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.
This commit is contained in:
Christoph Kords
parent
3d51dd36fa
commit
314ca3fe7f
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@ -434,8 +434,7 @@ endfunction
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!*********************************************************************
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!* This function calculates from state needed variables *
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!*********************************************************************
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subroutine constitutive_microstructure(Temperature,Tstar_v,Fe,Fp,ipc,ip,el)
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subroutine constitutive_microstructure(Temperature, Fe, ipc, ip, el)
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use prec, only: pReal,pInt
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use material, only: phase_constitution, &
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material_phase, &
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@ -460,10 +459,8 @@ integer(pInt), intent(in):: ipc, & ! component-ID of curren
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ip, & ! current integration point
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el ! current element
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real(pReal), intent(in) :: Temperature
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real(pReal), intent(in), dimension(6) :: Tstar_v ! 2nd Piola-Kirchhoff stress
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real(pReal), dimension(3,3,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
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Fe, & ! elastic deformation gradient
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Fp ! plastic deformation gradient
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Fe ! elastic deformation gradient
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!*** output variables ***!
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@ -485,7 +482,7 @@ select case (phase_constitution(material_phase(ipc,ip,el)))
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call constitutive_dislotwin_microstructure(Temperature,constitutive_state,ipc,ip,el)
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case (constitutive_nonlocal_label)
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call constitutive_nonlocal_microstructure(constitutive_state, Temperature, Tstar_v, Fe, Fp, ipc, ip, el)
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call constitutive_nonlocal_microstructure(constitutive_state, Temperature, Fe, ipc, ip, el)
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end select
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@ -800,19 +800,16 @@ endfunction
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!*********************************************************************
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!* calculates quantities characterizing the microstructure *
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!*********************************************************************
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subroutine constitutive_nonlocal_microstructure(state, Temperature, Tstar_v, Fe, Fp, g, ip, el)
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subroutine constitutive_nonlocal_microstructure(state, Temperature, Fe, g, ip, el)
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use prec, only: pReal, &
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pInt, &
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p_vec
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use math, only: math_Plain3333to99, &
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math_Mandel33to6, &
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math_Mandel6to33, &
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use IO, only: IO_error
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use math, only: math_Mandel33to6, &
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math_mul33x33, &
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math_mul3x3, &
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math_mul33x3, &
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math_inv3x3, &
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math_det3x3, &
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math_transpose3x3, &
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pi
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use debug, only: debug_verbosity, &
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@ -822,23 +819,17 @@ use debug, only: debug_verbosity, &
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debug_e
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use mesh, only: mesh_NcpElems, &
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mesh_maxNips, &
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mesh_maxNipNeighbors, &
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mesh_element, &
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FE_NipNeighbors, &
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mesh_ipNeighborhood, &
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mesh_ipVolume, &
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mesh_node, &
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FE_Nips, &
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mesh_ipCenterOfGravity, &
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mesh_ipAreaNormal
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mesh_ipVolume, &
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mesh_periodicSurface
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use material, only: homogenization_maxNgrains, &
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material_phase, &
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phase_localConstitution, &
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phase_constitutionInstance
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use lattice, only: lattice_Sslip, &
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lattice_Sslip_v, &
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lattice_maxNslipFamily, &
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lattice_NslipSystem, &
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lattice_maxNslip, &
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lattice_sd, &
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use lattice, only: lattice_sd, &
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lattice_sn, &
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lattice_st
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@ -850,11 +841,7 @@ integer(pInt), intent(in) :: g, & ! current grain ID
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el ! current element
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real(pReal), intent(in) :: Temperature ! temperature
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real(pReal), dimension(3,3,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
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Fe, & ! elastic deformation gradient
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Fp ! plastic deformation gradient
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real(pReal), dimension(6), intent(in) :: &
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Tstar_v ! 2nd Piola-Kirchhoff stress in Mandel notation
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Fe ! elastic deformation gradient
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!*** input/output variables
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type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(inout) :: &
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@ -863,184 +850,280 @@ type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), in
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!*** output variables
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!*** local variables
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integer(pInt) myInstance, & ! current instance of this constitution
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myStructure, & ! current lattice structure
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myPhase, &
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ns, & ! short notation for the total number of active slip systems
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neighboring_el, & ! element number of my neighbor
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neighboring_ip, & ! integration point of my neighbor
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opposite_el, & ! element number of my opposite neighbor
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opposite_ip, & ! integration point of my opposite neighbor
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integer(pInt) neighboring_el, & ! element number of neighboring material point
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neighboring_ip, & ! integration point of neighboring material point
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instance, & ! my instance of this constitution
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neighboring_instance, & ! instance of this constitution of neighboring material point
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latticeStruct, & ! my lattice structure
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neighboring_latticeStruct, & ! lattice structure of neighboring material point
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phase, &
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neighboring_phase, &
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ns, & ! total number of active slip systems at my material point
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neighboring_ns, & ! total number of active slip systems at neighboring material point
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c, & ! index of dilsocation character (edge, screw)
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n, & ! index of my current neighbor
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opposite_n, & ! index of my opposite neighbor
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s, & ! index of my current slip system
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s, & ! slip system index
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s2, & ! slip system index according to ordering in "lattice.f90"
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t, & ! index of dilsocation type (e+, e-, s+, s-, used e+, used e-, used s+, used s-)
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sLattice, & ! index of my current slip system according to lattice order
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i, &
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j
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real(pReal) nu ! poisson's ratio
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real(pReal), dimension(3) :: deltaCoG ! difference of two centers of gravities (distance vector to my neighbor in reference configuration)
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real(pReal), dimension(3,2) :: rhoExcessDifference, & ! finite differences of excess density (in 3 directions for edge and screw)
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disloGradients ! spatial gradient in excess dislocation density (in 3 directions for edge and screw)
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real(pReal), dimension(3,3) :: sigma, & ! dislocation stress for one slip system in its slip system frame
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lattice2slip, & ! orthogonal transformation matrix from lattice coordinate system to slip coordinate system with e1=bxn, e2=b, e3=n (passive rotation!!!)
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F, & ! total deformation gradient
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neighboring_F, & ! total deformation gradient of neighbor
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invFe, & ! inverse elastic deformation gradient
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Q ! inverse transpose of 3x3 matrix with finite differences of opposing position vectors
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real(pReal), dimension(6) :: Tdislocation_v ! dislocation stress (resulting from the neighboring excess dislocation densities) as 2nd Piola-Kirchhoff stress in Mandel notation
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real(pReal), dimension(2,constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))) :: &
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rhoExcess ! central excess density
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real(pReal), dimension(6,2,constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))) :: &
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neighboring_rhoExcess ! excess density for each neighbor, dislo character and slip system
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real(pReal), dimension(3,6) :: neighboring_position ! position vector of each neighbor when seen from the centreal material point's lattice frame
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dir, &
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deltaX, deltaY, deltaZ, &
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side
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integer(pInt), dimension(2,3) :: periodicImages
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real(pReal) nu, & ! poisson's ratio
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x, y, z, & ! coordinates of connection vector in neighboring lattice frame
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xsquare, ysquare, zsquare, & ! squares of respective coordinates
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distance, & ! length of connection vector
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segmentLength, & ! segment length of dislocations
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neighboring_Nexcess, & ! excess number of dislocation segments at neighboring material point for specific slip system and dislocation character
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lambda, &
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R, Rsquare, Rcube, &
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denominator, &
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flipSign
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real(pReal), dimension(3) :: connection, & ! connection vector between me and my neighbor in the deformed configuration
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connection_neighboringLattice, & ! connection vector between me and my neighbor in the lattice configuration of my neighbor
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connection_neighboringSlip, & ! connection vector between me and my neighbor in the slip system frame of my neighbor
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maxCoord, minCoord, &
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meshSize, &
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ipCoords, &
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neighboring_ipCoords
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real(pReal), dimension(3,3) :: sigma, & ! dislocation stress for one slip system in neighboring material point's slip system frame
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neighboringLattice2neighboringSlip, & ! orthogonal transformation matrix from lattice coordinate system to slip coordinate system (passive rotation ! ! !)
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Tdislo_neighboringLattice, & ! dislocation stress as 2nd Piola-Kirchhoff stress at neighboring material point
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Tdislo, & ! dislocation stress as 2nd Piola-Kirchhoff stress at my material point
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invFe, & ! inverse of my elastic deformation gradient
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neighboringLattice2myLattice ! mapping from neighboring MPs lattice configuration to my lattice configuration
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real(pReal), dimension(2,maxval(constitutive_nonlocal_totalNslip)) :: &
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neighboring_rhoExcess ! excess density at neighboring material point
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real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el))),8) :: &
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rhoSgl ! single dislocation density (edge+, edge-, screw+, screw-, used edge+, used edge-, used screw+, used screw-)
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real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el))),2) :: &
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rhoDip ! dipole dislocation density (edge, screw)
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real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))) :: &
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transmissivity, & ! transmissivity
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rhoForest, & ! forest dislocation density
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tauThreshold, & ! threshold shear stress
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tau ! resolved shear stress
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myPhase = material_phase(g,ip,el)
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myInstance = phase_constitutionInstance(myPhase)
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myStructure = constitutive_nonlocal_structure(myInstance)
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ns = constitutive_nonlocal_totalNslip(myInstance)
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phase = material_phase(g,ip,el)
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instance = phase_constitutionInstance(phase)
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latticeStruct = constitutive_nonlocal_structure(instance)
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ns = constitutive_nonlocal_totalNslip(instance)
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!**********************************************************************
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!*** get basic states
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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
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forall (t = 5:8) rhoSgl(1:ns,t) = state(g,ip,el)%p((t-1)*ns+1:t*ns)
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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
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where(rhoSgl(1:ns,1:4) < min(0.1, 0.01*constitutive_nonlocal_aTolRho(myInstance))) &
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where(rhoSgl(1:ns,1:4) < min(0.1, 0.01*constitutive_nonlocal_aTolRho(instance))) &
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rhoSgl(1:ns,1:4) = 0.0_pReal ! delete non-significant single density
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!**********************************************************************
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!*** calculate dependent states
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!*** calculate the forest dislocation density
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!*** (= projection of screw and edge dislocations)
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forall (s = 1:ns) &
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rhoForest(s) = dot_product((sum(abs(rhoSgl(1:ns,(/1,2,5,6/))),2) + rhoDip(1:ns,1)), &
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constitutive_nonlocal_forestProjectionEdge(s, 1:ns, myInstance) ) &
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constitutive_nonlocal_forestProjectionEdge(s,1:ns,instance)) &
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+ dot_product((sum(abs(rhoSgl(1:ns,(/3,4,7,8/))),2) + rhoDip(1:ns,2)), &
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constitutive_nonlocal_forestProjectionScrew(s, 1:ns, myInstance) ) ! calculation of forest dislocation density as projection of screw and edge dislocations
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constitutive_nonlocal_forestProjectionScrew(s,1:ns,instance))
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!*** calculate the threshold shear stress for dislocation slip
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forall (s = 1:ns) &
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tauThreshold(s) = constitutive_nonlocal_Gmod(myInstance) &
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* constitutive_nonlocal_burgersPerSlipSystem(s, myInstance) &
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tauThreshold(s) = constitutive_nonlocal_Gmod(instance) &
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* constitutive_nonlocal_burgersPerSlipSystem(s,instance) &
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* sqrt(dot_product((sum(abs(rhoSgl),2) + sum(abs(rhoDip),2)), &
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constitutive_nonlocal_interactionMatrixSlipSlip(s, 1:ns, myInstance) ) )
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constitutive_nonlocal_interactionMatrixSlipSlip(s,1:ns,instance)))
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!*** calculate the dislocation stress of the neighboring excess dislocation densities
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!*** zero for material points of local constitution
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Tdislocation_v = 0.0_pReal
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Tdislo = 0.0_pReal
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if (.not. phase_localConstitution(myPhase)) then ! only calculate dislocation stress for nonlocal material
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if (.not. phase_localConstitution(phase)) then
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invFe = math_inv3x3(Fe(1:3,1:3,1,ip,el))
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F = math_mul33x33(Fe(1:3,1:3,g,ip,el), Fp(1:3,1:3,g,ip,el))
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invFe = math_inv3x3(Fe(1:3,1:3,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(1:3,n) = 0.0_pReal
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neighboring_rhoExcess(n,1:2,1:ns) = 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(1:3,n) = 0.0_pReal
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neighboring_rhoExcess(n,1:2,1:ns) = rhoExcess
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elseif (myPhase /= material_phase(1,neighboring_ip,neighboring_el)) then ! for neighbors with different phase
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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(1:3,n) = 0.0_pReal
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neighboring_rhoExcess(n,1:2,1:ns) = rhoExcess
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else
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transmissivity = sum(constitutive_nonlocal_compatibility(2,1:ns,1:ns,n,ip,el)**2.0_pReal, 1)
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if ( any(transmissivity < 0.9_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(1:3,n) = 0.0_pReal
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neighboring_rhoExcess(n,1:2,1:ns) = rhoExcess
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else
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neighboring_F = math_mul33x33(Fe(1:3,1:3,g,neighboring_ip,neighboring_el), Fp(1:3,1:3,g,neighboring_ip,neighboring_el))
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deltaCoG = mesh_ipCenterOfGravity(1:3,neighboring_ip,neighboring_el) - mesh_ipCenterOfGravity(1:3,ip,el)
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if (math_mul3x3(deltaCoG, mesh_ipAreaNormal(1:3,n,neighboring_ip,neighboring_el)) < 0.0_pReal) then ! periodic surface, so this is a twin
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opposite_n = n + mod(n,2) - mod(n+1,2)
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opposite_el = mesh_ipNeighborhood(1,opposite_n,ip,el)
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opposite_ip = mesh_ipNeighborhood(2,opposite_n,ip,el)
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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
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endif
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neighboring_position(1:3,n) = 0.5_pReal * math_mul33x3(math_mul33x33(invFe,neighboring_F) + Fp(1:3,1:3,g,ip,el), deltaCoG)
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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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endif
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!* in case of periodic surfaces we have to find out how many periodic images in each direction we need
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do dir = 1,3
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maxCoord(dir) = maxval(mesh_node(dir,:))
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minCoord(dir) = minval(mesh_node(dir,:))
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enddo
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meshSize = maxCoord - minCoord
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ipCoords = mesh_ipCenterOfGravity(1:3,ip,el)
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periodicImages = 0_pInt
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do dir = 1,3
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if (mesh_periodicSurface(dir)) then
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periodicImages(1,dir) = floor((ipCoords(dir) - constitutive_nonlocal_R(instance) - minCoord(dir)) / meshSize(dir), pInt)
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periodicImages(2,dir) = ceiling((ipCoords(dir) + constitutive_nonlocal_R(instance) - maxCoord(dir)) / meshSize(dir), pInt)
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endif
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enddo
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Q = math_inv3x3(math_transpose3x3(neighboring_position(1:3,(/1,3,5/)) - neighboring_position(1:3,(/2,4,6/))))
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do s = 1,ns
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!* loop through all material points (also through their periodic images if present),
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!* but only consider nonlocal neighbors within a certain cutoff radius R
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lattice2slip = math_transpose3x3(reshape((/ &
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lattice_sd(1:3, constitutive_nonlocal_slipSystemLattice(s,myInstance), myStructure), &
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-lattice_st(1:3, constitutive_nonlocal_slipSystemLattice(s,myInstance), myStructure), &
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lattice_sn(1:3, constitutive_nonlocal_slipSystemLattice(s,myInstance), myStructure)/), (/3,3/)))
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do neighboring_el = 1,mesh_NcpElems
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do neighboring_ip = 1,FE_Nips(mesh_element(2,neighboring_el))
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neighboring_phase = material_phase(g,neighboring_ip,neighboring_el)
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neighboring_instance = phase_constitutionInstance(neighboring_phase)
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neighboring_latticeStruct = constitutive_nonlocal_structure(neighboring_instance)
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neighboring_ns = constitutive_nonlocal_totalNslip(neighboring_instance)
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nu = constitutive_nonlocal_nu(neighboring_instance)
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Tdislo_neighboringLattice = 0.0_pReal
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do deltaX = periodicImages(1,1),periodicImages(2,1)
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do deltaY = periodicImages(1,2),periodicImages(2,2)
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do deltaZ = periodicImages(1,3),periodicImages(2,3)
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if (neighboring_el == el .and. neighboring_ip == ip &
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.and. deltaX == 0 .and. deltaY == 0 .and. deltaZ == 0) then
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cycle ! this is myself
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endif
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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
|
||||
|
||||
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)))
|
||||
|
||||
!* 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
|
||||
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)
|
||||
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)
|
||||
|
||||
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)))
|
||||
!* scale stresses and map them into the neighboring material point's lattice configuration
|
||||
|
||||
enddo
|
||||
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
|
||||
|
||||
|
|
|
|||
|
|
@ -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
|
||||
|
|
|
|||
Loading…
Reference in New Issue