submodule(phase:mechanical) elastic type :: tParameters real(pReal),dimension(3) :: & C_11 = 0.0_pReal, & C_12 = 0.0_pReal, & C_13 = 0.0_pReal, & C_33 = 0.0_pReal, & C_44 = 0.0_pReal, & C_66 = 0.0_pReal real(pReal) :: & T_ref end type tParameters type(tParameters), allocatable, dimension(:) :: param contains !-------------------------------------------------------------------------------------------------- !> @brief initialize elasticity !-------------------------------------------------------------------------------------------------- module subroutine elastic_init(phases) class(tNode), pointer :: & phases integer :: & ph class(tNode), pointer :: & phase, & mech, & elastic print'(/,1x,a)', '<<<+- phase:mechanical:elastic init -+>>>' print'(/,1x,a)', '<<<+- phase:mechanical:elastic:Hooke init -+>>>' print'(/,a,i0)', ' # phases: ',phases%length; flush(IO_STDOUT) allocate(param(phases%length)) do ph = 1, phases%length phase => phases%get(ph) mech => phase%get('mechanical') elastic => mech%get('elastic') if (elastic%get_asString('type') /= 'Hooke') call IO_error(200,ext_msg=elastic%get_asString('type')) associate(prm => param(ph)) prm%T_ref = elastic%get_asFloat('T_ref', defaultVal=T_ROOM) prm%C_11(1) = elastic%get_asFloat('C_11') prm%C_11(2) = elastic%get_asFloat('C_11,T', defaultVal=0.0_pReal) prm%C_11(3) = elastic%get_asFloat('C_11,T^2',defaultVal=0.0_pReal) prm%C_12(1) = elastic%get_asFloat('C_12') prm%C_12(2) = elastic%get_asFloat('C_12,T', defaultVal=0.0_pReal) prm%C_12(3) = elastic%get_asFloat('C_12,T^2',defaultVal=0.0_pReal) prm%C_44(1) = elastic%get_asFloat('C_44') prm%C_44(2) = elastic%get_asFloat('C_44,T', defaultVal=0.0_pReal) prm%C_44(3) = elastic%get_asFloat('C_44,T^2',defaultVal=0.0_pReal) if (any(phase_lattice(ph) == ['hP','tI'])) then prm%C_13(1) = elastic%get_asFloat('C_13') prm%C_13(2) = elastic%get_asFloat('C_13,T', defaultVal=0.0_pReal) prm%C_13(3) = elastic%get_asFloat('C_13,T^2',defaultVal=0.0_pReal) prm%C_33(1) = elastic%get_asFloat('C_33') prm%C_33(2) = elastic%get_asFloat('C_33,T', defaultVal=0.0_pReal) prm%C_33(3) = elastic%get_asFloat('C_33,T^2',defaultVal=0.0_pReal) end if if (phase_lattice(ph) == 'tI') then prm%C_66(1) = elastic%get_asFloat('C_66') prm%C_66(2) = elastic%get_asFloat('C_66,T', defaultVal=0.0_pReal) prm%C_66(3) = elastic%get_asFloat('C_66,T^2',defaultVal=0.0_pReal) end if end associate end do end subroutine elastic_init !-------------------------------------------------------------------------------------------------- !> @brief return 6x6 elasticity tensor !-------------------------------------------------------------------------------------------------- pure module function elastic_C66(ph,en) result(C66) integer, intent(in) :: & ph, & en real(pReal), dimension(6,6) :: C66 real(pReal) :: T associate(prm => param(ph)) C66 = 0.0_pReal T = thermal_T(ph,en) C66(1,1) = prm%C_11(1) & + prm%C_11(2)*(T - prm%T_ref) & + prm%C_11(3)*(T - prm%T_ref)**2 C66(1,2) = prm%C_12(1) & + prm%C_12(2)*(T - prm%T_ref) & + prm%C_12(3)*(T - prm%T_ref)**2 C66(4,4) = prm%C_44(1) & + prm%C_44(2)*(T - prm%T_ref) & + prm%C_44(3)*(T - prm%T_ref)**2 if (any(phase_lattice(ph) == ['hP','tI'])) then C66(1,3) = prm%C_13(1) & + prm%C_13(2)*(T - prm%T_ref) & + prm%C_13(3)*(T - prm%T_ref)**2 C66(3,3) = prm%C_33(1) & + prm%C_33(2)*(T - prm%T_ref) & + prm%C_33(3)*(T - prm%T_ref)**2 end if if (phase_lattice(ph) == 'tI') then C66(6,6) = prm%C_66(1) & + prm%C_66(2)*(T - prm%T_ref) & + prm%C_66(3)*(T - prm%T_ref)**2 end if C66 = lattice_symmetrize_C66(C66,phase_lattice(ph)) end associate end function elastic_C66 !-------------------------------------------------------------------------------------------------- !> @brief return shear modulus !-------------------------------------------------------------------------------------------------- pure module function elastic_mu(ph,en) result(mu) integer, intent(in) :: & ph, & en real(pReal) :: & mu mu = lattice_equivalent_mu(elastic_C66(ph,en),'voigt') end function elastic_mu !-------------------------------------------------------------------------------------------------- !> @brief return Poisson ratio !-------------------------------------------------------------------------------------------------- pure module function elastic_nu(ph,en) result(nu) integer, intent(in) :: & ph, & en real(pReal) :: & nu nu = lattice_equivalent_nu(elastic_C66(ph,en),'voigt') end function elastic_nu !-------------------------------------------------------------------------------------------------- !> @brief return the 2nd Piola-Kirchhoff stress tensor and its tangent with respect to !> the elastic and intermediate deformation gradients using Hooke's law ! ToDo: Use Voigt matrix directly !-------------------------------------------------------------------------------------------------- module subroutine phase_hooke_SandItsTangents(S, dS_dFe, dS_dFi, & Fe, Fi, ph, en) integer, intent(in) :: & ph, & en real(pReal), intent(in), dimension(3,3) :: & Fe, & !< elastic deformation gradient Fi !< intermediate deformation gradient real(pReal), intent(out), dimension(3,3) :: & S !< 2nd Piola-Kirchhoff stress tensor in lattice configuration real(pReal), intent(out), dimension(3,3,3,3) :: & dS_dFe, & !< derivative of 2nd P-K stress with respect to elastic deformation gradient dS_dFi !< derivative of 2nd P-K stress with respect to intermediate deformation gradient real(pReal), dimension(3,3) :: E real(pReal), dimension(6,6) :: C66 real(pReal), dimension(3,3,3,3) :: C integer :: & i, j C66 = phase_damage_C66(phase_homogenizedC66(ph,en),ph,en) C = math_Voigt66to3333(C66) E = 0.5_pReal*(matmul(transpose(Fe),Fe)-math_I3) !< Green-Lagrange strain in unloaded configuration S = math_Voigt6to33_stress(matmul(C66,math_33toVoigt6_strain(matmul(matmul(transpose(Fi),E),Fi))))!< 2PK stress in lattice configuration in work conjugate with GL strain pulled back to lattice configuration do i =1,3; do j=1,3 dS_dFe(i,j,1:3,1:3) = matmul(Fe,matmul(matmul(Fi,C(i,j,1:3,1:3)),transpose(Fi))) !< dS_ij/dFe_kl = C_ijmn * Fi_lm * Fi_on * Fe_ko dS_dFi(i,j,1:3,1:3) = 2.0_pReal*matmul(matmul(E,Fi),C(i,j,1:3,1:3)) !< dS_ij/dFi_kl = C_ijln * E_km * Fe_mn end do; end do end subroutine phase_hooke_SandItsTangents !-------------------------------------------------------------------------------------------------- !> @brief Return the homogenized elasticity matrix. !-------------------------------------------------------------------------------------------------- module function phase_homogenizedC66(ph,en) result(C) real(pReal), dimension(6,6) :: C integer, intent(in) :: ph, en plasticType: select case (phase_plasticity(ph)) case (PLASTIC_DISLOTWIN_ID) plasticType C = plastic_dislotwin_homogenizedC(ph,en) case default plasticType C = elastic_C66(ph,en) end select plasticType end function phase_homogenizedC66 end submodule elastic