From 314ca3fe7fcdeffac2e40c8b5b448162e94c79b9 Mon Sep 17 00:00:00 2001 From: Christoph Kords Date: Tue, 29 Mar 2011 07:34:33 +0000 Subject: [PATCH] Internal stress calculation in nonlocal model: instead of integration of excess gradients (->Bayley) we now sum up contributions from adjacent superdislocations within a certain radius R. When periodicity is used, also periodic images are considered in stress evaluation. --- code/constitutive.f90 | 23 +- code/constitutive_nonlocal.f90 | 419 ++++++++++++++++++++------------- code/crystallite.f90 | 25 +- 3 files changed, 269 insertions(+), 198 deletions(-) diff --git a/code/constitutive.f90 b/code/constitutive.f90 index 0d0f866df..bd6141d5d 100644 --- a/code/constitutive.f90 +++ b/code/constitutive.f90 @@ -434,15 +434,14 @@ endfunction !********************************************************************* !* This function calculates from state needed variables * !********************************************************************* -subroutine constitutive_microstructure(Temperature,Tstar_v,Fe,Fp,ipc,ip,el) - -use prec, only: pReal,pInt -use material, only: phase_constitution, & - material_phase, & - homogenization_maxNgrains -use mesh, only: mesh_NcpElems, & - mesh_maxNips, & - mesh_maxNipNeighbors +subroutine constitutive_microstructure(Temperature, Fe, ipc, ip, el) +use prec, only: pReal,pInt +use material, only: phase_constitution, & + material_phase, & + homogenization_maxNgrains +use mesh, only: mesh_NcpElems, & + mesh_maxNips, & + mesh_maxNipNeighbors use constitutive_j2, only: constitutive_j2_label, & constitutive_j2_microstructure use constitutive_phenopowerlaw, only: constitutive_phenopowerlaw_label, & @@ -460,10 +459,8 @@ integer(pInt), intent(in):: ipc, & ! component-ID of curren ip, & ! current integration point el ! current element real(pReal), intent(in) :: Temperature -real(pReal), intent(in), dimension(6) :: Tstar_v ! 2nd Piola-Kirchhoff stress real(pReal), dimension(3,3,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: & - Fe, & ! elastic deformation gradient - Fp ! plastic deformation gradient + Fe ! elastic deformation gradient !*** output variables ***! @@ -485,7 +482,7 @@ select case (phase_constitution(material_phase(ipc,ip,el))) call constitutive_dislotwin_microstructure(Temperature,constitutive_state,ipc,ip,el) case (constitutive_nonlocal_label) - call constitutive_nonlocal_microstructure(constitutive_state, Temperature, Tstar_v, Fe, Fp, ipc, ip, el) + call constitutive_nonlocal_microstructure(constitutive_state, Temperature, Fe, ipc, ip, el) end select diff --git a/code/constitutive_nonlocal.f90 b/code/constitutive_nonlocal.f90 index 75290b359..ce6663e19 100644 --- a/code/constitutive_nonlocal.f90 +++ b/code/constitutive_nonlocal.f90 @@ -800,19 +800,16 @@ endfunction !********************************************************************* !* calculates quantities characterizing the microstructure * !********************************************************************* -subroutine constitutive_nonlocal_microstructure(state, Temperature, Tstar_v, Fe, Fp, g, ip, el) +subroutine constitutive_nonlocal_microstructure(state, Temperature, Fe, g, ip, el) use prec, only: pReal, & pInt, & p_vec -use math, only: math_Plain3333to99, & - math_Mandel33to6, & - math_Mandel6to33, & +use IO, only: IO_error +use math, only: math_Mandel33to6, & math_mul33x33, & - math_mul3x3, & math_mul33x3, & math_inv3x3, & - math_det3x3, & math_transpose3x3, & pi use debug, only: debug_verbosity, & @@ -822,225 +819,311 @@ use debug, only: debug_verbosity, & debug_e use mesh, only: mesh_NcpElems, & mesh_maxNips, & - mesh_maxNipNeighbors, & mesh_element, & - FE_NipNeighbors, & - mesh_ipNeighborhood, & - mesh_ipVolume, & + mesh_node, & + FE_Nips, & mesh_ipCenterOfGravity, & - mesh_ipAreaNormal + mesh_ipVolume, & + mesh_periodicSurface use material, only: homogenization_maxNgrains, & material_phase, & phase_localConstitution, & phase_constitutionInstance -use lattice, only: lattice_Sslip, & - lattice_Sslip_v, & - lattice_maxNslipFamily, & - lattice_NslipSystem, & - lattice_maxNslip, & - lattice_sd, & +use lattice, only: lattice_sd, & lattice_sn, & lattice_st implicit none !*** input variables -integer(pInt), intent(in) :: g, & ! current grain ID - ip, & ! current integration point - el ! current element -real(pReal), intent(in) :: Temperature ! temperature +integer(pInt), intent(in) :: g, & ! current grain ID + ip, & ! current integration point + el ! current element +real(pReal), intent(in) :: Temperature ! temperature real(pReal), dimension(3,3,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: & - Fe, & ! elastic deformation gradient - Fp ! plastic deformation gradient -real(pReal), dimension(6), intent(in) :: & - Tstar_v ! 2nd Piola-Kirchhoff stress in Mandel notation + Fe ! elastic deformation gradient - -!*** input/output variables + !*** input/output variables type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(inout) :: & - state ! microstructural state + state ! microstructural state -!*** output variables + !*** output variables -!*** local variables -integer(pInt) myInstance, & ! current instance of this constitution - myStructure, & ! current lattice structure - myPhase, & - ns, & ! short notation for the total number of active slip systems - neighboring_el, & ! element number of my neighbor - neighboring_ip, & ! integration point of my neighbor - opposite_el, & ! element number of my opposite neighbor - opposite_ip, & ! integration point of my opposite neighbor - c, & ! index of dilsocation character (edge, screw) - n, & ! index of my current neighbor - opposite_n, & ! index of my opposite neighbor - s, & ! index of my current slip system - t, & ! index of dilsocation type (e+, e-, s+, s-, used e+, used e-, used s+, used s-) - sLattice, & ! index of my current slip system according to lattice order - i, & - j -real(pReal) nu ! poisson's ratio -real(pReal), dimension(3) :: deltaCoG ! difference of two centers of gravities (distance vector to my neighbor in reference configuration) -real(pReal), dimension(3,2) :: rhoExcessDifference, & ! finite differences of excess density (in 3 directions for edge and screw) - disloGradients ! spatial gradient in excess dislocation density (in 3 directions for edge and screw) -real(pReal), dimension(3,3) :: sigma, & ! dislocation stress for one slip system in its slip system frame - lattice2slip, & ! orthogonal transformation matrix from lattice coordinate system to slip coordinate system with e1=bxn, e2=b, e3=n (passive rotation!!!) - F, & ! total deformation gradient - neighboring_F, & ! total deformation gradient of neighbor - invFe, & ! inverse elastic deformation gradient - Q ! inverse transpose of 3x3 matrix with finite differences of opposing position vectors -real(pReal), dimension(6) :: Tdislocation_v ! dislocation stress (resulting from the neighboring excess dislocation densities) as 2nd Piola-Kirchhoff stress in Mandel notation -real(pReal), dimension(2,constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))) :: & - rhoExcess ! central excess density -real(pReal), dimension(6,2,constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))) :: & - neighboring_rhoExcess ! excess density for each neighbor, dislo character and slip system -real(pReal), dimension(3,6) :: neighboring_position ! position vector of each neighbor when seen from the centreal material point's lattice frame + !*** local variables +integer(pInt) neighboring_el, & ! element number of neighboring material point + neighboring_ip, & ! integration point of neighboring material point + instance, & ! my instance of this constitution + neighboring_instance, & ! instance of this constitution of neighboring material point + latticeStruct, & ! my lattice structure + neighboring_latticeStruct, & ! lattice structure of neighboring material point + phase, & + neighboring_phase, & + ns, & ! total number of active slip systems at my material point + neighboring_ns, & ! total number of active slip systems at neighboring material point + c, & ! index of dilsocation character (edge, screw) + s, & ! slip system index + s2, & ! slip system index according to ordering in "lattice.f90" + t, & ! index of dilsocation type (e+, e-, s+, s-, used e+, used e-, used s+, used s-) + dir, & + deltaX, deltaY, deltaZ, & + side +integer(pInt), dimension(2,3) :: periodicImages +real(pReal) nu, & ! poisson's ratio + x, y, z, & ! coordinates of connection vector in neighboring lattice frame + xsquare, ysquare, zsquare, & ! squares of respective coordinates + distance, & ! length of connection vector + segmentLength, & ! segment length of dislocations + neighboring_Nexcess, & ! excess number of dislocation segments at neighboring material point for specific slip system and dislocation character + lambda, & + R, Rsquare, Rcube, & + denominator, & + flipSign +real(pReal), dimension(3) :: connection, & ! connection vector between me and my neighbor in the deformed configuration + connection_neighboringLattice, & ! connection vector between me and my neighbor in the lattice configuration of my neighbor + connection_neighboringSlip, & ! connection vector between me and my neighbor in the slip system frame of my neighbor + maxCoord, minCoord, & + meshSize, & + ipCoords, & + neighboring_ipCoords +real(pReal), dimension(3,3) :: sigma, & ! dislocation stress for one slip system in neighboring material point's slip system frame + neighboringLattice2neighboringSlip, & ! orthogonal transformation matrix from lattice coordinate system to slip coordinate system (passive rotation ! ! !) + Tdislo_neighboringLattice, & ! dislocation stress as 2nd Piola-Kirchhoff stress at neighboring material point + Tdislo, & ! dislocation stress as 2nd Piola-Kirchhoff stress at my material point + invFe, & ! inverse of my elastic deformation gradient + neighboringLattice2myLattice ! mapping from neighboring MPs lattice configuration to my lattice configuration +real(pReal), dimension(2,maxval(constitutive_nonlocal_totalNslip)) :: & + neighboring_rhoExcess ! excess density at neighboring material point real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el))),8) :: & - rhoSgl ! single dislocation density (edge+, edge-, screw+, screw-, used edge+, used edge-, used screw+, used screw-) + rhoSgl ! single dislocation density (edge+, edge-, screw+, screw-, used edge+, used edge-, used screw+, used screw-) real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el))),2) :: & - rhoDip ! dipole dislocation density (edge, screw) + rhoDip ! dipole dislocation density (edge, screw) real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))) :: & - transmissivity, & ! transmissivity - rhoForest, & ! forest dislocation density - tauThreshold, & ! threshold shear stress - tau ! resolved shear stress + rhoForest, & ! forest dislocation density + tauThreshold, & ! threshold shear stress + tau ! resolved shear stress + +phase = material_phase(g,ip,el) +instance = phase_constitutionInstance(phase) +latticeStruct = constitutive_nonlocal_structure(instance) +ns = constitutive_nonlocal_totalNslip(instance) -myPhase = material_phase(g,ip,el) -myInstance = phase_constitutionInstance(myPhase) -myStructure = constitutive_nonlocal_structure(myInstance) -ns = constitutive_nonlocal_totalNslip(myInstance) -!********************************************************************** !*** get basic states forall (t = 1:4) rhoSgl(1:ns,t) = max(state(g,ip,el)%p((t-1)*ns+1:t*ns), 0.0_pReal) ! ensure positive single mobile densities forall (t = 5:8) rhoSgl(1:ns,t) = state(g,ip,el)%p((t-1)*ns+1:t*ns) forall (c = 1:2) rhoDip(1:ns,c) = max(state(g,ip,el)%p((c+7)*ns+1:(c+8)*ns), 0.0_pReal) ! ensure positive dipole densities -where(rhoSgl(1:ns,1:4) < min(0.1, 0.01*constitutive_nonlocal_aTolRho(myInstance))) & - rhoSgl(1:ns,1:4) = 0.0_pReal ! delete non-significant single density +where(rhoSgl(1:ns,1:4) < min(0.1, 0.01*constitutive_nonlocal_aTolRho(instance))) & + rhoSgl(1:ns,1:4) = 0.0_pReal ! delete non-significant single density -!********************************************************************** -!*** calculate dependent states !*** calculate the forest dislocation density +!*** (= projection of screw and edge dislocations) forall (s = 1:ns) & - rhoForest(s) = dot_product( ( sum(abs(rhoSgl(1:ns,(/1,2,5,6/))),2) + rhoDip(1:ns,1) ), & - constitutive_nonlocal_forestProjectionEdge(s, 1:ns, myInstance) ) & - + dot_product( ( sum(abs(rhoSgl(1:ns,(/3,4,7,8/))),2) + rhoDip(1:ns,2) ), & - constitutive_nonlocal_forestProjectionScrew(s, 1:ns, myInstance) ) ! calculation of forest dislocation density as projection of screw and edge dislocations + rhoForest(s) = dot_product((sum(abs(rhoSgl(1:ns,(/1,2,5,6/))),2) + rhoDip(1:ns,1)), & + constitutive_nonlocal_forestProjectionEdge(s,1:ns,instance)) & + + dot_product((sum(abs(rhoSgl(1:ns,(/3,4,7,8/))),2) + rhoDip(1:ns,2)), & + constitutive_nonlocal_forestProjectionScrew(s,1:ns,instance)) + !*** calculate the threshold shear stress for dislocation slip forall (s = 1:ns) & - tauThreshold(s) = constitutive_nonlocal_Gmod(myInstance) & - * constitutive_nonlocal_burgersPerSlipSystem(s, myInstance) & - * sqrt( dot_product( ( sum(abs(rhoSgl),2) + sum(abs(rhoDip),2) ), & - constitutive_nonlocal_interactionMatrixSlipSlip(s, 1:ns, myInstance) ) ) + tauThreshold(s) = constitutive_nonlocal_Gmod(instance) & + * constitutive_nonlocal_burgersPerSlipSystem(s,instance) & + * sqrt(dot_product((sum(abs(rhoSgl),2) + sum(abs(rhoDip),2)), & + constitutive_nonlocal_interactionMatrixSlipSlip(s,1:ns,instance))) + !*** calculate the dislocation stress of the neighboring excess dislocation densities +!*** zero for material points of local constitution -Tdislocation_v = 0.0_pReal +Tdislo = 0.0_pReal -if (.not. phase_localConstitution(myPhase)) then ! only calculate dislocation stress for nonlocal material +if (.not. phase_localConstitution(phase)) then + invFe = math_inv3x3(Fe(1:3,1:3,1,ip,el)) - F = math_mul33x33(Fe(1:3,1:3,g,ip,el), Fp(1:3,1:3,g,ip,el)) - invFe = math_inv3x3(Fe(1:3,1:3,g,ip,el)) - nu = constitutive_nonlocal_nu(myInstance) + + !* in case of periodic surfaces we have to find out how many periodic images in each direction we need - 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 - 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 ... - neighboring_el = el ! ... use central values instead of neighboring values - neighboring_ip = ip - neighboring_position(1:3,n) = 0.0_pReal - neighboring_rhoExcess(n,1:2,1:ns) = rhoExcess - elseif (phase_localConstitution(material_phase(1,neighboring_ip,neighboring_el))) then ! for neighbors with local constitution - neighboring_el = el ! ... use central values instead of neighboring values - neighboring_ip = ip - neighboring_position(1:3,n) = 0.0_pReal - neighboring_rhoExcess(n,1:2,1:ns) = rhoExcess - elseif (myPhase /= material_phase(1,neighboring_ip,neighboring_el)) then ! for neighbors with different phase - neighboring_el = el ! ... use central values instead of neighboring values - neighboring_ip = ip - neighboring_position(1:3,n) = 0.0_pReal - neighboring_rhoExcess(n,1:2,1:ns) = rhoExcess - else - transmissivity = sum(constitutive_nonlocal_compatibility(2,1:ns,1:ns,n,ip,el)**2.0_pReal, 1) - if ( any(transmissivity < 0.9_pReal) ) then ! at grain boundary (=significantly decreased transmissivity) ... - neighboring_el = el ! ... use central values instead of neighboring values - neighboring_ip = ip - neighboring_position(1:3,n) = 0.0_pReal - neighboring_rhoExcess(n,1:2,1:ns) = rhoExcess - else - neighboring_F = math_mul33x33(Fe(1:3,1:3,g,neighboring_ip,neighboring_el), Fp(1:3,1:3,g,neighboring_ip,neighboring_el)) - deltaCoG = mesh_ipCenterOfGravity(1:3,neighboring_ip,neighboring_el) - mesh_ipCenterOfGravity(1:3,ip,el) - if (math_mul3x3(deltaCoG, mesh_ipAreaNormal(1:3,n,neighboring_ip,neighboring_el)) < 0.0_pReal) then ! periodic surface, so this is a twin - opposite_n = n + mod(n,2) - mod(n+1,2) - opposite_el = mesh_ipNeighborhood(1,opposite_n,ip,el) - opposite_ip = mesh_ipNeighborhood(2,opposite_n,ip,el) - deltaCoG = mesh_ipCenterOfGravity(1:3,ip,el) - mesh_ipCenterOfGravity(1:3,opposite_ip,opposite_el) ! assume that the twin neighbor has the same size as the opposite neighbor - endif - neighboring_position(1:3,n) = 0.5_pReal * math_mul33x3(math_mul33x33(invFe,neighboring_F) + Fp(1:3,1:3,g,ip,el), deltaCoG) - forall (s = 1:ns, c = 1:2) & - neighboring_rhoExcess(n,c,s) = state(g,neighboring_ip,neighboring_el)%p((2*c-2)*ns+s) & - + abs(state(g,neighboring_ip,neighboring_el)%p((2*c+2)*ns+s)) & - - state(g,neighboring_ip,neighboring_el)%p((2*c-1)*ns+s) & - - abs(state(g,neighboring_ip,neighboring_el)%p((2*c+3)*ns+s)) - endif - endif + do dir = 1,3 + maxCoord(dir) = maxval(mesh_node(dir,:)) + minCoord(dir) = minval(mesh_node(dir,:)) enddo - - Q = math_inv3x3(math_transpose3x3(neighboring_position(1:3,(/1,3,5/)) - neighboring_position(1:3,(/2,4,6/)))) - - do s = 1,ns - - lattice2slip = math_transpose3x3(reshape((/ & - lattice_sd(1:3, constitutive_nonlocal_slipSystemLattice(s,myInstance), myStructure), & - -lattice_st(1:3, constitutive_nonlocal_slipSystemLattice(s,myInstance), myStructure), & - lattice_sn(1:3, constitutive_nonlocal_slipSystemLattice(s,myInstance), myStructure)/), (/3,3/))) - - rhoExcessDifference = neighboring_rhoExcess((/1,3,5/),1:2,s) - neighboring_rhoExcess((/2,4,6/),1:2,s) - forall (c = 1:2) & - disloGradients(1:3,c) = math_mul33x3(lattice2slip, math_mul33x3(Q, rhoExcessDifference(1:3,c))) - - sigma = 0.0_pReal - sigma(1,1) = + 0.375_pReal / (1.0_pReal-nu) * disloGradients(3,1) - sigma(2,2) = + 0.5_pReal * nu / (1.0_pReal-nu) * disloGradients(3,1) - sigma(3,3) = + 0.125_pReal / (1.0_pReal-nu) * disloGradients(3,1) - sigma(1,2) = + 0.25_pReal * disloGradients(3,2) - sigma(1,3) = - 0.125_pReal / (1.0_pReal-nu) * disloGradients(1,1) - 0.25_pReal * disloGradients(2,2) - sigma(2,1) = sigma(1,2) - sigma(3,1) = sigma(1,3) - - forall (i=1:3, j=1:3) & - sigma(i,j) = sigma(i,j) * constitutive_nonlocal_Gmod(myInstance) * constitutive_nonlocal_burgersPerSlipSystem(s,myInstance) & - * constitutive_nonlocal_R(myInstance)**2.0_pReal - - Tdislocation_v = Tdislocation_v + math_Mandel33to6(math_mul33x33(math_transpose3x3(lattice2slip), & - math_mul33x33(sigma, lattice2slip))) + meshSize = maxCoord - minCoord + ipCoords = mesh_ipCenterOfGravity(1:3,ip,el) + periodicImages = 0_pInt + do dir = 1,3 + if (mesh_periodicSurface(dir)) then + periodicImages(1,dir) = floor((ipCoords(dir) - constitutive_nonlocal_R(instance) - minCoord(dir)) / meshSize(dir), pInt) + periodicImages(2,dir) = ceiling((ipCoords(dir) + constitutive_nonlocal_R(instance) - maxCoord(dir)) / meshSize(dir), pInt) + endif + enddo + - enddo + !* loop through all material points (also through their periodic images if present), + !* but only consider nonlocal neighbors within a certain cutoff radius R + do neighboring_el = 1,mesh_NcpElems + do neighboring_ip = 1,FE_Nips(mesh_element(2,neighboring_el)) + neighboring_phase = material_phase(g,neighboring_ip,neighboring_el) + neighboring_instance = phase_constitutionInstance(neighboring_phase) + neighboring_latticeStruct = constitutive_nonlocal_structure(neighboring_instance) + neighboring_ns = constitutive_nonlocal_totalNslip(neighboring_instance) + nu = constitutive_nonlocal_nu(neighboring_instance) + Tdislo_neighboringLattice = 0.0_pReal + do deltaX = periodicImages(1,1),periodicImages(2,1) + do deltaY = periodicImages(1,2),periodicImages(2,2) + do deltaZ = periodicImages(1,3),periodicImages(2,3) + if (neighboring_el == el .and. neighboring_ip == ip & + .and. deltaX == 0 .and. deltaY == 0 .and. deltaZ == 0) then + cycle ! this is myself + endif + neighboring_ipCoords = mesh_ipCenterOfGravity(1:3,neighboring_ip,neighboring_el) + dble(deltaX) * meshSize(1) & + + dble(deltaY) * meshSize(2) & + + dble(deltaZ) * meshSize(3) + connection = neighboring_ipCoords - ipCoords + distance = sqrt(sum(connection ** 2.0_pReal)) + if (.not. phase_localConstitution(neighboring_phase) & + .and. distance <= constitutive_nonlocal_R(instance)) then + + + !* determine the effective number of dislocations + !* the segment length is the minimum of the third root of the control volume and the ip distance + !* this ensures, that the central MP never sits on a neighboring dislocation segment + + connection_neighboringLattice = math_mul33x3(math_inv3x3(Fe(1:3,1:3,1,neighboring_ip,neighboring_el)), connection) + forall (s = 1:neighboring_ns, c = 1:2) & + neighboring_rhoExcess(c,s) = state(g,neighboring_ip,neighboring_el)%p((2*c-2)*neighboring_ns+s) & + + abs(state(g,neighboring_ip,neighboring_el)%p((2*c+2)*neighboring_ns+s)) & + - state(g,neighboring_ip,neighboring_el)%p((2*c-1)*neighboring_ns+s) & + - abs(state(g,neighboring_ip,neighboring_el)%p((2*c+3)*neighboring_ns+s)) + segmentLength = min(mesh_ipVolume(neighboring_ip,neighboring_el)**(1.0_pReal/3.0_pReal), distance) + + + !* loop through all slip systems of the neighboring material point + !* and add up the stress contributions from egde and screw excess on these slip systems + + do s = 1,neighboring_ns + if (all(abs(neighboring_rhoExcess(:,s)) < 1.0_pReal)) then + cycle ! not significant + endif + + + !* map the connection vector from the lattice into the slip system frame + + s2 = constitutive_nonlocal_slipSystemLattice(s,neighboring_instance) + neighboringLattice2neighboringSlip = math_transpose3x3( & + reshape((/ lattice_sd(1:3, s2, neighboring_latticeStruct), & + -lattice_st(1:3, s2, neighboring_latticeStruct), & + lattice_sn(1:3, s2, neighboring_latticeStruct)/), (/3,3/))) + connection_neighboringSlip = math_mul33x3(neighboringLattice2neighboringSlip, connection_neighboringLattice) + x = connection_neighboringSlip(1) + y = connection_neighboringSlip(2) + z = connection_neighboringSlip(3) + xsquare = x ** 2.0_pReal + ysquare = y ** 2.0_pReal + zsquare = z ** 2.0_pReal + + + !* edge contribution to stress + + sigma = 0.0_pReal + neighboring_Nexcess = neighboring_rhoExcess(1,s) * mesh_ipVolume(neighboring_ip,neighboring_el) / segmentLength + flipSign = sign(1.0_pReal, -y) + do side = 1,-1,-2 + lambda = dble(side) * 0.5_pReal * segmentLength - y + R = sqrt(xsquare + zsquare + lambda**2.0_pReal) + Rsquare = R ** 2.0_pReal + Rcube = R**3.0_pReal + denominator = R * (R + flipSign * lambda) + if (denominator == 0.0_pReal) then + call IO_error(237,el,ip,g) + endif + + sigma(1,1) = sigma(1,1) - dble(side) * flipSign * z / denominator & + * (1.0_pReal + xsquare / Rsquare + xsquare / denominator) & + * neighboring_Nexcess + sigma(2,2) = sigma(2,2) - dble(side) * (flipSign * 2.0_pReal * nu * z / denominator + z * lambda / Rcube) & + * neighboring_Nexcess + sigma(3,3) = sigma(3,3) + dble(side) * flipSign * z / denominator & + * (1.0_pReal - zsquare / Rsquare - zsquare / denominator) & + * neighboring_Nexcess + sigma(1,2) = sigma(1,2) + dble(side) * x * z / Rcube * neighboring_Nexcess + sigma(1,3) = sigma(1,3) + dble(side) * flipSign * x / denominator & + * (1.0_pReal - zsquare / Rsquare - zsquare / denominator) & + * neighboring_Nexcess + sigma(2,3) = sigma(2,3) - dble(side) * (nu / R - zsquare / Rcube) * neighboring_Nexcess + enddo + + + !* screw contribution to stress + + neighboring_Nexcess = neighboring_rhoExcess(2,s) * mesh_ipVolume(neighboring_ip,neighboring_el) / segmentLength + flipSign = sign(1.0_pReal, x) + do side = 1,-1,-2 + lambda = x + dble(side) * 0.5_pReal * segmentLength + R = sqrt(ysquare + zsquare + lambda**2.0_pReal) + Rsquare = R ** 2.0_pReal + Rcube = R**3.0_pReal + denominator = R * (R + flipSign * lambda) + if (denominator == 0.0_pReal) then + call IO_error(237,el,ip,g) + endif + + sigma(1,2) = sigma(1,2) - dble(side) * flipSign * z * (1.0_pReal - nu) / denominator * neighboring_Nexcess + sigma(1,3) = sigma(1,3) + dble(side) * flipSign * y * (1.0_pReal - nu) / denominator * neighboring_Nexcess + enddo + + + !* copy symmetric parts + + sigma(2,1) = sigma(1,2) + sigma(3,1) = sigma(1,3) + sigma(3,2) = sigma(2,3) + + + !* scale stresses and map them into the neighboring material point's lattice configuration + + sigma = sigma * constitutive_nonlocal_Gmod(neighboring_instance) & + * constitutive_nonlocal_burgersPerSlipSystem(s,neighboring_instance) & + / (4.0_pReal * pi * (1.0_pReal - nu)) + Tdislo_neighboringLattice = Tdislo_neighboringLattice & + + math_mul33x33(math_transpose3x3(neighboringLattice2neighboringSlip), & + math_mul33x33(sigma, neighboringLattice2neighboringSlip)) + + enddo ! slip system loop + endif + enddo ! deltaZ loop + enddo ! deltaY loop + enddo ! deltaX loop + + + !* map the stress from the neighboring MP's lattice configuration into the deformed configuration + !* and back into my lattice configuration + + neighboringLattice2myLattice = math_mul33x33(invFe, Fe(1:3,1:3,1,neighboring_ip,neighboring_el)) + Tdislo = Tdislo + math_mul33x33(neighboringLattice2myLattice, & + math_mul33x33(Tdislo_neighboringLattice, math_transpose3x3(neighboringLattice2myLattice))) + + enddo ! ip loop + enddo ! element loop + endif -!********************************************************************** !*** set states state(g,ip,el)%p(1:8*ns) = reshape(rhoSgl,(/8*ns/)) ! ensure positive single mobile densities state(g,ip,el)%p(8*ns+1:10*ns) = reshape(rhoDip,(/2*ns/)) ! ensure positive dipole densities state(g,ip,el)%p(10*ns+1:11*ns) = rhoForest state(g,ip,el)%p(11*ns+1:12*ns) = tauThreshold -state(g,ip,el)%p(12*ns+1:12*ns+6) = Tdislocation_v +state(g,ip,el)%p(12*ns+1:12*ns+6) = math_Mandel33to6(Tdislo) #ifndef _OPENMP @@ -1050,7 +1133,7 @@ state(g,ip,el)%p(12*ns+1:12*ns+6) = Tdislocation_v write(6,*) write(6,'(a,/,12(x),12(e10.3,x))') '<< CONST >> rhoForest', rhoForest write(6,'(a,/,12(x),12(f10.5,x))') '<< CONST >> tauThreshold / MPa', tauThreshold/1e6 - write(6,'(a,/,3(12(x),3(f10.5,x),/))') '<< CONST >> Tdislocation / MPa', math_Mandel6to33(Tdislocation_v)/1e6 + write(6,'(a,/,3(12(x),3(f10.5,x),/))') '<< CONST >> Tdislocation / MPa', Tdislo/1e6 endif #endif diff --git a/code/crystallite.f90 b/code/crystallite.f90 index 0447bd529..ec462d7ad 100644 --- a/code/crystallite.f90 +++ b/code/crystallite.f90 @@ -209,7 +209,6 @@ allocate(crystallite_localConstitution(gMax,iMax,eMax)); crystallite_loc allocate(crystallite_requested(gMax,iMax,eMax)); crystallite_requested = .false. allocate(crystallite_todo(gMax,iMax,eMax)); crystallite_todo = .false. allocate(crystallite_converged(gMax,iMax,eMax)); crystallite_converged = .true. - allocate(crystallite_output(maxval(crystallite_Noutput), & material_Ncrystallite)) ; crystallite_output = '' allocate(crystallite_sizePostResults(material_Ncrystallite)) ; crystallite_sizePostResults = 0_pInt @@ -349,8 +348,7 @@ crystallite_orientation0 = crystallite_orientation ! Store initial o myNgrains = homogenization_Ngrains(mesh_element(3,e)) do i = FEsolving_execIP(1,e),FEsolving_execIP(2,e) do g = 1,myNgrains - call constitutive_microstructure(crystallite_Temperature(g,i,e), crystallite_Tstar0_v(1:6,g,i,e), & - crystallite_Fe, crystallite_Fp0, g, i, e) ! update dependent state variables to be consistent with basic states + call constitutive_microstructure(crystallite_Temperature(g,i,e), crystallite_Fe, g, i, e) ! update dependent state variables to be consistent with basic states enddo enddo enddo @@ -986,8 +984,7 @@ do n = 1,4 !$OMP DO do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains if (crystallite_todo(g,i,e)) then - call constitutive_microstructure(crystallite_Temperature(g,i,e), crystallite_Tstar_v(1:6,g,i,e), & - crystallite_Fe, crystallite_Fp, g, i, e) ! update dependent state variables to be consistent with basic states + call constitutive_microstructure(crystallite_Temperature(g,i,e), crystallite_Fe, g, i, e) ! update dependent state variables to be consistent with basic states endif enddo; enddo; enddo !$OMP ENDDO @@ -1339,8 +1336,7 @@ do n = 1,5 !$OMP DO do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains if (crystallite_todo(g,i,e)) then - call constitutive_microstructure(crystallite_Temperature(g,i,e), crystallite_Tstar_v(1:6,g,i,e), & - crystallite_Fe, crystallite_Fp, g, i, e) ! update dependent state variables to be consistent with basic states + call constitutive_microstructure(crystallite_Temperature(g,i,e), crystallite_Fe, g, i, e) ! update dependent state variables to be consistent with basic states endif constitutive_dotState(g,i,e)%p = 0.0_pReal ! reset dotState to zero enddo; enddo; enddo @@ -1518,8 +1514,7 @@ relTemperatureResiduum = 0.0_pReal !$OMP DO do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains if (crystallite_todo(g,i,e)) then - call constitutive_microstructure(crystallite_Temperature(g,i,e), crystallite_Tstar_v(1:6,g,i,e), & - crystallite_Fe, crystallite_Fp, g, i, e) ! update dependent state variables to be consistent with basic states + call constitutive_microstructure(crystallite_Temperature(g,i,e), crystallite_Fe, g, i, e) ! update dependent state variables to be consistent with basic states endif enddo; enddo; enddo !$OMP ENDDO @@ -1717,8 +1712,7 @@ stateResiduum = 0.0_pReal !$OMP DO do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains if (crystallite_todo(g,i,e)) then - call constitutive_microstructure(crystallite_Temperature(g,i,e), crystallite_Tstar_v(1:6,g,i,e), & - crystallite_Fe, crystallite_Fp, g, i, e) ! update dependent state variables to be consistent with basic states + call constitutive_microstructure(crystallite_Temperature(g,i,e), crystallite_Fe, g, i, e) ! update dependent state variables to be consistent with basic states endif constitutive_dotState(g,i,e)%p = 0.0_pReal ! reset dotState to zero enddo; enddo; enddo @@ -1992,8 +1986,7 @@ endif !$OMP DO do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains if (crystallite_todo(g,i,e)) then - call constitutive_microstructure(crystallite_Temperature(g,i,e), crystallite_Tstar_v(1:6,g,i,e), & - crystallite_Fe, crystallite_Fp, g, i, e) ! update dependent state variables to be consistent with basic states + call constitutive_microstructure(crystallite_Temperature(g,i,e), crystallite_Fe, g, i, e) ! update dependent state variables to be consistent with basic states endif enddo; enddo; enddo !$OMP ENDDO @@ -2165,8 +2158,7 @@ endif !$OMP DO do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains if (crystallite_todo(g,i,e)) then - call constitutive_microstructure(crystallite_Temperature(g,i,e), crystallite_Tstar_v(1:6,g,i,e), & - crystallite_Fe, crystallite_Fp, g, i, e) ! update dependent state variables to be consistent with basic states + call constitutive_microstructure(crystallite_Temperature(g,i,e), crystallite_Fe, g, i, e) ! update dependent state variables to be consistent with basic states endif constitutive_previousDotState2(g,i,e)%p = constitutive_previousDotState(g,i,e)%p ! age previous dotState constitutive_previousDotState(g,i,e)%p = constitutive_dotState(g,i,e)%p ! age previous dotState @@ -2273,8 +2265,7 @@ do while (any(crystallite_todo) .and. NiterationState < nState ) !$OMP DO do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains if (crystallite_todo(g,i,e)) then - call constitutive_microstructure(crystallite_Temperature(g,i,e), crystallite_Tstar_v(1:6,g,i,e), & - crystallite_Fe, crystallite_Fp, g, i, e) ! update dependent state variables to be consistent with basic states + call constitutive_microstructure(crystallite_Temperature(g,i,e), crystallite_Fe, g, i, e) ! update dependent state variables to be consistent with basic states endif constitutive_previousDotState2(g,i,e)%p = constitutive_previousDotState(g,i,e)%p ! age previous dotState constitutive_previousDotState(g,i,e)%p = constitutive_dotState(g,i,e)%p ! age previous dotState