* 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)

code/IO.f90

@@ -1227,6 +1227,8 @@ endfunction
    msg = 'Non-positive wall depth'
  case (237)
    msg = 'Non-positive obstacle strength'
+ case (238)
+   msg = 'Negative scatter for dislocation density'
  case (240)
    msg = 'Non-positive Taylor factor'
  case (241)

code/constitutive_nonlocal.f90

@@ -62,7 +62,8 @@ real(pReal), dimension(:), allocatable ::                 constitutive_nonlocal_
                                                           constitutive_nonlocal_d0, &                           ! wall depth as multiple of b
                                                           constitutive_nonlocal_tauObs, &                       ! obstacle strength in Pa
                                                           constitutive_nonlocal_fattack, &                      ! attack frequency in Hz
-                                                          constitutive_nonlocal_vs                              ! maximum dislocation velocity = velocity of sound
+                                                          constitutive_nonlocal_vs, &                           ! maximum dislocation velocity = velocity of sound
+                                                          constitutive_nonlocal_rhoSglScatter                   ! standard deviation of scatter in initial dislocation density
 real(pReal), dimension(:,:,:), allocatable ::             constitutive_nonlocal_Cslip_66                        ! elasticity matrix in Mandel notation for each instance
 real(pReal), dimension(:,:,:,:,:), allocatable ::         constitutive_nonlocal_Cslip_3333                      ! elasticity matrix for each instance
 real(pReal), dimension(:,:), allocatable ::               constitutive_nonlocal_rhoSglEdgePos0, &               ! initial edge_pos dislocation density per slip system for each family and instance
@@ -222,6 +223,7 @@ allocate(constitutive_nonlocal_d0(maxNinstance))
 allocate(constitutive_nonlocal_tauObs(maxNinstance))
 allocate(constitutive_nonlocal_vs(maxNinstance))
 allocate(constitutive_nonlocal_fattack(maxNinstance))
+allocate(constitutive_nonlocal_rhoSglScatter(maxNinstance))
 constitutive_nonlocal_CoverA = 0.0_pReal 
 constitutive_nonlocal_C11 = 0.0_pReal
 constitutive_nonlocal_C12 = 0.0_pReal
@@ -241,6 +243,7 @@ constitutive_nonlocal_d0 = 0.0_pReal
 constitutive_nonlocal_tauObs = 0.0_pReal
 constitutive_nonlocal_vs = 0.0_pReal
 constitutive_nonlocal_fattack = 0.0_pReal
+constitutive_nonlocal_rhoSglScatter = 0.0_pReal
 
 allocate(constitutive_nonlocal_rhoSglEdgePos0(lattice_maxNslipFamily, maxNinstance))
 allocate(constitutive_nonlocal_rhoSglEdgeNeg0(lattice_maxNslipFamily, maxNinstance))
@@ -349,6 +352,8 @@ do
         constitutive_nonlocal_vs(i) = IO_floatValue(line,positions,2)
       case('fattack')
         constitutive_nonlocal_fattack(i) = IO_floatValue(line,positions,2)
+      case('rhosglscatter')
+        constitutive_nonlocal_rhoSglScatter(i) = IO_floatValue(line,positions,2)
     end select
   endif
 enddo
@@ -392,6 +397,7 @@ enddo
   if (constitutive_nonlocal_tauObs(i) <= 0.0_pReal)                                         call IO_error(237)
   if (constitutive_nonlocal_vs(i) <= 0.0_pReal)                                             call IO_error(226)
   if (constitutive_nonlocal_fattack(i) <= 0.0_pReal)                                        call IO_error(235)
+  if (constitutive_nonlocal_rhoSglScatter(i) < 0.0_pReal)                                   call IO_error(238)
   
   
 !*** determine total number of active slip systems
@@ -629,11 +635,13 @@ endsubroutine
 !*********************************************************************
 !* initial microstructural state (just the "basic" states)           *
 !*********************************************************************
-pure function constitutive_nonlocal_stateInit(myInstance)
+function constitutive_nonlocal_stateInit(myInstance)
 
 use prec,     only: pReal, &
                     pInt
 use lattice,  only: lattice_maxNslipFamily
+use math,     only: math_sampleGaussVar
+
 implicit none
 
 !*** input variables
@@ -661,8 +669,9 @@ integer(pInt)                 ns, &                           ! short notation f
                               f, &                            ! index of lattice family
                               from, &
                               upto, &
-                              s                               ! index of slip system
+                              s, &                            ! index of slip system
-
+                              i
+real(pReal), dimension(2) ::  noise
 
 constitutive_nonlocal_stateInit = 0.0_pReal
 ns = constitutive_nonlocal_totalNslip(myInstance)
@@ -670,12 +679,17 @@ ns = constitutive_nonlocal_totalNslip(myInstance)
 !*** set the basic state variables
 
 do f = 1,lattice_maxNslipFamily
-  from = 1+sum(constitutive_nonlocal_Nslip(1:f-1,myInstance))
+  from = 1 + sum(constitutive_nonlocal_Nslip(1:f-1,myInstance))
   upto = sum(constitutive_nonlocal_Nslip(1:f,myInstance))
-  rhoSglEdgePos(from:upto)  = constitutive_nonlocal_rhoSglEdgePos0(f, myInstance)
+  do s = from,upto
-  rhoSglEdgeNeg(from:upto)  = constitutive_nonlocal_rhoSglEdgeNeg0(f, myInstance)
+    do i = 1,2
-  rhoSglScrewPos(from:upto) = constitutive_nonlocal_rhoSglScrewPos0(f, myInstance)
+      noise(i) = math_sampleGaussVar(0.0_pReal, constitutive_nonlocal_rhoSglScatter(myInstance))
-  rhoSglScrewNeg(from:upto) = constitutive_nonlocal_rhoSglScrewNeg0(f, myInstance)
+    enddo
+    rhoSglEdgePos(s) = constitutive_nonlocal_rhoSglEdgePos0(f, myInstance) + noise(1)
+    rhoSglEdgeNeg(s) = constitutive_nonlocal_rhoSglEdgeNeg0(f, myInstance) + noise(1)
+    rhoSglScrewPos(s) = constitutive_nonlocal_rhoSglScrewPos0(f, myInstance) + noise(2)
+    rhoSglScrewNeg(s) = constitutive_nonlocal_rhoSglScrewNeg0(f, myInstance) + noise(2)
+  enddo 
   rhoSglEdgePosUsed(from:upto)  = 0.0_pReal
   rhoSglEdgeNegUsed(from:upto)  = 0.0_pReal
   rhoSglScrewPosUsed(from:upto) = 0.0_pReal
@@ -905,14 +919,17 @@ forall (s = 1:ns) &
 !*** calculate the dislocation stress of the neighboring excess dislocation densities
 
 Tdislocation_v = 0.0_pReal
-F = math_mul33x33(Fe(:,:,g,ip,el), Fp(:,:,g,ip,el))
-invFe = math_inv3x3(Fe(:,:,g,ip,el))
-nu = constitutive_nonlocal_nu(myInstance)
 
-forall (s = 1:ns, c = 1:2) &
+if (.not. phase_localConstitution(material_phase(g,ip,el))) then                                          ! only calculate dislocation stress for nonlocal material
+
+  F = math_mul33x33(Fe(:,:,g,ip,el), Fp(:,:,g,ip,el))
+  invFe = math_inv3x3(Fe(:,:,g,ip,el))
+  nu = constitutive_nonlocal_nu(myInstance)
+  
+  forall (s = 1:ns, c = 1:2) &
     rhoExcess(c,s) =  state(g,ip,el)%p((2*c-2)*ns+s) + abs(state(g,ip,el)%p((2*c+2)*ns+s)) &
                     - state(g,ip,el)%p((2*c-1)*ns+s) - abs(state(g,ip,el)%p((2*c+3)*ns+s))
-do n = 1,6
+  do n = 1,6
     neighboring_el = mesh_ipNeighborhood(1,n,ip,el)
     neighboring_ip = mesh_ipNeighborhood(2,n,ip,el)  
     if ( neighboring_ip == 0 .or. neighboring_el == 0 ) then                                                ! at free surfaces ...
@@ -950,11 +967,11 @@ do n = 1,6
                                         mesh_ipCenterOfGravity(:,neighboring_ip,neighboring_el) - mesh_ipCenterOfGravity(:,ip,el) )
       endif
     endif  
-enddo
+  enddo
   
-invPositionDifference = math_inv3x3(neighboring_position((/1,3,5/),:) - neighboring_position((/2,4,6/),:))
+  invPositionDifference = math_inv3x3(neighboring_position((/1,3,5/),:) - neighboring_position((/2,4,6/),:))
   
-do s = 1,ns
+  do s = 1,ns
   
     lattice2slip = transpose( reshape( (/ lattice_st(:, constitutive_nonlocal_slipSystemLattice(s,myInstance), myStructure), &
                                           lattice_sd(:, constitutive_nonlocal_slipSystemLattice(s,myInstance), myStructure), &
@@ -980,7 +997,9 @@ do s = 1,ns
   
     Tdislocation_v = Tdislocation_v + math_Mandel33to6( math_mul33x33(transpose(lattice2slip), math_mul33x33(sigma, lattice2slip) ) )
       
-enddo
+  enddo
+  
+endif
 
 
 !**********************************************************************

code/material.config

@@ -230,6 +230,7 @@ rhoSglScrewPos0         1e11  0  0  0            # Initial positive screw single
 rhoSglScrewNeg0         1e11  0  0  0            # Initial negative screw single dislocation density in m/m**3
 rhoDipEdge0             1e8  0  0  0             # Initial edge dipole dislocation density in m/m**3
 rhoDipScrew0            1e8  0  0  0             # Initial screw dipole dislocation density in m/m**3
+rhoSglScatter           0                        # standard deviation of scatter in initial single dislocation density
 r                       10e-6                    # cutoff radius for dislocation stress in m
 vs                      3500  0  0  0            # maximum dislocation velocity (velocity of sound) in m/s
 dDipMinEdge             1e-9  0  0  0            # minimum distance for stable edge dipoles in m

code/math.f90

@@ -1957,6 +1957,51 @@ endif
 
 
 
+!********************************************************************
+!   draw a random sample from Gauss variable
+!********************************************************************
+function math_sampleGaussVar(meanvalue, stddev, width)
+
+use prec, only: pReal, pInt
+implicit none
+
+!*** input variables
+real(pReal), intent(in) ::            meanvalue, &      ! meanvalue of gauss distribution
+                                      stddev            ! standard deviation of gauss distribution
+real(pReal), intent(in), optional ::  width             ! width of considered values as multiples of standard deviation
+
+!*** output variables
+real(pReal)                           math_sampleGaussVar
+
+!*** local variables
+real(pReal), dimension(2) ::          rnd               ! random numbers
+real(pReal)                           scatter, &        ! normalized scatter around meanvalue
+                                      myWidth
+
+if (stddev == 0.0) then
+    math_sampleGaussVar = meanvalue
+    return
+endif
+
+if (present(width)) then
+  myWidth = width
+else
+  myWidth = 3.0_pReal                                         ! use +-3*sigma as default value for scatter
+endif
+
+do
+  call halton(2, rnd)
+  scatter = myWidth * (2.0_pReal * rnd(1) - 1.0_pReal)
+  if (rnd(2) <= exp(-0.5_pReal * scatter ** 2.0_pReal)) &     ! test if scattered value is drawn
+    exit
+enddo
+
+math_sampleGaussVar = scatter * stddev
+
+endfunction
+ 
+
+
 !****************************************************************
  pure subroutine math_pDecomposition(FE,U,R,error)
 !-----FE = R.U