!-------------------------------------------------------------------------------------------------- !> @author Pratheek Shanthraj, Max-Planck-Institut für Eisenforschung GmbH !> @brief material subroutine incorporating kinematics resulting from thermal expansion !> @details to be done !-------------------------------------------------------------------------------------------------- module kinematics_thermal_expansion use prec, only: & pReal, & pInt implicit none private type, private :: tParameters real(pReal), allocatable, dimension(:,:,:) :: & expansion end type tParameters type(tParameters), dimension(:), allocatable :: param public :: & kinematics_thermal_expansion_init, & kinematics_thermal_expansion_initialStrain, & kinematics_thermal_expansion_LiAndItsTangent contains !-------------------------------------------------------------------------------------------------- !> @brief module initialization !> @details reads in material parameters, allocates arrays, and does sanity checks !-------------------------------------------------------------------------------------------------- subroutine kinematics_thermal_expansion_init() use debug, only: & debug_level,& debug_constitutive,& debug_levelBasic use material, only: & phase_kinematics, & KINEMATICS_thermal_expansion_label, & KINEMATICS_thermal_expansion_ID use config, only: & config_phase implicit none integer(pInt) :: & Ninstance, & p, i real(pReal), dimension(:), allocatable :: & temp write(6,'(/,a)') ' <<<+- kinematics_'//KINEMATICS_thermal_expansion_LABEL//' init -+>>>' Ninstance = int(count(phase_kinematics == KINEMATICS_thermal_expansion_ID),pInt) if (iand(debug_level(debug_constitutive),debug_levelBasic) /= 0_pInt) & write(6,'(a16,1x,i5,/)') '# instances:',Ninstance allocate(param(Ninstance)) do p = 1_pInt, size(phase_kinematics) if (all(phase_kinematics(:,p) /= KINEMATICS_thermal_expansion_ID)) cycle ! ToDo: Here we need to decide how to extend the concept of instances to ! kinetics and sources. I would suggest that the same mechanism exists at maximum once per phase ! read up to three parameters (constant, linear, quadratic with T) temp = config_phase(p)%getFloats('thermal_expansion11') !lattice_thermalExpansion33(1,1,1:size(temp),p) = temp temp = config_phase(p)%getFloats('thermal_expansion22', & defaultVal=[(0.0_pReal, i=1,size(temp))],requiredSize=size(temp)) !lattice_thermalExpansion33(2,2,1:size(temp),p) = temp temp = config_phase(p)%getFloats('thermal_expansion33', & defaultVal=[(0.0_pReal, i=1,size(temp))],requiredSize=size(temp)) enddo end subroutine kinematics_thermal_expansion_init !-------------------------------------------------------------------------------------------------- !> @brief report initial thermal strain based on current temperature deviation from reference !-------------------------------------------------------------------------------------------------- pure function kinematics_thermal_expansion_initialStrain(homog,phase,offset) use material, only: & temperature use lattice, only: & lattice_thermalExpansion33, & lattice_referenceTemperature implicit none integer(pInt), intent(in) :: & phase, & homog, offset real(pReal), dimension(3,3) :: & kinematics_thermal_expansion_initialStrain !< initial thermal strain (should be small strain, though) kinematics_thermal_expansion_initialStrain = & (temperature(homog)%p(offset) - lattice_referenceTemperature(phase))**1 / 1. * & lattice_thermalExpansion33(1:3,1:3,1,phase) + & ! constant coefficient (temperature(homog)%p(offset) - lattice_referenceTemperature(phase))**2 / 2. * & lattice_thermalExpansion33(1:3,1:3,2,phase) + & ! linear coefficient (temperature(homog)%p(offset) - lattice_referenceTemperature(phase))**3 / 3. * & lattice_thermalExpansion33(1:3,1:3,3,phase) ! quadratic coefficient end function kinematics_thermal_expansion_initialStrain !-------------------------------------------------------------------------------------------------- !> @brief contains the constitutive equation for calculating the velocity gradient !-------------------------------------------------------------------------------------------------- subroutine kinematics_thermal_expansion_LiAndItsTangent(Li, dLi_dTstar, ipc, ip, el) use material, only: & material_phase, & material_homog, & temperature, & temperatureRate, & thermalMapping use lattice, only: & lattice_thermalExpansion33, & lattice_referenceTemperature implicit none integer(pInt), intent(in) :: & ipc, & !< grain number ip, & !< integration point number el !< element number real(pReal), intent(out), dimension(3,3) :: & Li !< thermal velocity gradient real(pReal), intent(out), dimension(3,3,3,3) :: & dLi_dTstar !< derivative of Li with respect to Tstar (4th-order tensor defined to be zero) integer(pInt) :: & phase, & homog, offset real(pReal) :: & T, TRef, TDot phase = material_phase(ipc,ip,el) homog = material_homog(ip,el) offset = thermalMapping(homog)%p(ip,el) T = temperature(homog)%p(offset) TDot = temperatureRate(homog)%p(offset) TRef = lattice_referenceTemperature(phase) Li = TDot * ( & lattice_thermalExpansion33(1:3,1:3,1,phase)*(T - TRef)**0 & ! constant coefficient + lattice_thermalExpansion33(1:3,1:3,2,phase)*(T - TRef)**1 & ! linear coefficient + lattice_thermalExpansion33(1:3,1:3,3,phase)*(T - TRef)**2 & ! quadratic coefficient ) / & (1.0_pReal & + lattice_thermalExpansion33(1:3,1:3,1,phase)*(T - TRef)**1 / 1. & + lattice_thermalExpansion33(1:3,1:3,2,phase)*(T - TRef)**2 / 2. & + lattice_thermalExpansion33(1:3,1:3,3,phase)*(T - TRef)**3 / 3. & ) dLi_dTstar = 0.0_pReal end subroutine kinematics_thermal_expansion_LiAndItsTangent end module kinematics_thermal_expansion