonlocal_Nslip(1:f-1,myInstance))
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upto = sum(constitutive_nonlocal_Nslip(1:f,myInstance))
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rhoSglEdgePos(from:upto) = constitutive_nonlocal_rhoSglEdgePos0(f, myInstance)
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rhoSglEdgeNeg(from:upto) = constitutive_nonlocal_rhoSglEdgeNeg0(f, myInstance)
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rhoSglScrewPos(from:upto) = constitutive_nonlocal_rhoSglScrewPos0(f, myInstance)
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rhoSglScrewNeg(from:upto) = constitutive_nonlocal_rhoSglScrewNeg0(f, myInstance)
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do s = from,upto
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do i = 1,2
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noise(i) = math_sampleGaussVar(0.0_pReal, constitutive_nonlocal_rhoSglScatter(myInstance))
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enddo
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rhoSglEdgePos(s) = constitutive_nonlocal_rhoSglEdgePos0(f, myInstance) + noise(1)
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rhoSglEdgeNeg(s) = constitutive_nonlocal_rhoSglEdgeNeg0(f, myInstance) + noise(1)
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rhoSglScrewPos(s) = constitutive_nonlocal_rhoSglScrewPos0(f, myInstance) + noise(2)
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rhoSglScrewNeg(s) = constitutive_nonlocal_rhoSglScrewNeg0(f, myInstance) + noise(2)
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enddo
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rhoSglEdgePosUsed(from:upto) = 0.0_pReal
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rhoSglEdgeNegUsed(from:upto) = 0.0_pReal
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rhoSglScrewPosUsed(from:upto) = 0.0_pReal
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@ -905,82 +919,87 @@ forall (s = 1:ns) &
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!*** calculate the dislocation stress of the neighboring excess dislocation densities
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Tdislocation_v = 0.0_pReal
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F = math_mul33x33(Fe(:,:,g,ip,el), Fp(:,:,g,ip,el))
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invFe = math_inv3x3(Fe(:,:,g,ip,el))
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nu = constitutive_nonlocal_nu(myInstance)
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forall (s = 1:ns, c = 1:2) &
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rhoExcess(c,s) = state(g,ip,el)%p((2*c-2)*ns+s) + abs(state(g,ip,el)%p((2*c+2)*ns+s)) &
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- state(g,ip,el)%p((2*c-1)*ns+s) - abs(state(g,ip,el)%p((2*c+3)*ns+s))
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do n = 1,6
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neighboring_el = mesh_ipNeighborhood(1,n,ip,el)
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neighboring_ip = mesh_ipNeighborhood(2,n,ip,el)
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if ( neighboring_ip == 0 .or. neighboring_el == 0 ) then ! at free surfaces ...
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neighboring_el = el ! ... use central values instead of neighboring values
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neighboring_ip = ip
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neighboring_position(n,:) = 0.0_pReal
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neighboring_rhoExcess(n,:,:) = rhoExcess
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elseif (phase_localConstitution(material_phase(1,neighboring_ip,neighboring_el))) then ! for neighbors with local constitution
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neighboring_el = el ! ... use central values instead of neighboring values
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neighboring_ip = ip
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neighboring_position(n,:) = 0.0_pReal
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neighboring_rhoExcess(n,:,:) = rhoExcess
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elseif (myStructure /= &
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constitutive_nonlocal_structure(phase_constitutionInstance(material_phase(1,neighboring_ip,neighboring_el)))) then ! for neighbors with different crystal structure
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neighboring_el = el ! ... use central values instead of neighboring values
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neighboring_ip = ip
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neighboring_position(n,:) = 0.0_pReal
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neighboring_rhoExcess(n,:,:) = rhoExcess
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else
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forall (s = 1:ns, c = 1:2) &
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neighboring_rhoExcess(n,c,s) = state(g,neighboring_ip,neighboring_el)%p((2*c-2)*ns+s) &
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+ abs(state(g,neighboring_ip,neighboring_el)%p((2*c+2)*ns+s)) &
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- state(g,neighboring_ip,neighboring_el)%p((2*c-1)*ns+s) &
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- abs(state(g,neighboring_ip,neighboring_el)%p((2*c+3)*ns+s))
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transmissivity = sum(constitutive_nonlocal_compatibility(2,:,:,n,ip,el)**2.0_pReal, 1)
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if ( any(transmissivity < 0.99_pReal) ) then ! at grain boundary (=significantly decreased transmissivity) ...
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neighboring_el = el ! ... use central values instead of neighboring values
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if (.not. phase_localConstitution(material_phase(g,ip,el))) then ! only calculate dislocation stress for nonlocal material
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F = math_mul33x33(Fe(:,:,g,ip,el), Fp(:,:,g,ip,el))
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invFe = math_inv3x3(Fe(:,:,g,ip,el))
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nu = constitutive_nonlocal_nu(myInstance)
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forall (s = 1:ns, c = 1:2) &
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rhoExcess(c,s) = state(g,ip,el)%p((2*c-2)*ns+s) + abs(state(g,ip,el)%p((2*c+2)*ns+s)) &
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- state(g,ip,el)%p((2*c-1)*ns+s) - abs(state(g,ip,el)%p((2*c+3)*ns+s))
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do n = 1,6
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neighboring_el = mesh_ipNeighborhood(1,n,ip,el)
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neighboring_ip = mesh_ipNeighborhood(2,n,ip,el)
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if ( neighboring_ip == 0 .or. neighboring_el == 0 ) then ! at free surfaces ...
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neighboring_el = el ! ... use central values instead of neighboring values
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neighboring_ip = ip
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neighboring_position(n,:) = 0.0_pReal
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neighboring_rhoExcess(n,:,:) = rhoExcess
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else
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neighboring_F = math_mul33x33(Fe(:,:,g,neighboring_ip,neighboring_el), Fp(:,:,g,neighboring_ip,neighboring_el))
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neighboring_position(n,:) = &
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0.5_pReal * math_mul33x3( math_mul33x33(invFe,neighboring_F) + Fp(:,:,g,ip,el), &
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mesh_ipCenterOfGravity(:,neighboring_ip,neighboring_el) - mesh_ipCenterOfGravity(:,ip,el) )
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endif
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endif
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enddo
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invPositionDifference = math_inv3x3(neighboring_position((/1,3,5/),:) - neighboring_position((/2,4,6/),:))
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do s = 1,ns
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lattice2slip = transpose( reshape( (/ lattice_st(:, constitutive_nonlocal_slipSystemLattice(s,myInstance), myStructure), &
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lattice_sd(:, constitutive_nonlocal_slipSystemLattice(s,myInstance), myStructure), &
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lattice_sn(:, constitutive_nonlocal_slipSystemLattice(s,myInstance), myStructure) /), &
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(/ 3,3 /) ) )
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rhoExcessDifference = neighboring_rhoExcess((/1,3,5/),:,s) - neighboring_rhoExcess((/2,4,6/),:,s)
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forall (c = 1:2) &
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disloGradients(:,c) = math_mul33x3( lattice2slip, math_mul33x3(invPositionDifference, rhoExcessDifference(:,c)) )
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elseif (phase_localConstitution(material_phase(1,neighboring_ip,neighboring_el))) then ! for neighbors with local constitution
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neighboring_el = el ! ... use central values instead of neighboring values
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neighboring_ip = ip
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neighboring_position(n,:) = 0.0_pReal
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neighboring_rhoExcess(n,:,:) = rhoExcess
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elseif (myStructure /= &
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constitutive_nonlocal_structure(phase_constitutionInstance(material_phase(1,neighboring_ip,neighboring_el)))) then ! for neighbors with different crystal structure
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neighboring_el = el ! ... use central values instead of neighboring values
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neighboring_ip = ip
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neighboring_position(n,:) = 0.0_pReal
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neighboring_rhoExcess(n,:,:) = rhoExcess
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else
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forall (s = 1:ns, c = 1:2) &
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neighboring_rhoExcess(n,c,s) = state(g,neighboring_ip,neighboring_el)%p((2*c-2)*ns+s) &
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+ abs(state(g,neighboring_ip,neighboring_el)%p((2*c+2)*ns+s)) &
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- state(g,neighboring_ip,neighboring_el)%p((2*c-1)*ns+s) &
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- abs(state(g,neighboring_ip,neighboring_el)%p((2*c+3)*ns+s))
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transmissivity = sum(constitutive_nonlocal_compatibility(2,:,:,n,ip,el)**2.0_pReal, 1)
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if ( any(transmissivity < 0.99_pReal) ) then ! at grain boundary (=significantly decreased transmissivity) ...
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neighboring_el = el ! ... use central values instead of neighboring values
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neighboring_ip = ip
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neighboring_position(n,:) = 0.0_pReal
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neighboring_rhoExcess(n,:,:) = rhoExcess
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else
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neighboring_F = math_mul33x33(Fe(:,:,g,neighboring_ip,neighboring_el), Fp(:,:,g,neighboring_ip,neighboring_el))
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neighboring_position(n,:) = &
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0.5_pReal * math_mul33x3( math_mul33x33(invFe,neighboring_F) + Fp(:,:,g,ip,el), &
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mesh_ipCenterOfGravity(:,neighboring_ip,neighboring_el) - mesh_ipCenterOfGravity(:,ip,el) )
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endif
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endif
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enddo
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sigma = 0.0_pReal
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sigma(1,1) = + (-0.06066_pReal + nu*0.41421_pReal) / (1.0_pReal-nu) * disloGradients(3,1)
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sigma(2,2) = + 0.32583_pReal / (1.0_pReal-nu) * disloGradients(3,1)
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sigma(3,3) = + 0.14905_pReal / (1.0_pReal-nu) * disloGradients(3,1)
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sigma(1,2) = + 0.20711_pReal * disloGradients(3,2)
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sigma(2,3) = - 0.08839_pReal / (1.0_pReal-nu) * disloGradients(2,1) - 0.20711_pReal * disloGradients(1,2)
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sigma(2,1) = sigma(1,2)
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sigma(3,2) = sigma(2,3)
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invPositionDifference = math_inv3x3(neighboring_position((/1,3,5/),:) - neighboring_position((/2,4,6/),:))
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forall (i=1:3, j=1:3) &
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sigma(i,j) = sigma(i,j) * constitutive_nonlocal_Gmod(myInstance) * constitutive_nonlocal_burgersPerSlipSystem(s,myInstance) &
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* constitutive_nonlocal_R(myInstance)**2.0_pReal
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Tdislocation_v = Tdislocation_v + math_Mandel33to6( math_mul33x33(transpose(lattice2slip), math_mul33x33(sigma, lattice2slip) ) )
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do s = 1,ns
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lattice2slip = transpose( reshape( (/ lattice_st(:, constitutive_nonlocal_slipSystemLattice(s,myInstance), myStructure), &
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lattice_sd(:, constitutive_nonlocal_slipSystemLattice(s,myInstance), myStructure), &
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lattice_sn(:, constitutive_nonlocal_slipSystemLattice(s,myInstance), myStructure) /), &
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(/ 3,3 /) ) )
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rhoExcessDifference = neighboring_rhoExcess((/1,3,5/),:,s) - neighboring_rhoExcess((/2,4,6/),:,s)
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forall (c = 1:2) &
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disloGradients(:,c) = math_mul33x3( lattice2slip, math_mul33x3(invPositionDifference, rhoExcessDifference(:,c)) )
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enddo
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sigma = 0.0_pReal
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sigma(1,1) = + (-0.06066_pReal + nu*0.41421_pReal) / (1.0_pReal-nu) * disloGradients(3,1)
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sigma(2,2) = + 0.32583_pReal / (1.0_pReal-nu) * disloGradients(3,1)
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sigma(3,3) = + 0.14905_pReal / (1.0_pReal-nu) * disloGradients(3,1)
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sigma(1,2) = + 0.20711_pReal * disloGradients(3,2)
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sigma(2,3) = - 0.08839_pReal / (1.0_pReal-nu) * disloGradients(2,1) - 0.20711_pReal * disloGradients(1,2)
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sigma(2,1) = sigma(1,2)
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sigma(3,2) = sigma(2,3)
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forall (i=1:3, j=1:3) &
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sigma(i,j) = sigma(i,j) * constitutive_nonlocal_Gmod(myInstance) * constitutive_nonlocal_burgersPerSlipSystem(s,myInstance) &
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* constitutive_nonlocal_R(myInstance)**2.0_pReal
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Tdislocation_v = Tdislocation_v + math_Mandel33to6( math_mul33x33(transpose(lattice2slip), math_mul33x33(sigma, lattice2slip) ) )
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enddo
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endif
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!**********************************************************************
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@ -230,6 +230,7 @@ rhoSglScrewPos0 1e11 0 0 0 # Initial positive screw single
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rhoSglScrewNeg0 1e11 0 0 0 # Initial negative screw single dislocation density in m/m**3
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rhoDipEdge0 1e8 0 0 0 # Initial edge dipole dislocation density in m/m**3
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rhoDipScrew0 1e8 0 0 0 # Initial screw dipole dislocation density in m/m**3
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rhoSglScatter 0 # standard deviation of scatter in initial single dislocation density
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r 10e-6 # cutoff radius for dislocation stress in m
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vs 3500 0 0 0 # maximum dislocation velocity (velocity of sound) in m/s
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dDipMinEdge 1e-9 0 0 0 # minimum distance for stable edge dipoles in m
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@ -1957,6 +1957,51 @@ endif
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!********************************************************************
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! draw a random sample from Gauss variable
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!********************************************************************
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function math_sampleGaussVar(meanvalue, stddev, width)
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use prec, only: pReal, pInt
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implicit none
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!*** input variables
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real(pReal), intent(in) :: meanvalue, & ! meanvalue of gauss distribution
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stddev ! standard deviation of gauss distribution
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real(pReal), intent(in), optional :: width ! width of considered values as multiples of standard deviation
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!*** output variables
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real(pReal) math_sampleGaussVar
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!*** local variables
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real(pReal), dimension(2) :: rnd ! random numbers
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real(pReal) scatter, & ! normalized scatter around meanvalue
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myWidth
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if (stddev == 0.0) then
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math_sampleGaussVar = meanvalue
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return
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endif
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if (present(width)) then
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myWidth = width
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else
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myWidth = 3.0_pReal ! use +-3*sigma as default value for scatter
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endif
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do
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call halton(2, rnd)
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scatter = myWidth * (2.0_pReal * rnd(1) - 1.0_pReal)
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if (rnd(2) <= exp(-0.5_pReal * scatter ** 2.0_pReal)) & ! test if scattered value is drawn
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exit
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enddo
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math_sampleGaussVar = scatter * stddev
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endfunction
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!****************************************************************
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pure subroutine math_pDecomposition(FE,U,R,error)
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!-----FE = R.U
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