calculation of shear modulus for cubic crystals can be simplifieid, tests added for different crystal symmetries
This commit is contained in:
Sharan Roongta
Sharan
parent
1264d8dfc1
commit
8b5fa37428
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@ -9,7 +9,7 @@ phase:
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lattice: cF
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mechanical:
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output: [F, P, F_e, F_p, L_p, O]
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elastic: {type: Hooke, C_11: 106.75e+9, C_12: 60.41e+9, C_44: 28.34e+9, modulus_type: 'Voigt'}
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elastic: {type: Hooke, C_11: 106.75e+9, C_12: 60.41e+9, C_44: 28.34e+9}
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plastic:
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type: phenopowerlaw
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N_sl: [12]
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@ -9,6 +9,7 @@
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submodule(homogenization:mechanical) RGC
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use rotations
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use lattice
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use phase
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type :: tParameters
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integer, dimension(:), allocatable :: &
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@ -652,9 +653,9 @@ module function RGC_updateState(P,F,avgF,dt,dPdF,ce) result(doneAndHappy)
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real(pReal), dimension(6,6) :: C
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C = phase_homogenizedC66(material_phaseID(co,ce),material_phaseEntry(co,ce)) ! damage not included!
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equivalentMu = lattice_equivalent_mu(C,'voigt')
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equivalentMu = lattice_isotropic_mu(C,'voigt',phase_lattice_structure(co,ce))
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end function equivalentMu
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@ -376,8 +376,8 @@ module lattice
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public :: &
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lattice_init, &
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lattice_equivalent_nu, &
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lattice_equivalent_mu, &
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lattice_isotropic_nu, &
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lattice_isotropic_mu, &
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lattice_symmetrize_33, &
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lattice_symmetrize_C66, &
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lattice_SchmidMatrix_slip, &
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@ -2149,10 +2149,11 @@ end function getlabels
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!> @brief Equivalent Poisson's ratio (ν)
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!> @details https://doi.org/10.1143/JPSJ.20.635
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!--------------------------------------------------------------------------------------------------
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pure function lattice_equivalent_nu(C,assumption) result(nu)
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pure function lattice_isotropic_nu(C,assumption,lattice) result(nu)
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real(pReal), dimension(6,6), intent(in) :: C !< Stiffness tensor (Voigt notation)
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character(len=5), intent(in) :: assumption !< Assumption ('Voigt' = isostrain, 'Reuss' = isostress)
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character(len=2), intent(in) :: lattice
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real(pReal) :: nu
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real(pReal) :: K, mu
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@ -2172,20 +2173,22 @@ pure function lattice_equivalent_nu(C,assumption) result(nu)
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error stop 'invalid assumption'
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end if
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mu = lattice_equivalent_mu(C,assumption)
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mu = lattice_isotropic_mu(C,assumption,lattice)
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nu = (1.5_pReal*K-mu)/(3.0_pReal*K+mu)
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end function lattice_equivalent_nu
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end function lattice_isotropic_nu
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!--------------------------------------------------------------------------------------------------
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!> @brief Equivalent shear modulus (μ)
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!> @details https://doi.org/10.1143/JPSJ.20.635
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!> @details Nonlinear Mechanics of Crystals 10.1007/978-94-007-0350-6, pp 563
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!--------------------------------------------------------------------------------------------------
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pure function lattice_equivalent_mu(C,assumption) result(mu)
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pure function lattice_isotropic_mu(C,assumption,lattice) result(mu)
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real(pReal), dimension(6,6), intent(in) :: C !< Stiffness tensor (Voigt notation)
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character(len=5), intent(in) :: assumption !< Assumption ('Voigt' = isostrain, 'Reuss' = isostress)
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character(len=2), intent(in) :: lattice
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real(pReal) :: mu
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logical :: error
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@ -2193,18 +2196,32 @@ pure function lattice_equivalent_mu(C,assumption) result(mu)
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if (IO_lc(assumption) == 'voigt') then
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mu = (1.0_pReal*(C(1,1)+C(2,2)+C(3,3)) -1.0_pReal*(C(1,2)+C(2,3)+C(1,3)) +3.0_pReal*(C(4,4)+C(5,5)+C(6,6))) &
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/ 15.0_pReal
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select case(lattice)
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case('cF','cI')
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mu = ( C(1,1) - C(1,2) + C(4,4)*3.0_pReal) / 5.0_pReal
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case default
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mu = ( C(1,1)+C(2,2)+C(3,3) &
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-(C(1,2)+C(2,3)+C(1,3)) &
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+(C(4,4)+C(5,5)+C(6,6)) * 3.0_pReal &
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) / 15.0_pReal
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end select
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elseif (IO_lc(assumption) == 'reuss') then
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call math_invert(S,error,C)
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if (error) error stop 'matrix inversion failed'
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mu = 15.0_pReal &
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/ (4.0_pReal*(S(1,1)+S(2,2)+S(3,3)) -4.0_pReal*(S(1,2)+S(2,3)+S(1,3)) +3.0_pReal*(S(4,4)+S(5,5)+S(6,6)))
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select case(lattice)
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case('cF','cI')
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mu = 1.0_pReal &
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/ ((4.0_pReal/(5.0_pReal * (C(1,1)-C(1,2)))) + (3.0_pReal/(5.0_pReal*C(4,4))))
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case default
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call math_invert(S,error,C)
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if (error) error stop 'matrix inversion failed'
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mu = 15.0_pReal &
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/ (4.0_pReal*(S(1,1)+S(2,2)+S(3,3)) -4.0_pReal*(S(1,2)+S(2,3)+S(1,3)) +3.0_pReal*(S(4,4)+S(5,5)+S(6,6)))
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end select
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else
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error stop 'invalid assumption'
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end if
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end function lattice_equivalent_mu
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end function lattice_isotropic_mu
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!--------------------------------------------------------------------------------------------------
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@ -2270,16 +2287,42 @@ subroutine selfTest
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call random_number(C)
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C(1,1) = C(1,1) + C(1,2) + 0.1_pReal
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C(1,3) = C(1,2)
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C(3,3) = C(1,1)
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C(4,4) = 0.5_pReal * (C(1,1) - C(1,2))
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C = lattice_symmetrize_C66(C,'cI')
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if (dNeq(C(4,4),lattice_equivalent_mu(C,'voigt'),1.0e-12_pReal)) error stop 'equivalent_mu/voigt'
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if (dNeq(C(4,4),lattice_equivalent_mu(C,'reuss'),1.0e-12_pReal)) error stop 'equivalent_mu/reuss'
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C(6,6) = C(4,4)
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C_cI = lattice_symmetrize_C66(C,'cI')
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if (dNeq(C_cI(4,4),lattice_isotropic_mu(C_cI,'voigt','cI'),1.0e-12_pReal)) error stop 'isotropic_mu/cI/voigt'
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if (dNeq(C_cI(4,4),lattice_isotropic_mu(C_cI,'reuss','cI'),1.0e-12_pReal)) error stop 'isotropic_mu/cI/reuss'
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lambda = C_cI(1,2)
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if (dNeq(lambda*0.5_pReal/(lambda+lattice_isotropic_mu(C_cI,'voigt','cI')), &
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lattice_isotropic_nu(C_cI,'voigt','cI'),1.0e-12_pReal)) error stop 'isotropic_nu/cI/voigt'
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if (dNeq(lambda*0.5_pReal/(lambda+lattice_isotropic_mu(C_cI,'reuss','cI')), &
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lattice_isotropic_nu(C_cI,'reuss','cI'),1.0e-12_pReal)) error stop 'isotropic_nu/cI/reuss'
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C_hP = lattice_symmetrize_C66(C,'hP')
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if (dNeq(C(4,4),lattice_isotropic_mu(C_hP,'voigt','hP'),1.0e-12_pReal)) error stop 'isotropic_mu/hP/voigt'
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if (dNeq(C(4,4),lattice_isotropic_mu(C_hP,'reuss','hP'),1.0e-12_pReal)) error stop 'isotropic_mu/hP/reuss'
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lambda = C_hP(1,2)
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if (dNeq(lambda*0.5_pReal/(lambda+lattice_isotropic_mu(C_hP,'voigt','hP')), &
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lattice_isotropic_nu(C_hP,'voigt','hP'),1.0e-12_pReal)) error stop 'isotropic_nu/hP/voigt'
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if (dNeq(lambda*0.5_pReal/(lambda+lattice_isotropic_mu(C_hP,'reuss','hP')), &
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lattice_isotropic_nu(C_hP,'reuss','hP'),1.0e-12_pReal)) error stop 'isotropic_nu/hP/reuss'
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C_tI = lattice_symmetrize_C66(C,'tI')
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if (dNeq(C(6,6),lattice_isotropic_mu(C_tI,'voigt','tI'),1.0e-12_pReal)) error stop 'isotropic_mu/tI/voigt'
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if (dNeq(C(6,6),lattice_isotropic_mu(C_tI,'reuss','tI'),1.0e-12_pReal)) error stop 'isotropic_mu/tI/reuss'
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lambda = C_tI(1,2)
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if (dNeq(lambda*0.5_pReal/(lambda+lattice_isotropic_mu(C_tI,'voigt','tI')), &
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lattice_isotropic_nu(C_tI,'voigt','tI'),1.0e-12_pReal)) error stop 'isotropic_nu/tI/voigt'
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if (dNeq(lambda*0.5_pReal/(lambda+lattice_isotropic_mu(C_tI,'reuss','tI')), &
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lattice_isotropic_nu(C_tI,'reuss','tI'),1.0e-12_pReal)) error stop 'isotropic_nu/tI/reuss'
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lambda = C(1,2)
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if (dNeq(lambda*0.5_pReal/(lambda+lattice_equivalent_mu(C,'voigt')), &
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lattice_equivalent_nu(C,'voigt'),1.0e-12_pReal)) error stop 'equivalent_nu/voigt'
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if (dNeq(lambda*0.5_pReal/(lambda+lattice_equivalent_mu(C,'reuss')), &
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lattice_equivalent_nu(C,'reuss'),1.0e-12_pReal)) error stop 'equivalent_nu/reuss'
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end subroutine selfTest
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@ -347,6 +347,7 @@ module phase
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phase_K_T, &
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phase_mu_phi, &
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phase_mu_T, &
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phase_lattice_structure, &
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phase_results, &
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phase_allocateState, &
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phase_forward, &
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@ -434,6 +435,20 @@ subroutine phase_init
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end subroutine phase_init
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!--------------------------------------------------------------------------------------------------
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!> @brief Get lattice structure for a given phase
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!--------------------------------------------------------------------------------------------------
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function phase_lattice_structure(co,ce) result(lattice)
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integer, intent(in) :: co, ce
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character(len=2) :: lattice
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lattice = phase_lattice(material_phaseID(co,ce))
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end function phase_lattice_structure
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!--------------------------------------------------------------------------------------------------
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!> @brief Allocate the components of the state structure for a given phase
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!--------------------------------------------------------------------------------------------------
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@ -169,14 +169,16 @@ submodule(phase) mechanical
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integer, intent(in) :: ph, en
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end function elastic_C66
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pure module function elastic_mu(ph,en) result(mu)
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pure module function elastic_mu(ph,en,isotropic_bound) result(mu)
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real(pReal) :: mu
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integer, intent(in) :: ph, en
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character(len=5), intent(in) :: isotropic_bound
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end function elastic_mu
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pure module function elastic_nu(ph,en) result(nu)
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pure module function elastic_nu(ph,en,isotropic_bound) result(nu)
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real(pReal) :: nu
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integer, intent(in) :: ph, en
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character(len=5), intent(in) :: isotropic_bound
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end function elastic_nu
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end interface
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@ -8,7 +8,6 @@ submodule(phase:mechanical) elastic
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C_33, &
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C_44, &
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C_66
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character(len=pStringLen) :: modulus_type
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end type tParameters
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type(tParameters), allocatable, dimension(:) :: param
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@ -58,8 +57,6 @@ module subroutine elastic_init(phases)
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if (phase_lattice(ph) == 'tI') &
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prm%C_66 = polynomial(elastic%asDict(),'C_66','T')
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prm%modulus_type=elastic%get_asString('modulus_type',defaultVal='Voigt')
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end associate
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end do
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@ -105,17 +102,18 @@ end function elastic_C66
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!--------------------------------------------------------------------------------------------------
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!> @brief return shear modulus
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!--------------------------------------------------------------------------------------------------
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pure module function elastic_mu(ph,en) result(mu)
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pure module function elastic_mu(ph,en,isotropic_bound) result(mu)
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integer, intent(in) :: &
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ph, &
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en
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character(len=5), intent(in) :: isotropic_bound
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real(pReal) :: &
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mu
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associate(prm => param(ph))
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mu = lattice_equivalent_mu(elastic_C66(ph,en),prm%modulus_type)
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mu = lattice_isotropic_mu(elastic_C66(ph,en),isotropic_bound,phase_lattice(ph))
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end associate
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@ -125,17 +123,18 @@ end function elastic_mu
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!--------------------------------------------------------------------------------------------------
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!> @brief return Poisson ratio
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!--------------------------------------------------------------------------------------------------
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pure module function elastic_nu(ph,en) result(nu)
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pure module function elastic_nu(ph,en,isotropic_bound) result(nu)
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integer, intent(in) :: &
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ph, &
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en
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character(len=5), intent(in) :: isotropic_bound
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real(pReal) :: &
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nu
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associate(prm => param(ph))
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nu = lattice_equivalent_nu(elastic_C66(ph,en),prm%modulus_type)
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nu = lattice_isotropic_nu(elastic_C66(ph,en),isotropic_bound,phase_lattice(ph))
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end associate
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@ -35,6 +35,8 @@ submodule(phase:plastic) dislotungsten
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P_nS_neg
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integer :: &
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sum_N_sl !< total number of active slip system
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character(len=5) :: &
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isotropic_bound
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character(len=pStringLen), allocatable, dimension(:) :: &
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output
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logical :: &
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@ -130,6 +132,8 @@ module function plastic_dislotungsten_init() result(myPlasticity)
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#else
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prm%output = pl%get_as1dString('output',defaultVal=emptyStringArray)
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#endif
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prm%isotropic_bound = pl%get_asString('isotropic_bound',defaultVal='Voigt')
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!--------------------------------------------------------------------------------------------------
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! slip related parameters
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@ -333,7 +337,7 @@ module function dislotungsten_dotState(Mp,ph,en) result(dotState)
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dot_rho_dip => dotState(indexDotState(ph)%rho_dip(1):indexDotState(ph)%rho_dip(2)), &
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dot_gamma_sl => dotState(indexDotState(ph)%gamma_sl(1):indexDotState(ph)%gamma_sl(2)))
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mu = elastic_mu(ph,en)
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mu = elastic_mu(ph,en,prm%isotropic_bound)
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T = thermal_T(ph,en)
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call kinetics(Mp,T,ph,en,&
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@ -384,7 +388,7 @@ module subroutine dislotungsten_dependentState(ph,en)
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associate(prm => param(ph), stt => state(ph), dst => dependentState(ph))
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dst%tau_pass(:,en) = elastic_mu(ph,en)*prm%b_sl &
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dst%tau_pass(:,en) = elastic_mu(ph,en,prm%isotropic_bound)*prm%b_sl &
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* sqrt(matmul(prm%h_sl_sl,stt%rho_mob(:,en)+stt%rho_dip(:,en)))
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Lambda_sl_inv = 1.0_pReal/prm%D &
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@ -74,6 +74,8 @@ submodule(phase:plastic) dislotwin
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fcc_twinNucleationSlipPair ! ToDo: Better name? Is also use for trans
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character(len=:), allocatable :: &
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lattice_tr
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character(len=5) :: &
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isotropic_bound
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character(len=pStringLen), allocatable, dimension(:) :: &
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output
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logical :: &
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@ -186,6 +188,8 @@ module function plastic_dislotwin_init() result(myPlasticity)
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prm%output = pl%get_as1dString('output',defaultVal=emptyStringArray)
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#endif
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prm%isotropic_bound = pl%get_asString('isotropic_bound',defaultVal='Voigt')
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!--------------------------------------------------------------------------------------------------
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! slip related parameters
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N_sl = pl%get_as1dInt('N_sl',defaultVal=emptyIntArray)
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@ -644,8 +648,8 @@ module function dislotwin_dotState(Mp,ph,en) result(dotState)
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dot_f_tw => dotState(indexDotState(ph)%f_tw(1):indexDotState(ph)%f_tw(2)), &
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dot_f_tr => dotState(indexDotState(ph)%f_tr(1):indexDotState(ph)%f_tr(2)))
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mu = elastic_mu(ph,en)
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nu = elastic_nu(ph,en)
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mu = elastic_mu(ph,en,prm%isotropic_bound)
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nu = elastic_nu(ph,en,prm%isotropic_bound)
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T = thermal_T(ph,en)
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f_matrix = 1.0_pReal &
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@ -732,7 +736,7 @@ module subroutine dislotwin_dependentState(ph,en)
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associate(prm => param(ph), stt => state(ph), dst => dependentState(ph))
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mu = elastic_mu(ph,en)
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mu = elastic_mu(ph,en,prm%isotropic_bound)
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sumf_tw = sum(stt%f_tw(1:prm%sum_N_tw,en))
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sumf_tr = sum(stt%f_tr(1:prm%sum_N_tr,en))
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@ -930,8 +934,8 @@ pure subroutine kinetics_tw(Mp,T,abs_dot_gamma_sl,ph,en,&
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associate(prm => param(ph), stt => state(ph), dst => dependentState(ph))
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mu = elastic_mu(ph,en)
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nu = elastic_nu(ph,en)
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mu = elastic_mu(ph,en,prm%isotropic_bound)
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nu = elastic_nu(ph,en,prm%isotropic_bound)
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Gamma_sf = prm%Gamma_sf%at(T)
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tau_hat = 3.0_pReal*prm%b_tw(1)*mu/prm%L_tw &
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@ -1006,8 +1010,8 @@ pure subroutine kinetics_tr(Mp,T,abs_dot_gamma_sl,ph,en,&
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associate(prm => param(ph), stt => state(ph), dst => dependentState(ph))
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mu = elastic_mu(ph,en)
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nu = elastic_nu(ph,en)
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mu = elastic_mu(ph,en,prm%isotropic_bound)
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nu = elastic_nu(ph,en,prm%isotropic_bound)
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Gamma_sf = prm%Gamma_sf%at(T)
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tau_hat = 3.0_pReal*prm%b_tr(1)*mu/prm%L_tr &
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@ -115,6 +115,8 @@ submodule(phase:plastic) nonlocal
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sum_N_sl = 0
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integer, dimension(:), allocatable :: &
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colinearSystem !< colinear system to the active slip system (only valid for fcc!)
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character(len=5) :: &
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isotropic_bound
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character(len=pStringLen), dimension(:), allocatable :: &
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output
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logical :: &
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@ -241,6 +243,7 @@ module function plastic_nonlocal_init() result(myPlasticity)
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prm%output = pl%get_as1dString('output',defaultVal=emptyStringArray)
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#endif
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prm%isotropic_bound = pl%get_asString('isotropic_bound',defaultVal='Voigt')
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prm%atol_rho = pl%get_asFloat('atol_rho',defaultVal=1.0_pReal)
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ini%N_sl = pl%get_as1dInt('N_sl',defaultVal=emptyIntArray)
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@ -609,8 +612,8 @@ module subroutine nonlocal_dependentState(ph, en)
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associate(prm => param(ph),dst => dependentState(ph), stt => state(ph))
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mu = elastic_mu(ph,en)
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nu = elastic_nu(ph,en)
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mu = elastic_mu(ph,en,prm%isotropic_bound)
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nu = elastic_nu(ph,en,prm%isotropic_bound)
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rho = getRho(ph,en)
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||||
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||||
stt%rho_forest(:,en) = matmul(prm%forestProjection_Edge, sum(abs(rho(:,edg)),2)) &
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||||
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|
@ -880,8 +883,8 @@ module subroutine plastic_nonlocal_deltaState(Mp,ph,en)
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||||
associate(prm => param(ph),dst => dependentState(ph),del => deltaState(ph))
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||||
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||||
mu = elastic_mu(ph,en)
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||||
nu = elastic_nu(ph,en)
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||||
mu = elastic_mu(ph,en,prm%isotropic_bound)
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||||
nu = elastic_nu(ph,en,prm%isotropic_bound)
|
||||
|
||||
!*** shortcut to state variables
|
||||
forall (s = 1:prm%sum_N_sl, t = 1:4) v(s,t) = plasticState(ph)%state(iV(s,t,ph),en)
|
||||
|
|
@ -994,8 +997,8 @@ module subroutine nonlocal_dotState(Mp,timestep, &
|
|||
|
||||
associate(prm => param(ph), dst => dependentState(ph), dot => dotState(ph), stt => state(ph))
|
||||
|
||||
mu = elastic_mu(ph,en)
|
||||
nu = elastic_nu(ph,en)
|
||||
mu = elastic_mu(ph,en,prm%isotropic_bound)
|
||||
nu = elastic_nu(ph,en,prm%isotropic_bound)
|
||||
Temperature = thermal_T(ph,en)
|
||||
|
||||
tau = 0.0_pReal
|
||||
|
|
|
|||
Loading…
Reference in New Issue