1058 lines
53 KiB
Fortran
1058 lines
53 KiB
Fortran
! Copyright 2011 Max-Planck-Institut für Eisenforschung GmbH
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!
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! This file is part of DAMASK,
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! the Düsseldorf Advanced MAterial Simulation Kit.
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!
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! DAMASK is free software: you can redistribute it and/or modify
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! it under the terms of the GNU General Public License as published by
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! the Free Software Foundation, either version 3 of the License, or
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! (at your option) any later version.
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!
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! DAMASK is distributed in the hope that it will be useful,
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! but WITHOUT ANY WARRANTY; without even the implied warranty of
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! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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! GNU General Public License for more details.
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!
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! You should have received a copy of the GNU General Public License
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! along with DAMASK. If not, see <http://www.gnu.org/licenses/>.
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!
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!##############################################################
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!* $Id$
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!************************************
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!* Module: LATTICE *
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!************************************
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!* contains: *
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!* - Lattice structure definition *
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!* - Slip system definition *
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!* - Schmid matrices calculation *
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!************************************
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module lattice
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use prec, only: pReal, &
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pInt
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implicit none
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private
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!************************************
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!* Lattice structures *
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!************************************
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integer(pInt), parameter, public :: &
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lattice_maxNslipFamily = 5_pInt, & !< max # of slip system families over lattice structures
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lattice_maxNtwinFamily = 4_pInt, & !< max # of twin system families over lattice structures
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lattice_maxNslip = 54_pInt, & !< max # of slip systems over lattice structures
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lattice_maxNtwin = 24_pInt, & !< max # of twin systems over lattice structures
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lattice_maxNinteraction = 30_pInt, & !< max # of interaction types (in hardening matrix part)
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lattice_maxNonSchmid = 6_pInt !< max # of non schmid contributions over lattice structures
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integer(pInt), allocatable, dimension(:,:), protected, public :: &
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lattice_NslipSystem, & !< # of slip systems in each family
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lattice_NtwinSystem !< # of twin systems in each family
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integer(pInt), allocatable, dimension(:,:,:), protected, public :: &
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lattice_interactionSlipSlip, & !< interaction type between slip/slip
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lattice_interactionSlipTwin, & !< interaction type between slip/twin
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lattice_interactionTwinSlip, & !< interaction type between twin/slip
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lattice_interactionTwinTwin !< interaction type between twin/twin
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real(pReal), allocatable, dimension(:,:,:,:), protected, public :: &
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lattice_Sslip_v, &
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lattice_Sslip !< Schmid matrices, normal, shear direction and d x n of slip systems
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real(pReal), allocatable, dimension(:,:,:), protected, public :: &
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lattice_sn, &
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lattice_sd, &
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lattice_st
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! rotation and Schmid matrices, normal, shear direction and d x n of twin systems
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real(pReal), allocatable, dimension(:,:,:,:), protected, public :: &
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lattice_Stwin, &
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lattice_Qtwin
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real(pReal), allocatable, dimension(:,:,:), protected, public :: &
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lattice_Stwin_v, &
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lattice_tn, &
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lattice_td, &
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lattice_tt
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real(pReal), allocatable, dimension(:,:), protected, public :: &
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lattice_shearTwin !< characteristic twin shear
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integer(pInt), private :: &
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lattice_Nhexagonal, & !< # of hexagonal lattice structure (from tag CoverA_ratio)
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lattice_Nstructure !< # of lattice structures (1: fcc,2: bcc,3+: hexagonal)
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integer(pInt), dimension(:,:), pointer, private :: &
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interactionSlipSlip, &
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interactionSlipTwin, &
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interactionTwinSlip, &
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interactionTwinTwin
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integer(pInt), allocatable, dimension(:), protected, public :: &
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NnonSchmid !< # of Non Schmid contributions for each structure
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!--------------------------------------------------------------------------------------------------
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! fcc (1)
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integer(pInt), dimension(lattice_maxNslipFamily), parameter, private :: &
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lattice_fcc_NslipSystem = int([12, 0, 0, 0, 0],pInt)
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integer(pInt), dimension(lattice_maxNtwinFamily), parameter, private :: &
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lattice_fcc_NtwinSystem = int([12, 0, 0, 0],pInt)
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integer(pInt), parameter, private :: &
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lattice_fcc_Nslip = 12_pInt, & ! sum(lattice_fcc_NslipSystem)
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lattice_fcc_Ntwin = 12_pInt ! sum(lattice_fcc_NtwinSystem)
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integer(pInt), private :: &
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lattice_fcc_Nstructure = 0_pInt
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real(pReal), dimension(3+3,lattice_fcc_Nslip), parameter, private :: &
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lattice_fcc_systemSlip = reshape(real([&
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0, 1,-1, 1, 1, 1, &
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-1, 0, 1, 1, 1, 1, &
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1,-1, 0, 1, 1, 1, &
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0,-1,-1, -1,-1, 1, &
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1, 0, 1, -1,-1, 1, &
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-1, 1, 0, -1,-1, 1, &
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0,-1, 1, 1,-1,-1, &
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-1, 0,-1, 1,-1,-1, &
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1, 1, 0, 1,-1,-1, &
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0, 1, 1, -1, 1,-1, &
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1, 0,-1, -1, 1,-1, &
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-1,-1, 0, -1, 1,-1 &
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],pReal),[ 3_pInt + 3_pInt,lattice_fcc_Nslip]) !< Slip system <110>{111} Sorted according to Eisenlohr & Hantcherli
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real(pReal), dimension(3+3,lattice_fcc_Ntwin), parameter, private :: &
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lattice_fcc_systemTwin = reshape(real( [&
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-2, 1, 1, 1, 1, 1, &
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1,-2, 1, 1, 1, 1, &
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1, 1,-2, 1, 1, 1, &
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2,-1, 1, -1,-1, 1, &
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-1, 2, 1, -1,-1, 1, &
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-1,-1,-2, -1,-1, 1, &
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-2,-1,-1, 1,-1,-1, &
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1, 2,-1, 1,-1,-1, &
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1,-1, 2, 1,-1,-1, &
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2, 1,-1, -1, 1,-1, &
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-1,-2,-1, -1, 1,-1, &
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-1, 1, 2, -1, 1,-1 &
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],pReal),[ 3_pInt + 3_pInt ,lattice_fcc_Ntwin]) !< Twin system <112>{111} Sorted according to Eisenlohr & Hantcherli
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real(pReal), dimension(lattice_fcc_Ntwin), parameter, private :: &
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lattice_fcc_shearTwin = reshape([&
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0.7071067812_pReal, &
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0.7071067812_pReal, &
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0.7071067812_pReal, &
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0.7071067812_pReal, &
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0.7071067812_pReal, &
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0.7071067812_pReal, &
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0.7071067812_pReal, &
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0.7071067812_pReal, &
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0.7071067812_pReal, &
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0.7071067812_pReal, &
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0.7071067812_pReal, &
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0.7071067812_pReal &
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],[lattice_fcc_Ntwin]) !< Twin system <112>{111} Sorted according to Eisenlohr & Hantcherli
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integer(pInt), dimension(lattice_fcc_Nslip,lattice_fcc_Nslip), target, private :: &
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lattice_fcc_interactionSlipSlip = reshape(int( [&
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1,2,2,4,6,5,3,5,5,4,5,6, & ! ---> slip
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2,1,2,6,4,5,5,4,6,5,3,5, & ! |
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2,2,1,5,5,3,5,6,4,6,5,4, & ! |
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4,6,5,1,2,2,4,5,6,3,5,5, & ! v slip
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6,4,5,2,1,2,5,3,5,5,4,6, &
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5,5,3,2,2,1,6,5,4,5,6,4, &
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3,5,5,4,5,6,1,2,2,4,6,5, &
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5,4,6,5,3,5,2,1,2,6,4,5, &
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5,6,4,6,5,4,2,2,1,5,5,3, &
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4,5,6,3,5,5,4,6,5,1,2,2, &
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5,3,5,5,4,6,6,4,5,2,1,2, &
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6,5,4,5,6,4,5,5,3,2,2,1 &
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],pInt),[lattice_fcc_Nslip,lattice_fcc_Nslip],order=[2,1])
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!< Interaction types
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!< 1 --- self interaction
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!< 2 --- coplanar interaction
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!< 3 --- collinear interaction
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!< 4 --- Hirth locks
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!< 5 --- glissile junctions
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!< 6 --- Lomer locks
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integer(pInt), dimension(lattice_fcc_Nslip,lattice_fcc_Ntwin), target, private :: &
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lattice_fcc_interactionSlipTwin = reshape(int( [&
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1,1,1,3,3,3,2,2,2,3,3,3, & ! ---> twin
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1,1,1,3,3,3,3,3,3,2,2,2, & ! |
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1,1,1,2,2,2,3,3,3,3,3,3, & ! |
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3,3,3,1,1,1,3,3,3,2,2,2, & ! v slip
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3,3,3,1,1,1,2,2,2,3,3,3, &
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2,2,2,1,1,1,3,3,3,3,3,3, &
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2,2,2,3,3,3,1,1,1,3,3,3, &
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3,3,3,2,2,2,1,1,1,3,3,3, &
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3,3,3,3,3,3,1,1,1,2,2,2, &
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3,3,3,2,2,2,3,3,3,1,1,1, &
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2,2,2,3,3,3,3,3,3,1,1,1, &
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3,3,3,3,3,3,2,2,2,1,1,1 &
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],pInt),[lattice_fcc_Nslip,lattice_fcc_Ntwin],order=[2,1])
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!< Interaction types
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!< 1 --- coplanar interaction
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!< 2 --- screw trace between slip system and twin habit plane (easy cross slip)
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!< 3 --- other interaction
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integer(pInt), dimension(lattice_fcc_Ntwin,lattice_fcc_Nslip), target, private :: &
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lattice_fcc_interactionTwinSlip = 0_pInt
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integer(pInt), dimension(lattice_fcc_Ntwin,lattice_fcc_Ntwin), target, private :: &
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lattice_fcc_interactionTwinTwin = reshape(int( [&
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1,1,1,2,2,2,2,2,2,2,2,2, & ! ---> twin
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1,1,1,2,2,2,2,2,2,2,2,2, & ! |
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1,1,1,2,2,2,2,2,2,2,2,2, & ! |
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2,2,2,1,1,1,2,2,2,2,2,2, & ! v twin
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2,2,2,1,1,1,2,2,2,2,2,2, &
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2,2,2,1,1,1,2,2,2,2,2,2, &
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2,2,2,2,2,2,1,1,1,2,2,2, &
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2,2,2,2,2,2,1,1,1,2,2,2, &
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2,2,2,2,2,2,1,1,1,2,2,2, &
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2,2,2,2,2,2,2,2,2,1,1,1, &
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2,2,2,2,2,2,2,2,2,1,1,1, &
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2,2,2,2,2,2,2,2,2,1,1,1 &
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],pInt),[lattice_fcc_Ntwin,lattice_fcc_Ntwin],order=[2,1])
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! Number of Non Schmid contributions for FCC
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integer(pInt), parameter, private :: NnonSchmid_fcc = 0_pInt
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! Tensor for each non schmid contribution
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real(pReal), dimension(3,3,2,NnonSchmid_fcc,lattice_fcc_Nslip), parameter, private :: &
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lattice_nonSchmid_fcc = 0.0_pReal ! reshape([],[3,3,2,NnonSchmid_fcc,lattice_fcc_Nslip])
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!--------------------------------------------------------------------------------------------------
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! bcc (2)
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integer(pInt), dimension(lattice_maxNslipFamily), parameter, private :: &
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lattice_bcc_NslipSystem = int([ 12, 12, 0, 0, 0], pInt)
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integer(pInt), dimension(lattice_maxNtwinFamily), parameter, private :: &
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lattice_bcc_NtwinSystem = int([ 12, 0, 0, 0], pInt)
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integer(pInt), parameter, private :: &
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lattice_bcc_Nslip = 24_pInt ! sum(lattice_bcc_NslipSystem)
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integer(pInt), parameter, private :: &
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lattice_bcc_Ntwin = 12_pInt ! sum(lattice_bcc_NtwinSystem)
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integer(pInt), private :: &
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lattice_bcc_Nstructure = 0_pInt
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real(pReal), dimension(3+3,lattice_bcc_Nslip), parameter, private :: &
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lattice_bcc_systemSlip = reshape(real([&
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! Slip system <111>{110}
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1,-1, 1, 0, 1, 1, &
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-1,-1, 1, 0, 1, 1, &
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1, 1, 1, 0,-1, 1, &
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-1, 1, 1, 0,-1, 1, &
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-1, 1, 1, 1, 0, 1, &
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-1,-1, 1, 1, 0, 1, &
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1, 1, 1, -1, 0, 1, &
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1,-1, 1, -1, 0, 1, &
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-1, 1, 1, 1, 1, 0, &
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-1, 1,-1, 1, 1, 0, &
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1, 1, 1, -1, 1, 0, &
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1, 1,-1, -1, 1, 0, &
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! Slip system <111>{112}
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-1, 1, 1, 2, 1, 1, &
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1, 1, 1, -2, 1, 1, &
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1, 1,-1, 2,-1, 1, &
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1,-1, 1, 2, 1,-1, &
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1,-1, 1, 1, 2, 1, &
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1, 1,-1, -1, 2, 1, &
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1, 1, 1, 1,-2, 1, &
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-1, 1, 1, 1, 2,-1, &
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1, 1,-1, 1, 1, 2, &
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1,-1, 1, -1, 1, 2, &
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-1, 1, 1, 1,-1, 2, &
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1, 1, 1, 1, 1,-2 &
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! Slip system <111>{123}
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! 1, 1,-1, 1, 2, 3, &
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! 1,-1, 1, -1, 2, 3, &
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! -1, 1, 1, 1,-2, 3, &
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! 1, 1, 1, 1, 2,-3, &
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! 1,-1, 1, 1, 3, 2, &
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! 1, 1,-1, -1, 3, 2, &
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! 1, 1, 1, 1,-3, 2, &
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! -1, 1, 1, 1, 3,-2, &
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! 1, 1,-1, 2, 1, 3, &
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! 1,-1, 1, -2, 1, 3, &
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! -1, 1, 1, 2,-1, 3, &
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! 1, 1, 1, 2, 1,-3, &
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! 1,-1, 1, 2, 3, 1, &
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! 1, 1,-1, -2, 3, 1, &
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! 1, 1, 1, 2,-3, 1, &
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! -1, 1, 1, 2, 3,-1, &
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! -1, 1, 1, 3, 1, 2, &
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! 1, 1, 1, -3, 1, 2, &
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! 1, 1,-1, 3,-1, 2, &
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! 1,-1, 1, 3, 1,-2, &
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! -1, 1, 1, 3, 2, 1, &
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! 1, 1, 1, -3, 2, 1, &
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! 1, 1,-1, 3,-2, 1, &
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! 1,-1, 1, 3, 2,-1 &
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],pReal),[ 3_pInt + 3_pInt ,lattice_bcc_Nslip])
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real(pReal), dimension(3+3,lattice_bcc_Ntwin), parameter, private :: &
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lattice_bcc_systemTwin = reshape(real([&
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! Twin system <111>{112}
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-1, 1, 1, 2, 1, 1, &
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1, 1, 1, -2, 1, 1, &
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1, 1,-1, 2,-1, 1, &
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1,-1, 1, 2, 1,-1, &
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1,-1, 1, 1, 2, 1, &
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1, 1,-1, -1, 2, 1, &
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1, 1, 1, 1,-2, 1, &
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-1, 1, 1, 1, 2,-1, &
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1, 1,-1, 1, 1, 2, &
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1,-1, 1, -1, 1, 2, &
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-1, 1, 1, 1,-1, 2, &
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1, 1, 1, 1, 1,-2 &
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],pReal),[ 3_pInt + 3_pInt,lattice_bcc_Ntwin])
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real(pReal), dimension(lattice_bcc_Ntwin), parameter, private :: &
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lattice_bcc_shearTwin = reshape([&
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0.7071067812_pReal, &
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0.7071067812_pReal, &
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0.7071067812_pReal, &
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0.7071067812_pReal, &
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0.7071067812_pReal, &
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0.7071067812_pReal, &
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0.7071067812_pReal, &
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0.7071067812_pReal, &
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0.7071067812_pReal, &
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0.7071067812_pReal, &
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0.7071067812_pReal, &
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0.7071067812_pReal &
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],[lattice_bcc_Ntwin])
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! slip--slip interactions for BCC structures (2) from Lee et al. Int J Plast 15 (1999) 625-645
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integer(pInt), dimension(lattice_bcc_Nslip,lattice_bcc_Nslip), target, private :: &
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lattice_bcc_interactionSlipSlip = reshape(int( [&
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1,3,6,6,5,4,4,2,4,2,5,4, 6,6,4,2,2,4,6,6,4,2,6,6, & ! ---> slip
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3,1,6,6,4,2,5,4,5,4,4,2, 6,6,2,4,4,2,6,6,2,4,6,6, & ! |
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6,6,1,3,4,5,2,4,4,5,2,4, 4,2,6,6,6,6,2,4,6,6,4,2, & ! |
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6,6,3,1,2,4,4,5,2,4,4,5, 2,4,6,6,6,6,4,2,6,6,2,4, & ! v slip
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5,4,4,2,1,3,6,6,2,4,5,4, 2,6,4,6,6,4,6,2,4,6,2,6, &
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4,2,5,4,3,1,6,6,4,5,4,2, 4,6,2,6,6,2,6,4,2,6,4,6, &
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4,5,2,4,6,6,1,3,5,4,2,4, 6,2,6,4,4,6,2,6,6,4,6,2, &
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2,4,4,5,6,6,3,1,4,2,4,5, 6,4,6,2,2,6,4,6,6,2,6,4, &
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4,5,4,2,2,4,5,4,1,3,6,6, 2,6,6,4,4,6,6,2,6,4,2,6, &
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2,4,5,4,4,5,4,2,3,1,6,6, 4,6,6,2,2,6,6,4,6,2,4,6, &
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5,4,2,4,5,4,2,4,6,6,1,3, 6,2,4,6,6,4,2,6,4,6,6,2, &
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4,2,4,5,4,2,4,5,6,6,3,1, 6,4,2,6,6,2,4,6,2,6,6,4, &
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!
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6,6,4,2,2,4,6,6,2,4,6,6, 1,5,6,6,5,6,6,2,5,6,2,6, &
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6,6,2,4,6,6,2,4,6,6,2,4, 5,1,6,6,6,5,2,6,6,5,6,2, &
|
|
4,2,6,6,4,2,6,6,6,6,4,2, 6,6,1,5,6,2,5,6,2,6,5,6, &
|
|
2,4,6,6,6,6,4,2,4,2,6,6, 6,6,5,1,2,6,6,5,6,2,6,5, &
|
|
2,4,6,6,6,6,4,2,4,2,6,6, 5,6,6,2,1,6,5,6,5,2,6,6, &
|
|
4,2,6,6,4,2,6,6,6,6,4,2, 6,5,2,6,6,1,6,5,2,5,6,6, &
|
|
6,6,2,4,6,6,2,4,6,6,2,4, 6,2,5,6,5,6,1,6,6,6,5,2, &
|
|
6,6,4,2,2,4,6,6,2,4,6,6, 2,6,6,5,6,5,6,1,6,6,2,5, &
|
|
4,2,6,6,4,2,6,6,6,6,4,2, 5,6,2,6,5,2,6,6,1,6,6,5, &
|
|
2,4,6,6,6,6,4,2,4,2,6,6, 6,5,6,2,2,5,6,6,6,1,5,6, &
|
|
6,6,4,2,2,4,6,6,2,4,6,6, 2,6,5,6,6,6,5,2,6,5,1,6, &
|
|
6,6,2,4,6,6,2,4,6,6,2,4, 6,2,6,5,6,6,2,5,5,6,6,1 &
|
|
],pInt),[lattice_bcc_Nslip,lattice_bcc_Nslip],order=[2,1])
|
|
!< Interaction types
|
|
!< 1 --- self interaction
|
|
!< 2 --- no interaction
|
|
!< 3 --- coplanar interaction
|
|
!< 4 --- glissile interaction
|
|
!< 5 --- weak sessile interaction
|
|
!< 6 --- strong sessile interaction
|
|
|
|
integer(pInt), dimension(lattice_bcc_Nslip,lattice_bcc_Ntwin), target, private :: &
|
|
lattice_bcc_interactionSlipTwin = reshape(int( [&
|
|
3,3,3,2,2,3,3,3,3,2,3,3, & ! ---> twin
|
|
3,3,2,3,3,2,3,3,2,3,3,3, & ! |
|
|
3,2,3,3,3,3,2,3,3,3,3,2, & ! |
|
|
2,3,3,3,3,3,3,2,3,3,2,3, & ! v slip
|
|
2,3,3,3,3,3,3,2,3,3,2,3, &
|
|
3,3,2,3,3,2,3,3,2,3,3,3, &
|
|
3,2,3,3,3,3,2,3,3,3,3,2, &
|
|
3,3,3,2,2,3,3,3,3,2,3,3, &
|
|
2,3,3,3,3,3,3,2,3,3,2,3, &
|
|
3,3,3,2,2,3,3,3,3,2,3,3, &
|
|
3,2,3,3,3,3,2,3,3,3,3,2, &
|
|
3,3,2,3,3,2,3,3,2,3,3,3, &
|
|
!
|
|
1,3,3,3,3,3,3,2,3,3,2,3, &
|
|
3,1,3,3,3,3,2,3,3,3,3,2, &
|
|
3,3,1,3,3,2,3,3,2,3,3,3, &
|
|
3,3,3,1,2,3,3,3,3,2,3,3, &
|
|
3,3,3,2,1,3,3,3,3,2,3,3, &
|
|
3,3,2,3,3,1,3,3,2,3,3,3, &
|
|
3,2,3,3,3,3,1,3,3,3,3,2, &
|
|
2,3,3,3,3,3,3,1,3,3,2,3, &
|
|
3,3,2,3,3,2,3,3,1,3,3,3, &
|
|
3,3,3,2,2,3,3,3,3,1,3,3, &
|
|
2,3,3,3,3,3,3,2,3,3,1,3, &
|
|
3,2,3,3,3,3,2,3,3,3,3,1 &
|
|
],pInt),[lattice_bcc_Nslip,lattice_bcc_Ntwin],order=[2,1])
|
|
!< Interaction types
|
|
!< 1 --- coplanar interaction
|
|
!< 2 --- screw trace between slip system and twin habit plane (easy cross slip)
|
|
!< 3 --- other interaction
|
|
|
|
! twin--slip interactions for BCC structures (2) MISSING: not implemented yet
|
|
integer(pInt), dimension(lattice_bcc_Ntwin,lattice_bcc_Nslip), target, private :: &
|
|
lattice_bcc_interactionTwinSlip = 0_pInt
|
|
|
|
! twin--twin interactions for BCC structures (2)
|
|
integer(pInt), dimension(lattice_bcc_Ntwin,lattice_bcc_Ntwin), target, private :: &
|
|
lattice_bcc_interactionTwinTwin = reshape(int( [&
|
|
1,3,3,3,3,3,3,2,3,3,2,3, & ! ---> twin
|
|
3,1,3,3,3,3,2,3,3,3,3,2, & ! |
|
|
3,3,1,3,3,2,3,3,2,3,3,3, & ! |
|
|
3,3,3,1,2,3,3,3,3,2,3,3, & ! v twin
|
|
3,3,3,2,1,3,3,3,3,2,3,3, &
|
|
3,3,2,3,3,1,3,3,2,3,3,3, &
|
|
3,2,3,3,3,3,1,3,3,3,3,2, &
|
|
2,3,3,3,3,3,3,1,3,3,2,3, &
|
|
3,3,2,3,3,2,3,3,1,3,3,3, &
|
|
3,3,3,2,2,3,3,3,3,1,3,3, &
|
|
2,3,3,3,3,3,3,2,3,3,1,3, &
|
|
3,2,3,3,3,3,2,3,3,3,3,1 &
|
|
],pInt),[lattice_bcc_Ntwin,lattice_bcc_Ntwin],order=[2,1])
|
|
!< Interaction types
|
|
!< 1 --- self interaction
|
|
!< 2 --- collinear interaction
|
|
!< 3 --- other interaction
|
|
|
|
! Number of Non Schmid contributions for BCC
|
|
integer(pInt), parameter, private :: NnonSchmid_bcc = 0_pInt
|
|
|
|
! Tensor for each non schmid contribution
|
|
real(pReal), dimension(3,3,2,NnonSchmid_bcc,lattice_bcc_Nslip), parameter, private :: &
|
|
lattice_nonSchmid_bcc = 0.0_pReal ! reshape([],[3,3,2,NnonSchmid_bcc,lattice_bcc_Nslip])
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! hex (3+)
|
|
|
|
integer(pInt), dimension(lattice_maxNslipFamily), parameter, private :: &
|
|
lattice_hex_NslipSystem = int([ 3, 3, 6, 12, 6],pInt)
|
|
|
|
integer(pInt), dimension(lattice_maxNtwinFamily), parameter, private :: &
|
|
lattice_hex_NtwinSystem = int([ 6, 6, 6, 6],pInt)
|
|
|
|
integer(pInt), parameter , private :: &
|
|
lattice_hex_Nslip = 30_pInt ! sum(lattice_hex_NslipSystem)
|
|
|
|
integer(pInt), parameter, private :: &
|
|
lattice_hex_Ntwin = 24_pInt ! sum(lattice_hex_NtwinSystem)
|
|
|
|
integer(pInt), private :: &
|
|
lattice_hex_Nstructure = 0_pInt
|
|
|
|
!* sorted by A. Alankar & P. Eisenlohr
|
|
real(pReal), dimension(4+4,lattice_hex_Nslip), parameter, private :: &
|
|
lattice_hex_systemSlip = reshape(real([&
|
|
! Basal systems <1120>{0001} (independent of c/a-ratio, Bravais notation (4 coordinate base))
|
|
2, -1, -1, 0, 0, 0, 0, 1, &
|
|
-1, 2, -1, 0, 0, 0, 0, 1, &
|
|
-1, -1, 2, 0, 0, 0, 0, 1, &
|
|
! 1st type prismatic systems <11.0>{10.0} (independent of c/a-ratio)
|
|
2, -1, -1, 0, 0, 1, -1, 0, &
|
|
-1, 2, -1, 0, -1, 0, 1, 0, &
|
|
-1, -1, 2, 0, 1, -1, 0, 0, &
|
|
! 1st type 1st order pyramidal systems <11.0>{10.1} -- plane normals depend on the c/a-ratio
|
|
2, -1, -1, 0, 0, 1, -1, 1, &
|
|
1, 1, -2, 0, -1, 1, 0, 1, &
|
|
-1, 2, -1, 0, -1, 0, 1, 1, &
|
|
-2, 1, 1, 0, 0, -1, 1, 1, &
|
|
-1, -1, 2, 0, 1, -1, 0, 1, &
|
|
1, -2, 1, 0, 1, 0, -1, 1, &
|
|
! pyramidal system: c+a slip <-21.-3>{-10.1} -- plane normals depend on the c/a-ratio
|
|
-1, 2, -1, -3, 0, 1, -1, 1, &
|
|
1, 1, -2, -3, 0, 1, -1, 1, &
|
|
-2, 1, 1, -3, -1, 1, 0, 1, &
|
|
-1, 2, -1, -3, -1, 1, 0, 1, &
|
|
-1, -1, 2, -3, -1, 0, 1, 1, &
|
|
-2, 1, 1, -3, -1, 0, 1, 1, &
|
|
1, -2, 1, -3, 0, -1, 1, 1, &
|
|
-1, -1, 2, -3, 0, -1, 1, 1, &
|
|
2, -1, -1, -3, 1, -1, 0, 1, &
|
|
1, -2, 1, -3, 1, -1, 0, 1, &
|
|
1, 1, -2, -3, 1, 0, -1, 1, &
|
|
2, -1, -1, -3, 1, 0, -1, 1, &
|
|
! pyramidal system: c+a slip <11.-3>{11.2} -- as for hexagonal Ice (Castelnau et al 1996, similar to twin system found below)
|
|
2, -1, -1, -3, 2, -1, -1, 2, & ! <11.-3>{11.2} shear = 2((c/a)^2-2)/(3 c/a)
|
|
1, 1, -2, -3, 1, 1, -2, 2, & ! not sorted, just copied from twin system
|
|
-1, 2, -1, -3, -1, 2, -1, 2, &
|
|
-2, 1, 1, -3, -2, 1, 1, 2, &
|
|
-1, -1, 2, -3, -1, -1, 2, 2, &
|
|
1, -2, 1, -3, 1, -2, 1, 2 &
|
|
],pReal),[ 4_pInt + 4_pInt,lattice_hex_Nslip])
|
|
|
|
real(pReal), dimension(4+4,lattice_hex_Ntwin), parameter, private :: &
|
|
lattice_hex_systemTwin = reshape(real([&
|
|
0, 1, -1, 1, 0, -1, 1, 2, & ! <-10.1>{10.2} shear = (3-(c/a)^2)/(sqrt(3) c/a)
|
|
-1, 1, 0, 1, 1, -1, 0, 2, &
|
|
-1, 0, 1, 1, 1, 0, -1, 2, & !!
|
|
0, -1, 1, 1, 0, 1, -1, 2, &
|
|
1, -1, 0, 1, -1, 1, 0, 2, &
|
|
1, 0, -1, 1, -1, 0, 1, 2, &
|
|
2, -1, -1, -3, 2, -1, -1, 2, & ! <11.-3>{11.2} shear = 2((c/a)^2-2)/(3 c/a)
|
|
1, 1, -2, -3, 1, 1, -2, 2, & !!
|
|
-1, 2, -1, -3, -1, 2, -1, 2, &
|
|
-2, 1, 1, -3, -2, 1, 1, 2, &
|
|
-1, -1, 2, -3, -1, -1, 2, 2, &
|
|
1, -2, 1, -3, 1, -2, 1, 2, &
|
|
-2, 1, 1, 6, 2, -1, -1, 1, & ! <-1-1.6>{11.1} shear = 1/(c/a)
|
|
-1, -1, 2, 6, 1, 1, -2, 1, & !!
|
|
1, -2, 1, 6, -1, 2, -1, 1, &
|
|
2, -1, -1, 6, -2, 1, 1, 1, &
|
|
1, 1, -2, 6, -1, -1, 2, 1, &
|
|
-1, 2, -1, 6, 1, -2, 1, 1, &
|
|
1, 0, -1, -2, 1, 0, -1, 1, & !! <10.-2>{10.1} shear = (4(c/a)^2-9)/(4 sqrt(3) c/a)
|
|
-1, 0, 1, -2, -1, 0, 1, 1, &
|
|
0, 1, -1, -2, 0, 1, -1, 1, &
|
|
0, -1, 1, -2, 0, -1, 1, 1, &
|
|
1, -1, 0, -2, 1, -1, 0, 1, &
|
|
-1, 1, 0, -2, -1, 1, 0, 1 &
|
|
],pReal),[ 4_pInt + 4_pInt ,lattice_hex_Ntwin]) !* Sort? Numbering of twin system follows Prof. Tom Bieler's scheme (to be consistent with his work); but numbering in data was restarted from 1 &
|
|
|
|
integer(pInt), dimension(lattice_hex_Ntwin), parameter, private :: &
|
|
lattice_hex_shearTwin = reshape(int( [& ! indicator to formula further below
|
|
1, & ! {10.2}<-10.1>
|
|
1, &
|
|
1, &
|
|
1, &
|
|
1, &
|
|
1, &
|
|
2, & ! {11.2}<11.-3>
|
|
2, &
|
|
2, &
|
|
2, &
|
|
2, &
|
|
2, &
|
|
3, & ! {11.1}<-1-1.6>
|
|
3, &
|
|
3, &
|
|
3, &
|
|
3, &
|
|
3, &
|
|
4, & ! {10.1}<10.-2>
|
|
4, &
|
|
4, &
|
|
4, &
|
|
4, &
|
|
4 &
|
|
],pInt),[lattice_hex_Ntwin])
|
|
|
|
!* four different interaction type matrix
|
|
!* 1. slip-slip interaction - 30 types
|
|
!* 2. slip-twin interaction - 20 types
|
|
!* 3. twin-twin interaction - 20 types
|
|
!* 4. twin-slip interaction - 16 types
|
|
|
|
integer(pInt), dimension(lattice_hex_Nslip,lattice_hex_Nslip), target, private :: &
|
|
lattice_hex_interactionSlipSlip = reshape(int( [&
|
|
1, 6, 6, 11,11,11, 15,15,15,15,15,15, 18,18,18,18,18,18,18,18,18,18,18,18, 20,20,20,20,20,20, & ! ---> slip
|
|
6, 1, 6, 11,11,11, 15,15,15,15,15,15, 18,18,18,18,18,18,18,18,18,18,18,18, 20,20,20,20,20,20, & ! |
|
|
6, 6, 1, 11,11,11, 15,15,15,15,15,15, 18,18,18,18,18,18,18,18,18,18,18,18, 20,20,20,20,20,20, & ! |
|
|
! v slip
|
|
21,21,21, 2, 7, 7, 12,12,12,12,12,12, 16,16,16,16,16,16,16,16,16,16,16,16, 19,19,19,19,19,19, &
|
|
21,21,21, 7, 2, 7, 12,12,12,12,12,12, 16,16,16,16,16,16,16,16,16,16,16,16, 19,19,19,19,19,19, &
|
|
21,21,21, 7, 7, 2, 12,12,12,12,12,12, 16,16,16,16,16,16,16,16,16,16,16,16, 19,19,19,19,19,19, &
|
|
!
|
|
25,25,25, 22,22,22, 3, 8, 8, 8, 8, 8, 13,13,13,13,13,13,13,13,13,13,13,13, 17,17,17,17,17,17, &
|
|
25,25,25, 22,22,22, 8, 3, 8, 8, 8, 8, 13,13,13,13,13,13,13,13,13,13,13,13, 17,17,17,17,17,17, &
|
|
25,25,25, 22,22,22, 8, 8, 3, 8, 8, 8, 13,13,13,13,13,13,13,13,13,13,13,13, 17,17,17,17,17,17, &
|
|
25,25,25, 22,22,22, 8, 8, 8, 3, 8, 8, 13,13,13,13,13,13,13,13,13,13,13,13, 17,17,17,17,17,17, &
|
|
25,25,25, 22,22,22, 8, 8, 8, 8, 3, 8, 13,13,13,13,13,13,13,13,13,13,13,13, 17,17,17,17,17,17, &
|
|
25,25,25, 22,22,22, 8, 8, 8, 8, 8, 3, 13,13,13,13,13,13,13,13,13,13,13,13, 17,17,17,17,17,17, &
|
|
!
|
|
28,28,28, 26,26,26, 23,23,23,23,23,23, 4, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 14,14,14,14,14,14, &
|
|
28,28,28, 26,26,26, 23,23,23,23,23,23, 9, 4, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 14,14,14,14,14,14, &
|
|
28,28,28, 26,26,26, 23,23,23,23,23,23, 9, 9, 4, 9, 9, 9, 9, 9, 9, 9, 9, 9, 14,14,14,14,14,14, &
|
|
28,28,28, 26,26,26, 23,23,23,23,23,23, 9, 9, 9, 4, 9, 9, 9, 9, 9, 9, 9, 9, 14,14,14,14,14,14, &
|
|
28,28,28, 26,26,26, 23,23,23,23,23,23, 9, 9, 9, 9, 4, 9, 9, 9, 9, 9, 9, 9, 14,14,14,14,14,14, &
|
|
28,28,28, 26,26,26, 23,23,23,23,23,23, 9, 9, 9, 9, 9, 4, 9, 9, 9, 9, 9, 9, 14,14,14,14,14,14, &
|
|
28,28,28, 26,26,26, 23,23,23,23,23,23, 9, 9, 9, 9, 9, 9, 4, 9, 9, 9, 9, 9, 14,14,14,14,14,14, &
|
|
28,28,28, 26,26,26, 23,23,23,23,23,23, 9, 9, 9, 9, 9, 9, 9, 4, 9, 9, 9, 9, 14,14,14,14,14,14, &
|
|
28,28,28, 26,26,26, 23,23,23,23,23,23, 9, 9, 9, 9, 9, 9, 9, 9, 4, 9, 9, 9, 14,14,14,14,14,14, &
|
|
28,28,28, 26,26,26, 23,23,23,23,23,23, 9, 9, 9, 9, 9, 9, 9, 9, 9, 4, 9, 9, 14,14,14,14,14,14, &
|
|
28,28,28, 26,26,26, 23,23,23,23,23,23, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 4, 9, 14,14,14,14,14,14, &
|
|
28,28,28, 26,26,26, 23,23,23,23,23,23, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 4, 14,14,14,14,14,14, &
|
|
!
|
|
30,30,30, 29,29,29, 27,27,27,27,27,27, 24,24,24,24,24,24,24,24,24,24,24,24, 5,10,10,10,10,10, &
|
|
30,30,30, 29,29,29, 27,27,27,27,27,27, 24,24,24,24,24,24,24,24,24,24,24,24, 10, 5,10,10,10,10, &
|
|
30,30,30, 29,29,29, 27,27,27,27,27,27, 24,24,24,24,24,24,24,24,24,24,24,24, 10,10, 5,10,10,10, &
|
|
30,30,30, 29,29,29, 27,27,27,27,27,27, 24,24,24,24,24,24,24,24,24,24,24,24, 10,10,10, 5,10,10, &
|
|
30,30,30, 29,29,29, 27,27,27,27,27,27, 24,24,24,24,24,24,24,24,24,24,24,24, 10,10,10,10, 5,10, &
|
|
30,30,30, 29,29,29, 27,27,27,27,27,27, 24,24,24,24,24,24,24,24,24,24,24,24, 10,10,10,10,10, 5 &
|
|
],pInt),[lattice_hex_Nslip,lattice_hex_Nslip],order=[2,1])
|
|
|
|
!* isotropic interaction at the moment
|
|
integer(pInt), dimension(lattice_hex_Nslip,lattice_hex_Ntwin), target, private :: &
|
|
lattice_hex_interactionSlipTwin = reshape(int( [&
|
|
1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, & ! --> twin
|
|
1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, & ! |
|
|
1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, & ! |
|
|
! v
|
|
5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, & ! slip
|
|
5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, &
|
|
5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, &
|
|
!
|
|
9, 9, 9, 9, 9, 9, 10,10,10,10,10,10, 11,11,11,11,11,11, 12,12,12,12,12,12, &
|
|
9, 9, 9, 9, 9, 9, 10,10,10,10,10,10, 11,11,11,11,11,11, 12,12,12,12,12,12, &
|
|
9, 9, 9, 9, 9, 9, 10,10,10,10,10,10, 11,11,11,11,11,11, 12,12,12,12,12,12, &
|
|
9, 9, 9, 9, 9, 9, 10,10,10,10,10,10, 11,11,11,11,11,11, 12,12,12,12,12,12, &
|
|
9, 9, 9, 9, 9, 9, 10,10,10,10,10,10, 11,11,11,11,11,11, 12,12,12,12,12,12, &
|
|
9, 9, 9, 9, 9, 9, 10,10,10,10,10,10, 11,11,11,11,11,11, 12,12,12,12,12,12, &
|
|
!
|
|
13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, &
|
|
13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, &
|
|
13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, &
|
|
13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, &
|
|
13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, &
|
|
13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, &
|
|
13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, &
|
|
13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, &
|
|
13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, &
|
|
13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, &
|
|
13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, &
|
|
13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, &
|
|
!
|
|
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, &
|
|
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, &
|
|
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, &
|
|
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, &
|
|
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, &
|
|
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20 &
|
|
],pInt),[lattice_hex_Nslip,lattice_hex_Ntwin],order=[2,1])
|
|
|
|
!* isotropic interaction at the moment
|
|
integer(pInt), dimension(lattice_hex_Ntwin,lattice_hex_Nslip), target, private :: &
|
|
lattice_hex_interactionTwinSlip = reshape(int( [&
|
|
1, 1, 1, 5, 5, 5, 9, 9, 9, 9, 9, 9, 13,13,13,13,13,13,13,13,13,13,13,13, 17,17,17,17,17,17, & ! --> slip
|
|
1, 1, 1, 5, 5, 5, 9, 9, 9, 9, 9, 9, 13,13,13,13,13,13,13,13,13,13,13,13, 17,17,17,17,17,17, & ! |
|
|
1, 1, 1, 5, 5, 5, 9, 9, 9, 9, 9, 9, 13,13,13,13,13,13,13,13,13,13,13,13, 17,17,17,17,17,17, & ! |
|
|
1, 1, 1, 5, 5, 5, 9, 9, 9, 9, 9, 9, 13,13,13,13,13,13,13,13,13,13,13,13, 17,17,17,17,17,17, & ! v
|
|
1, 1, 1, 5, 5, 5, 9, 9, 9, 9, 9, 9, 13,13,13,13,13,13,13,13,13,13,13,13, 17,17,17,17,17,17, & ! twin
|
|
1, 1, 1, 5, 5, 5, 9, 9, 9, 9, 9, 9, 13,13,13,13,13,13,13,13,13,13,13,13, 17,17,17,17,17,17, &
|
|
!
|
|
2, 2, 2, 6, 6, 6, 10,10,10,10,10,10, 14,14,14,14,14,14,14,14,14,14,14,14, 18,18,18,18,18,18, &
|
|
2, 2, 2, 6, 6, 6, 10,10,10,10,10,10, 14,14,14,14,14,14,14,14,14,14,14,14, 18,18,18,18,18,18, &
|
|
2, 2, 2, 6, 6, 6, 10,10,10,10,10,10, 14,14,14,14,14,14,14,14,14,14,14,14, 18,18,18,18,18,18, &
|
|
2, 2, 2, 6, 6, 6, 10,10,10,10,10,10, 14,14,14,14,14,14,14,14,14,14,14,14, 18,18,18,18,18,18, &
|
|
2, 2, 2, 6, 6, 6, 10,10,10,10,10,10, 14,14,14,14,14,14,14,14,14,14,14,14, 18,18,18,18,18,18, &
|
|
2, 2, 2, 6, 6, 6, 10,10,10,10,10,10, 14,14,14,14,14,14,14,14,14,14,14,14, 18,18,18,18,18,18, &
|
|
!
|
|
3, 3, 3, 7, 7, 7, 11,11,11,11,11,11, 15,15,15,15,15,15,15,15,15,15,15,15, 19,19,19,19,19,19, &
|
|
3, 3, 3, 7, 7, 7, 11,11,11,11,11,11, 15,15,15,15,15,15,15,15,15,15,15,15, 19,19,19,19,19,19, &
|
|
3, 3, 3, 7, 7, 7, 11,11,11,11,11,11, 15,15,15,15,15,15,15,15,15,15,15,15, 19,19,19,19,19,19, &
|
|
3, 3, 3, 7, 7, 7, 11,11,11,11,11,11, 15,15,15,15,15,15,15,15,15,15,15,15, 19,19,19,19,19,19, &
|
|
3, 3, 3, 7, 7, 7, 11,11,11,11,11,11, 15,15,15,15,15,15,15,15,15,15,15,15, 19,19,19,19,19,19, &
|
|
3, 3, 3, 7, 7, 7, 11,11,11,11,11,11, 15,15,15,15,15,15,15,15,15,15,15,15, 19,19,19,19,19,19, &
|
|
!
|
|
4, 4, 4, 8, 8, 8, 12,12,12,12,12,12, 16,16,16,16,16,16,16,16,16,16,16,16, 20,20,20,20,20,20, &
|
|
4, 4, 4, 8, 8, 8, 12,12,12,12,12,12, 16,16,16,16,16,16,16,16,16,16,16,16, 20,20,20,20,20,20, &
|
|
4, 4, 4, 8, 8, 8, 12,12,12,12,12,12, 16,16,16,16,16,16,16,16,16,16,16,16, 20,20,20,20,20,20, &
|
|
4, 4, 4, 8, 8, 8, 12,12,12,12,12,12, 16,16,16,16,16,16,16,16,16,16,16,16, 20,20,20,20,20,20, &
|
|
4, 4, 4, 8, 8, 8, 12,12,12,12,12,12, 16,16,16,16,16,16,16,16,16,16,16,16, 20,20,20,20,20,20, &
|
|
4, 4, 4, 8, 8, 8, 12,12,12,12,12,12, 16,16,16,16,16,16,16,16,16,16,16,16, 20,20,20,20,20,20 &
|
|
],pInt),[lattice_hex_Ntwin,lattice_hex_Nslip],order=[2,1])
|
|
|
|
|
|
integer(pInt), dimension(lattice_hex_Ntwin,lattice_hex_Ntwin), target, private :: &
|
|
lattice_hex_interactionTwinTwin = reshape(int( [&
|
|
1, 5, 5, 5, 5, 5, 9, 9, 9, 9, 9, 9, 12,12,12,12,12,12, 14,14,14,14,14,14, & ! ---> twin
|
|
5, 1, 5, 5, 5, 5, 9, 9, 9, 9, 9, 9, 12,12,12,12,12,12, 14,14,14,14,14,14, & ! |
|
|
5, 5, 1, 5, 5, 5, 9, 9, 9, 9, 9, 9, 12,12,12,12,12,12, 14,14,14,14,14,14, & ! |
|
|
5, 5, 5, 1, 5, 5, 9, 9, 9, 9, 9, 9, 12,12,12,12,12,12, 14,14,14,14,14,14, & ! v twin
|
|
5, 5, 5, 5, 1, 5, 9, 9, 9, 9, 9, 9, 12,12,12,12,12,12, 14,14,14,14,14,14, &
|
|
5, 5, 5, 5, 5, 1, 9, 9, 9, 9, 9, 9, 12,12,12,12,12,12, 14,14,14,14,14,14, &
|
|
!
|
|
15,15,15,15,15,15, 2, 6, 6, 6, 6, 6, 10,10,10,10,10,10, 13,13,13,13,13,13, &
|
|
15,15,15,15,15,15, 6, 2, 6, 6, 6, 6, 10,10,10,10,10,10, 13,13,13,13,13,13, &
|
|
15,15,15,15,15,15, 6, 6, 2, 6, 6, 6, 10,10,10,10,10,10, 13,13,13,13,13,13, &
|
|
15,15,15,15,15,15, 6, 6, 6, 2, 6, 6, 10,10,10,10,10,10, 13,13,13,13,13,13, &
|
|
15,15,15,15,15,15, 6, 6, 6, 6, 2, 6, 10,10,10,10,10,10, 13,13,13,13,13,13, &
|
|
15,15,15,15,15,15, 6, 6, 6, 6, 6, 2, 10,10,10,10,10,10, 13,13,13,13,13,13, &
|
|
!
|
|
18,18,18,18,18,18, 16,16,16,16,16,16, 3, 7, 7, 7, 7, 7, 11,11,11,11,11,11, &
|
|
18,18,18,18,18,18, 16,16,16,16,16,16, 7, 3, 7, 7, 7, 7, 11,11,11,11,11,11, &
|
|
18,18,18,18,18,18, 16,16,16,16,16,16, 7, 7, 3, 7, 7, 7, 11,11,11,11,11,11, &
|
|
18,18,18,18,18,18, 16,16,16,16,16,16, 7, 7, 7, 3, 7, 7, 11,11,11,11,11,11, &
|
|
18,18,18,18,18,18, 16,16,16,16,16,16, 7, 7, 7, 7, 3, 7, 11,11,11,11,11,11, &
|
|
18,18,18,18,18,18, 16,16,16,16,16,16, 7, 7, 7, 7, 7, 3, 11,11,11,11,11,11, &
|
|
!
|
|
20,20,20,20,20,20, 19,19,19,19,19,19, 17,17,17,17,17,17, 4, 8, 8, 8, 8, 8, &
|
|
20,20,20,20,20,20, 19,19,19,19,19,19, 17,17,17,17,17,17, 8, 4, 8, 8, 8, 8, &
|
|
20,20,20,20,20,20, 19,19,19,19,19,19, 17,17,17,17,17,17, 8, 8, 4, 8, 8, 8, &
|
|
20,20,20,20,20,20, 19,19,19,19,19,19, 17,17,17,17,17,17, 8, 8, 8, 4, 8, 8, &
|
|
20,20,20,20,20,20, 19,19,19,19,19,19, 17,17,17,17,17,17, 8, 8, 8, 8, 4, 8, &
|
|
20,20,20,20,20,20, 19,19,19,19,19,19, 17,17,17,17,17,17, 8, 8, 8, 8, 8, 4 &
|
|
],pInt),[lattice_hex_Ntwin,lattice_hex_Ntwin],order=[2,1])
|
|
|
|
! Number of Non Schmid contributions for hex
|
|
integer(pInt), parameter, private :: NnonSchmid_hex = 0_pInt
|
|
|
|
! Tensor for each non schmid contribution
|
|
real(pReal), dimension(3,3,2,NnonSchmid_hex,lattice_hex_Nslip), parameter, private :: &
|
|
lattice_nonSchmid_hex = 0.0_pReal ! reshape([],[3,3,2,NnonSchmid_hex,lattice_hex_Nslip])
|
|
|
|
public :: &
|
|
lattice_init, &
|
|
lattice_initializeStructure, &
|
|
lattice_symmetryType, &
|
|
lattice_symmetrizeC66
|
|
|
|
contains
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief Maps structure to symmetry type
|
|
!> @details fcc(1) and bcc(2) are cubic(1) hex(3+) is hexagonal(2)
|
|
!--------------------------------------------------------------------------------------------------
|
|
integer(pInt) pure function lattice_symmetryType(structName)
|
|
|
|
implicit none
|
|
character(len=32), intent(in) :: structName
|
|
|
|
select case(structName(1:3))
|
|
case ('fcc','bcc')
|
|
lattice_symmetryType = 1_pInt
|
|
case ('hex')
|
|
lattice_symmetryType = 2_pInt
|
|
case default
|
|
lattice_symmetryType = 0_pInt
|
|
end select
|
|
|
|
return
|
|
|
|
end function lattice_symmetryType
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief Symmetrizes stiffness matrix according to lattice type
|
|
!--------------------------------------------------------------------------------------------------
|
|
pure function lattice_symmetrizeC66(structName,C66)
|
|
|
|
implicit none
|
|
|
|
character(len=32), intent(in) :: structName
|
|
real(pReal), dimension(6,6), intent(in) :: C66
|
|
real(pReal), dimension(6,6) :: lattice_symmetrizeC66
|
|
integer(pInt) :: j,k
|
|
|
|
lattice_symmetrizeC66 = 0.0_pReal
|
|
|
|
select case(structName(1:3))
|
|
case ('iso')
|
|
forall(k=1_pInt:3_pInt)
|
|
forall(j=1_pInt:3_pInt) lattice_symmetrizeC66(k,j) = C66(1,2)
|
|
lattice_symmetrizeC66(k,k) = C66(1,1)
|
|
lattice_symmetrizeC66(k+3,k+3) = 0.5_pReal*(C66(1,1)-C66(1,2))
|
|
end forall
|
|
case ('fcc','bcc')
|
|
forall(k=1_pInt:3_pInt)
|
|
forall(j=1_pInt:3_pInt) lattice_symmetrizeC66(k,j) = C66(1,2)
|
|
lattice_symmetrizeC66(k,k) = C66(1,1)
|
|
lattice_symmetrizeC66(k+3_pInt,k+3_pInt) = C66(4,4)
|
|
end forall
|
|
case ('hex')
|
|
lattice_symmetrizeC66(1,1) = C66(1,1)
|
|
lattice_symmetrizeC66(2,2) = C66(1,1)
|
|
lattice_symmetrizeC66(3,3) = C66(3,3)
|
|
lattice_symmetrizeC66(1,2) = C66(1,2)
|
|
lattice_symmetrizeC66(2,1) = C66(1,2)
|
|
lattice_symmetrizeC66(1,3) = C66(1,3)
|
|
lattice_symmetrizeC66(3,1) = C66(1,3)
|
|
lattice_symmetrizeC66(2,3) = C66(1,3)
|
|
lattice_symmetrizeC66(3,2) = C66(1,3)
|
|
lattice_symmetrizeC66(4,4) = C66(4,4)
|
|
lattice_symmetrizeC66(5,5) = C66(4,4)
|
|
lattice_symmetrizeC66(6,6) = 0.5_pReal*(C66(1,1)-C66(1,2))
|
|
case ('ort')
|
|
lattice_symmetrizeC66(1,1) = C66(1,1)
|
|
lattice_symmetrizeC66(2,2) = C66(2,2)
|
|
lattice_symmetrizeC66(3,3) = C66(3,3)
|
|
lattice_symmetrizeC66(1,2) = C66(1,2)
|
|
lattice_symmetrizeC66(2,1) = C66(1,2)
|
|
lattice_symmetrizeC66(1,3) = C66(1,3)
|
|
lattice_symmetrizeC66(3,1) = C66(1,3)
|
|
lattice_symmetrizeC66(2,3) = C66(2,3)
|
|
lattice_symmetrizeC66(3,2) = C66(2,3)
|
|
lattice_symmetrizeC66(4,4) = C66(4,4)
|
|
lattice_symmetrizeC66(5,5) = C66(5,5)
|
|
lattice_symmetrizeC66(6,6) = C66(6,6)
|
|
end select
|
|
|
|
return
|
|
|
|
end function lattice_symmetrizeC66
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief Module initialization
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine lattice_init
|
|
|
|
use, intrinsic :: iso_fortran_env ! to get compiler_version and compiler_options (at least for gfortran 4.6 at the moment)
|
|
use IO, only: IO_open_file,&
|
|
IO_open_jobFile_stat, &
|
|
IO_countSections, &
|
|
IO_countTagInPart, &
|
|
IO_error
|
|
use material, only: material_configfile, &
|
|
material_localFileExt, &
|
|
material_partPhase
|
|
use debug, only: debug_level, &
|
|
debug_lattice, &
|
|
debug_levelBasic
|
|
|
|
implicit none
|
|
integer(pInt), parameter :: fileunit = 200_pInt
|
|
integer(pInt) :: Nsections
|
|
|
|
!$OMP CRITICAL (write2out)
|
|
write(6,*)
|
|
write(6,*) '<<<+- lattice init -+>>>'
|
|
write(6,*) '$Id$'
|
|
#include "compilation_info.f90"
|
|
!$OMP END CRITICAL (write2out)
|
|
|
|
if (.not. IO_open_jobFile_stat(fileunit,material_localFileExt)) then ! no local material configuration present...
|
|
call IO_open_file(fileunit,material_configFile) ! ... open material.config file
|
|
endif
|
|
Nsections = IO_countSections(fileunit,material_partPhase)
|
|
lattice_Nstructure = 2_pInt + sum(IO_countTagInPart(fileunit,material_partPhase,'covera_ratio',Nsections)) ! fcc + bcc + all hex
|
|
! lattice_Nstructure = Nsections + 2_pInt ! most conservative assumption
|
|
close(fileunit)
|
|
|
|
if (iand(debug_level(debug_lattice),debug_levelBasic) /= 0_pInt) then
|
|
!$OMP CRITICAL (write2out)
|
|
write(6,'(a16,1x,i5)') '# phases:',Nsections
|
|
write(6,'(a16,1x,i5)') '# structures:',lattice_Nstructure
|
|
write(6,*)
|
|
!$OMP END CRITICAL (write2out)
|
|
endif
|
|
|
|
allocate(NnonSchmid(lattice_Nstructure)); NnonSchmid = 0_pInt
|
|
allocate(lattice_Sslip(3,3,lattice_maxNslip,lattice_Nstructure)); lattice_Sslip = 0.0_pReal
|
|
allocate(lattice_Sslip_v(6,1+2*lattice_maxNonSchmid,lattice_maxNslip,lattice_Nstructure)); lattice_Sslip_v = 0.0_pReal
|
|
allocate(lattice_sd(3,lattice_maxNslip,lattice_Nstructure)); lattice_sd = 0.0_pReal
|
|
allocate(lattice_st(3,lattice_maxNslip,lattice_Nstructure)); lattice_st = 0.0_pReal
|
|
allocate(lattice_sn(3,lattice_maxNslip,lattice_Nstructure)); lattice_sn = 0.0_pReal
|
|
|
|
allocate(lattice_Qtwin(3,3,lattice_maxNtwin,lattice_Nstructure)); lattice_Qtwin = 0.0_pReal
|
|
allocate(lattice_Stwin(3,3,lattice_maxNtwin,lattice_Nstructure)); lattice_Stwin = 0.0_pReal
|
|
allocate(lattice_Stwin_v(6,lattice_maxNtwin,lattice_Nstructure)); lattice_Stwin_v = 0.0_pReal
|
|
allocate(lattice_td(3,lattice_maxNtwin,lattice_Nstructure)); lattice_td = 0.0_pReal
|
|
allocate(lattice_tt(3,lattice_maxNtwin,lattice_Nstructure)); lattice_tt = 0.0_pReal
|
|
allocate(lattice_tn(3,lattice_maxNtwin,lattice_Nstructure)); lattice_tn = 0.0_pReal
|
|
|
|
allocate(lattice_shearTwin(lattice_maxNtwin,lattice_Nstructure)); lattice_shearTwin = 0.0_pReal
|
|
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allocate(lattice_NslipSystem(lattice_maxNslipFamily,lattice_Nstructure)); lattice_NslipSystem = 0_pInt
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allocate(lattice_NtwinSystem(lattice_maxNtwinFamily,lattice_Nstructure)); lattice_NtwinSystem = 0_pInt
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allocate(lattice_interactionSlipSlip(lattice_maxNslip,lattice_maxNslip,lattice_Nstructure))
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lattice_interactionSlipSlip = 0_pInt ! other:me
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allocate(lattice_interactionSlipTwin(lattice_maxNslip,lattice_maxNtwin,lattice_Nstructure))
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lattice_interactionSlipTwin = 0_pInt ! other:me
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allocate(lattice_interactionTwinSlip(lattice_maxNtwin,lattice_maxNslip,lattice_Nstructure))
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lattice_interactionTwinSlip = 0_pInt ! other:me
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allocate(lattice_interactionTwinTwin(lattice_maxNtwin,lattice_maxNtwin,lattice_Nstructure))
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lattice_interactionTwinTwin = 0_pInt ! other:me
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end subroutine lattice_init
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!--------------------------------------------------------------------------------------------------
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!> @brief Calculation of Schmid matrices, etc.
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!--------------------------------------------------------------------------------------------------
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integer(pInt) function lattice_initializeStructure(struct,CoverA)
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use prec, only: pReal,pInt
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use math, only: math_vectorproduct, &
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math_tensorproduct, &
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math_norm3, &
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math_trace33, &
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math_symmetric33, &
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math_Mandel33to6, &
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math_axisAngleToR, &
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INRAD
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use IO, only: IO_error
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implicit none
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character(len=*) struct
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real(pReal) CoverA
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real(pReal), dimension(3,lattice_maxNslip) :: sd = 0.0_pReal, &
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sn = 0.0_pReal
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real(pReal), dimension(12,lattice_maxNonSchmid,lattice_maxNslip) :: sns = 0.0_pReal
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real(pReal), dimension(3,lattice_maxNtwin) :: td = 0.0_pReal, &
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tn = 0.0_pReal
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real(pReal), dimension(lattice_maxNtwin) :: ts = 0.0_pReal
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integer(pInt), dimension(lattice_maxNslipFamily) :: myNslipSystem = 0_pInt
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integer(pInt), dimension(lattice_maxNtwinFamily) :: myNtwinSystem = 0_pInt
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integer(pInt) :: i,j,myNslip,myNtwin,myStructure = 0_pInt
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logical :: processMe
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processMe = .false.
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select case(struct(1:3)) ! check first three chars of structure name
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case ('fcc')
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myStructure = 1_pInt
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myNslipSystem = lattice_fcc_NslipSystem ! size of slip system families
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myNtwinSystem = lattice_fcc_NtwinSystem ! size of twin system families
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myNslip = lattice_fcc_Nslip ! overall number of slip systems
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myNtwin = lattice_fcc_Ntwin ! overall number of twin systems
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lattice_fcc_Nstructure = lattice_fcc_Nstructure + 1_pInt ! count fcc instances
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if (lattice_fcc_Nstructure == 1_pInt) then ! me is first fcc structure
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processMe = .true.
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NnonSchmid(myStructure) = NnonSchmid_fcc ! Currently no known non schmid contributions for FCC (to be changed later)
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do i = 1_pInt,myNslip ! assign slip system vectors
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sd(1:3,i) = lattice_fcc_systemSlip(1:3,i)
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sn(1:3,i) = lattice_fcc_systemSlip(4:6,i)
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do j = 1_pInt, NnonSchmid_fcc
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sns(1:6,j,i) = math_Mandel33to6(lattice_nonSchmid_fcc(1:3,1:3,1,j,i))
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sns(7:12,j,i) = math_Mandel33to6(lattice_nonSchmid_fcc(1:3,1:3,2,j,i))
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enddo
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enddo
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do i = 1_pInt,myNtwin ! assign twin system vectors and shears
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td(1:3,i) = lattice_fcc_systemTwin(1:3,i)
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tn(1:3,i) = lattice_fcc_systemTwin(4:6,i)
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ts(i) = lattice_fcc_shearTwin(i)
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enddo
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interactionSlipSlip => lattice_fcc_interactionSlipSlip
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interactionSlipTwin => lattice_fcc_interactionSlipTwin
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interactionTwinSlip => lattice_fcc_interactionTwinSlip
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interactionTwinTwin => lattice_fcc_interactionTwinTwin
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endif
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case ('bcc')
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myStructure = 2_pInt
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myNslipSystem = lattice_bcc_NslipSystem ! size of slip system families
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myNtwinSystem = lattice_bcc_NtwinSystem ! size of twin system families
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myNslip = lattice_bcc_Nslip ! overall number of slip systems
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myNtwin = lattice_bcc_Ntwin ! overall number of twin systems
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lattice_bcc_Nstructure = lattice_bcc_Nstructure + 1_pInt ! count bcc instances
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if (lattice_bcc_Nstructure == 1_pInt) then ! me is first bcc structure
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processMe = .true.
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NnonSchmid(myStructure) = NnonSchmid_BCC ! 5 known non schmid contributions for BCC (A. Koester, A. Ma, A. Hartmaier 2012)
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do i = 1_pInt,myNslip ! assign slip system vectors
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sd(1:3,i) = lattice_bcc_systemSlip(1:3,i)
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sn(1:3,i) = lattice_bcc_systemSlip(4:6,i)
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do j = 1_pInt, NnonSchmid_bcc
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sns(1:6,j,i) = math_Mandel33to6(lattice_nonSchmid_bcc(1:3,1:3,1,j,i))
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sns(7:12,j,i) = math_Mandel33to6(lattice_nonSchmid_bcc(1:3,1:3,2,j,i))
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enddo
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enddo
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do i = 1_pInt,myNtwin ! assign twin system vectors and shears
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td(1:3,i) = lattice_bcc_systemTwin(1:3,i)
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tn(1:3,i) = lattice_bcc_systemTwin(4:6,i)
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ts(i) = lattice_bcc_shearTwin(i)
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enddo
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interactionSlipSlip => lattice_bcc_interactionSlipSlip
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interactionSlipTwin => lattice_bcc_interactionSlipTwin
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interactionTwinSlip => lattice_bcc_interactionTwinSlip
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interactionTwinTwin => lattice_bcc_interactionTwinTwin
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endif
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case ('hex')
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if (CoverA >= 1.0_pReal) then ! checking physical significance of c/a
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lattice_hex_Nstructure = lattice_hex_Nstructure + 1_pInt ! count instances of hex structures
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myStructure = 2_pInt + lattice_hex_Nstructure ! 3,4,5,.. for hex
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myNslipSystem = lattice_hex_NslipSystem ! size of slip system families
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myNtwinSystem = lattice_hex_NtwinSystem ! size of twin system families
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myNslip = lattice_hex_Nslip ! overall number of slip systems
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myNtwin = lattice_hex_Ntwin ! overall number of twin systems
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processMe = .true.
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NnonSchmid(myStructure) = NnonSchmid_hex ! Currently no known non schmid contributions for hex (to be changed later)
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! converting from 4 axes coordinate system (a1=a2=a3=c) to ortho-hexgonal system (a, b, c)
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do i = 1_pInt,myNslip
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sd(1,i) = lattice_hex_systemSlip(1,i)*1.5_pReal ! direction [uvtw]->[3u/2 (u+2v)*sqrt(3)/2 w*(c/a)]
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sd(2,i) = (lattice_hex_systemSlip(1,i)+2.0_pReal*lattice_hex_systemSlip(2,i))*(0.5_pReal*sqrt(3.0_pReal))
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sd(3,i) = lattice_hex_systemSlip(4,i)*CoverA
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sn(1,i) = lattice_hex_systemSlip(5,i) ! plane (hkil)->(h (h+2k)/sqrt(3) l/(c/a))
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sn(2,i) = (lattice_hex_systemSlip(5,i)+2.0_pReal*lattice_hex_systemSlip(6,i))/sqrt(3.0_pReal)
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sn(3,i) = lattice_hex_systemSlip(8,i)/CoverA
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do j = 1_pInt, NnonSchmid_hex
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sns(1:6,j,i) = math_Mandel33to6(lattice_nonSchmid_hex(1:3,1:3,1,j,i))
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sns(7:12,j,i) = math_Mandel33to6(lattice_nonSchmid_hex(1:3,1:3,2,j,i))
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|
enddo
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enddo
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do i = 1_pInt,myNtwin
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td(1,i) = lattice_hex_systemTwin(1,i)*1.5_pReal
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|
td(2,i) = (lattice_hex_systemTwin(1,i)+2.0_pReal*lattice_hex_systemTwin(2,i))*(0.5_pReal*sqrt(3.0_pReal))
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|
td(3,i) = lattice_hex_systemTwin(4,i)*CoverA
|
|
tn(1,i) = lattice_hex_systemTwin(5,i)
|
|
tn(2,i) = (lattice_hex_systemTwin(5,i)+2.0_pReal*lattice_hex_systemTwin(6,i))/sqrt(3.0_pReal)
|
|
tn(3,i) = lattice_hex_systemTwin(8,i)/CoverA
|
|
|
|
select case(lattice_hex_shearTwin(i)) ! from Christian & Mahajan 1995 p.29
|
|
case (1_pInt) ! {10.2}<-10.1>
|
|
ts(i) = (3.0_pReal-CoverA*CoverA)/sqrt(3.0_pReal)/CoverA
|
|
case (2_pInt) ! {11.2}<11.-3>
|
|
ts(i) = 2.0_pReal*(CoverA*CoverA-2.0_pReal)/3.0_pReal/CoverA
|
|
case (3_pInt) ! {11.1}<-1-1.6>
|
|
ts(i) = 1.0_pReal/CoverA
|
|
case (4_pInt) ! {10.1}<10.-2>
|
|
ts(i) = (4.0_pReal*CoverA*CoverA-9.0_pReal)/4.0_pReal/sqrt(3.0_pReal)/CoverA
|
|
end select
|
|
|
|
enddo
|
|
interactionSlipSlip => lattice_hex_interactionSlipSlip
|
|
interactionSlipTwin => lattice_hex_interactionSlipTwin
|
|
interactionTwinSlip => lattice_hex_interactionTwinSlip
|
|
interactionTwinTwin => lattice_hex_interactionTwinTwin
|
|
endif
|
|
end select
|
|
|
|
if (processMe) then
|
|
if (myStructure > lattice_Nstructure) &
|
|
call IO_error(666_pInt,myStructure,ext_msg = 'structure index out of bounds') ! check for memory leakage
|
|
do i = 1_pInt,myNslip ! store slip system vectors and Schmid matrix for my structure
|
|
lattice_sd(1:3,i,myStructure) = sd(1:3,i)/math_norm3(sd(1:3,i)) ! make unit vector
|
|
lattice_sn(1:3,i,myStructure) = sn(1:3,i)/math_norm3(sn(1:3,i)) ! make unit vector
|
|
lattice_st(1:3,i,myStructure) = math_vectorproduct(lattice_sd(1:3,i,myStructure), &
|
|
lattice_sn(1:3,i,myStructure))
|
|
lattice_Sslip(1:3,1:3,i,myStructure) = math_tensorproduct(lattice_sd(1:3,i,myStructure), &
|
|
lattice_sn(1:3,i,myStructure))
|
|
lattice_Sslip_v(1:6,1,i,myStructure) = math_Mandel33to6(math_symmetric33(lattice_Sslip(1:3,1:3,i,myStructure)))
|
|
do j = 1_pInt, NnonSchmid(myStructure)
|
|
lattice_Sslip_v(1:6,2*j,i,myStructure) = sns(1:6,j,i)
|
|
lattice_Sslip_v(1:6,2*j+1,i,myStructure) = sns(7:12,j,i)
|
|
enddo
|
|
if (abs(math_trace33(lattice_Sslip(1:3,1:3,i,myStructure))) > 1.0e-8_pReal) &
|
|
call IO_error(0_pInt,myStructure,i,0_pInt,ext_msg = 'dilatational slip Schmid matrix')
|
|
enddo
|
|
do i = 1_pInt,myNtwin ! store twin system vectors and Schmid plus rotation matrix for my structure
|
|
lattice_td(1:3,i,myStructure) = td(1:3,i)/math_norm3(td(1:3,i)) ! make unit vector
|
|
lattice_tn(1:3,i,myStructure) = tn(1:3,i)/math_norm3(tn(1:3,i)) ! make unit vector
|
|
lattice_tt(1:3,i,myStructure) = math_vectorproduct(lattice_td(1:3,i,myStructure), &
|
|
lattice_tn(1:3,i,myStructure))
|
|
lattice_Stwin(1:3,1:3,i,myStructure) = math_tensorproduct(lattice_td(1:3,i,myStructure), &
|
|
lattice_tn(1:3,i,myStructure))
|
|
lattice_Stwin_v(1:6,i,myStructure) = math_Mandel33to6(math_symmetric33(lattice_Stwin(1:3,1:3,i,myStructure)))
|
|
lattice_Qtwin(1:3,1:3,i,myStructure) = math_AxisAngleToR(tn(1:3,i),180.0_pReal*INRAD)
|
|
lattice_shearTwin(i,myStructure) = ts(i)
|
|
if (abs(math_trace33(lattice_Stwin(1:3,1:3,i,myStructure))) > 1.0e-8_pReal) &
|
|
call IO_error(0_pInt,myStructure,i,0_pInt,ext_msg = 'dilatational twin Schmid matrix')
|
|
enddo
|
|
lattice_NslipSystem(1:lattice_maxNslipFamily,myStructure) = myNslipSystem ! number of slip systems in each family
|
|
lattice_NtwinSystem(1:lattice_maxNtwinFamily,myStructure) = myNtwinSystem ! number of twin systems in each family
|
|
lattice_interactionSlipSlip(1:myNslip,1:myNslip,myStructure) = interactionSlipSlip(1:myNslip,1:myNslip)
|
|
lattice_interactionSlipTwin(1:myNslip,1:myNtwin,myStructure) = interactionSlipTwin(1:myNslip,1:myNtwin)
|
|
lattice_interactionTwinSlip(1:myNtwin,1:myNslip,myStructure) = interactionTwinSlip(1:myNtwin,1:myNslip)
|
|
lattice_interactionTwinTwin(1:myNtwin,1:myNtwin,myStructure) = interactionTwinTwin(1:myNtwin,1:myNtwin)
|
|
endif
|
|
|
|
lattice_initializeStructure = myStructure ! report my structure index back
|
|
|
|
end function lattice_initializeStructure
|
|
|
|
end module lattice
|