thermal expansion coefficient alpha = a + b(T-T_0) + c(T-T_0)^2
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Philip Eisenlohr
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a901a81ba8
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bc998846ab
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@ -174,8 +174,12 @@ pure function kinematics_thermal_expansion_initialStrain(ipc, ip, el)
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offset = thermalMapping(homog)%p(ip,el)
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kinematics_thermal_expansion_initialStrain = &
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(temperature(homog)%p(offset) - lattice_referenceTemperature(phase)) * &
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lattice_thermalExpansion33(1:3,1:3,phase)
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(temperature(homog)%p(offset) - lattice_referenceTemperature(phase))**1 / 1. * &
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lattice_thermalExpansion33(1:3,1:3,1,phase) + & ! constant coefficient
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(temperature(homog)%p(offset) - lattice_referenceTemperature(phase))**2 / 2. * &
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lattice_thermalExpansion33(1:3,1:3,2,phase) + & ! linear coefficient
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(temperature(homog)%p(offset) - lattice_referenceTemperature(phase))**3 / 3. * &
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lattice_thermalExpansion33(1:3,1:3,3,phase) ! quadratic coefficient
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end function kinematics_thermal_expansion_initialStrain
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@ -215,9 +219,16 @@ subroutine kinematics_thermal_expansion_LiAndItsTangent(Li, dLi_dTstar3333, ipc,
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TDot = temperatureRate(homog)%p(offset)
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TRef = lattice_referenceTemperature(phase)
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Li = TDot* &
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lattice_thermalExpansion33(1:3,1:3,phase)/ &
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(1.0_pReal + lattice_thermalExpansion33(1:3,1:3,phase)*(T - TRef))
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Li = TDot * ( &
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lattice_thermalExpansion33(1:3,1:3,1,phase)*(T - TRef)**0 & ! constant coefficient
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+ lattice_thermalExpansion33(1:3,1:3,2,phase)*(T - TRef)**1 & ! linear coefficient
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+ lattice_thermalExpansion33(1:3,1:3,3,phase)*(T - TRef)**2 & ! quadratic coefficient
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) / &
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(1.0_pReal \
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+ lattice_thermalExpansion33(1:3,1:3,1,phase)*(T - TRef)**1 / 1. &
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+ lattice_thermalExpansion33(1:3,1:3,2,phase)*(T - TRef)**2 / 2. &
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+ lattice_thermalExpansion33(1:3,1:3,3,phase)*(T - TRef)**3 / 3. &
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)
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dLi_dTstar3333 = 0.0_pReal
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end subroutine kinematics_thermal_expansion_LiAndItsTangent
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@ -1082,9 +1082,10 @@ module lattice
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lattice_nu, &
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lattice_trans_mu, &
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lattice_trans_nu
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real(pReal), dimension(:,:,:,:), allocatable, public, protected :: & ! with higher-order parameters (e.g. temperature-dependent)
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lattice_thermalExpansion33
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real(pReal), dimension(:,:,:), allocatable, public, protected :: &
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lattice_thermalConductivity33, &
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lattice_thermalExpansion33, &
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lattice_damageDiffusion33, &
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lattice_vacancyfluxDiffusion33, &
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lattice_vacancyfluxMobility33, &
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@ -1380,8 +1381,8 @@ subroutine lattice_init
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allocate(lattice_C3333(3,3,3,3,Nphases), source=0.0_pReal)
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allocate(lattice_trans_C66(6,6,Nphases), source=0.0_pReal)
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allocate(lattice_trans_C3333(3,3,3,3,Nphases), source=0.0_pReal)
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allocate(lattice_thermalExpansion33 (3,3,3,Nphases), source=0.0_pReal) ! constant, linear, quadratic coefficients
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allocate(lattice_thermalConductivity33 (3,3,Nphases), source=0.0_pReal)
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allocate(lattice_thermalExpansion33 (3,3,Nphases), source=0.0_pReal)
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allocate(lattice_damageDiffusion33 (3,3,Nphases), source=0.0_pReal)
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allocate(lattice_vacancyfluxDiffusion33 (3,3,Nphases), source=0.0_pReal)
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allocate(lattice_vacancyfluxMobility33 (3,3,Nphases), source=0.0_pReal)
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@ -1545,11 +1546,17 @@ subroutine lattice_init
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case ('thermal_conductivity33')
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lattice_thermalConductivity33(3,3,section) = IO_floatValue(line,chunkPos,2_pInt)
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case ('thermal_expansion11')
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lattice_thermalExpansion33(1,1,section) = IO_floatValue(line,chunkPos,2_pInt)
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do i = 2_pInt, min(4,chunkPos(1)) ! read up to three parameters (constant, linear, quadratic with T)
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lattice_thermalExpansion33(1,1,i-1_pInt,section) = IO_floatValue(line,chunkPos,i)
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enddo
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case ('thermal_expansion22')
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lattice_thermalExpansion33(2,2,section) = IO_floatValue(line,chunkPos,2_pInt)
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do i = 2_pInt, min(4,chunkPos(1)) ! read up to three parameters (constant, linear, quadratic with T)
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lattice_thermalExpansion33(2,2,i-1_pInt,section) = IO_floatValue(line,chunkPos,i)
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enddo
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case ('thermal_expansion33')
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lattice_thermalExpansion33(3,3,section) = IO_floatValue(line,chunkPos,2_pInt)
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do i = 2_pInt, min(4,chunkPos(1)) ! read up to three parameters (constant, linear, quadratic with T)
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lattice_thermalExpansion33(3,3,i-1_pInt,section) = IO_floatValue(line,chunkPos,i)
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enddo
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case ('specific_heat')
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lattice_specificHeat(section) = IO_floatValue(line,chunkPos,2_pInt)
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case ('vacancyformationenergy')
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@ -1756,22 +1763,24 @@ subroutine lattice_initializeStructure(myPhase,CoverA,CoverA_trans,a_fcc,a_bcc)
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end select
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end select
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lattice_thermalConductivity33(1:3,1:3,myPhase) = lattice_symmetrize33(lattice_structure(myPhase),&
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lattice_thermalConductivity33(1:3,1:3,myPhase))
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lattice_thermalExpansion33(1:3,1:3,myPhase) = lattice_symmetrize33(lattice_structure(myPhase),&
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lattice_thermalExpansion33(1:3,1:3,myPhase))
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lattice_DamageDiffusion33(1:3,1:3,myPhase) = lattice_symmetrize33(lattice_structure(myPhase),&
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lattice_DamageDiffusion33(1:3,1:3,myPhase))
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lattice_vacancyfluxDiffusion33(1:3,1:3,myPhase) = lattice_symmetrize33(lattice_structure(myPhase),&
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lattice_vacancyfluxDiffusion33(1:3,1:3,myPhase))
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lattice_vacancyfluxMobility33(1:3,1:3,myPhase) = lattice_symmetrize33(lattice_structure(myPhase),&
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lattice_vacancyfluxMobility33(1:3,1:3,myPhase))
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lattice_PorosityDiffusion33(1:3,1:3,myPhase) = lattice_symmetrize33(lattice_structure(myPhase),&
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lattice_PorosityDiffusion33(1:3,1:3,myPhase))
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forall (i = 1_pInt:3_pInt) &
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lattice_thermalExpansion33 (1:3,1:3,i,myPhase) = lattice_symmetrize33(lattice_structure(myPhase),&
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lattice_thermalExpansion33 (1:3,1:3,i,myPhase))
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lattice_thermalConductivity33 (1:3,1:3,myPhase) = lattice_symmetrize33(lattice_structure(myPhase),&
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lattice_thermalConductivity33 (1:3,1:3,myPhase))
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lattice_DamageDiffusion33 (1:3,1:3,myPhase) = lattice_symmetrize33(lattice_structure(myPhase),&
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lattice_DamageDiffusion33 (1:3,1:3,myPhase))
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lattice_vacancyfluxDiffusion33 (1:3,1:3,myPhase) = lattice_symmetrize33(lattice_structure(myPhase),&
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lattice_vacancyfluxDiffusion33 (1:3,1:3,myPhase))
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lattice_vacancyfluxMobility33 (1:3,1:3,myPhase) = lattice_symmetrize33(lattice_structure(myPhase),&
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lattice_vacancyfluxMobility33 (1:3,1:3,myPhase))
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lattice_PorosityDiffusion33 (1:3,1:3,myPhase) = lattice_symmetrize33(lattice_structure(myPhase),&
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lattice_PorosityDiffusion33 (1:3,1:3,myPhase))
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lattice_hydrogenfluxDiffusion33(1:3,1:3,myPhase) = lattice_symmetrize33(lattice_structure(myPhase),&
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lattice_hydrogenfluxDiffusion33(1:3,1:3,myPhase))
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lattice_hydrogenfluxMobility33(1:3,1:3,myPhase) = lattice_symmetrize33(lattice_structure(myPhase),&
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lattice_hydrogenfluxMobility33(1:3,1:3,myPhase))
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lattice_hydrogenfluxDiffusion33(1:3,1:3,myPhase))
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lattice_hydrogenfluxMobility33 (1:3,1:3,myPhase) = lattice_symmetrize33(lattice_structure(myPhase),&
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lattice_hydrogenfluxMobility33 (1:3,1:3,myPhase))
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select case(lattice_structure(myPhase))
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!--------------------------------------------------------------------------------------------------
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