completed correspondence_matrix

This commit is contained in:
achalhp 2024-04-08 18:30:52 +05:30
parent 632d7571b2
commit 31dadd67ca
3 changed files with 118 additions and 9 deletions

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@ -1,16 +1,76 @@
module math
implicit none
contains
function math_axisAngleToR(axis,omega) result(math_axisAngleToR1)
implicit none
real, dimension(3), intent(in) :: axis
real, intent(in) :: omega
real, dimension(3) :: n
real :: norm,s,c,c1
real, dimension(3,3), parameter :: &
I3 = real(reshape([&
1, 0, 0, &
0, 1, 0, &
0, 0, 1 &
],shape(I3))) !< 3x3 Identity
real, dimension(3,3) :: math_axisAngleToR1
norm = norm2(axis)
wellDefined: if (norm > 1.0e-8) then
n = axis/norm ! normalize axis to be sure
s = sin(omega)
c = cos(omega)
c1 = 1.0 - c
math_axisAngleToR1(1,1) = c + c1*n(1)**2.0
math_axisAngleToR1(1,2) = c1*n(1)*n(2) - s*n(3)
math_axisAngleToR1(1,3) = c1*n(1)*n(3) + s*n(2)
math_axisAngleToR1(2,1) = c1*n(1)*n(2) + s*n(3)
math_axisAngleToR1(2,2) = c + c1*n(2)**2.0
math_axisAngleToR1(2,3) = c1*n(2)*n(3) - s*n(1)
math_axisAngleToR1(3,1) = c1*n(1)*n(3) - s*n(2)
math_axisAngleToR1(3,2) = c1*n(2)*n(3) + s*n(1)
math_axisAngleToR1(3,3) = c + c1*n(3)**2.0
else wellDefined
math_axisAngleToR1 = I3
endif wellDefined
end function
end module math
program corresponcence_matrix program corresponcence_matrix
implicit none use math
implicit none
integer, dimension(4) :: & integer, dimension(4) :: &
active = [6,0,6,0], & active = [6,6,6,6], & !< number of active twin systems
potential = [6,6,6,6] potential = [6,6,6,6] !< all the potential twin systems
real, dimension(3) :: & real, dimension(3) :: &
direction, normal direction, normal
real, dimension(3,12) :: normal_vector real, dimension(3,24) :: normal_vector, direction_vector
real, dimension(3,3,24) :: SchmidMatrix, corresponcenceMatrix
real, dimension(24) :: characteristicShear
real :: cOverA = 1.6235 real :: cOverA = 1.6235
real :: pi = 3.14159274
real, dimension(8,24) :: & real, dimension(8,24) :: &
system = reshape(real([& system = reshape(real([&
! <-10.1>{10.2} systems, shear = (3-(c/a)^2)/(sqrt(3) c/a) ! <-10.1>{10.2} systems, shear = (3-(c/a)^2)/(sqrt(3) c/a)
@ -47,11 +107,21 @@ program corresponcence_matrix
2, -1, -1, -3, 2, -1, -1, 2 & 2, -1, -1, -3, 2, -1, -1, 2 &
]),shape(system)) ]),shape(system))
real, dimension(3,3), parameter :: &
I3 = real(reshape([&
1, 0, 0, &
0, 1, 0, &
0, 0, 1 &
],shape(I3))) !< 3x3 Identity
integer :: & integer :: &
a, & !< index of active system a, & !< index of active system
p, & !< index in potential system matrix p, & !< index in potential system matrix
f, & !< index of my family f, & !< index of my family
s !< index of my system in current family s, f1, s1, e1, i, j, k !< index of my system in current family
a = 0 a = 0
do f = 1, size(active,1) !< Loops 1 to 4 for hP do f = 1, size(active,1) !< Loops 1 to 4 for hP
@ -70,12 +140,51 @@ program corresponcence_matrix
normal_vector(1:3,a) = normal /norm2(normal) normal_vector(1:3,a) = normal /norm2(normal)
write(6,*)'normal vector', normal_vector direction_vector(1:3,a) = direction / norm2(direction)
end do end do
end do end do
do f = 1,size(active,1) do f1 = 1,size(active,1)
s1 = sum(active(:f1-1)) + 1
e1 = sum(active(:f1))
select case(f1)
case (1)
characteristicShear(s1:e1) = (3.0-cOverA**2)/sqrt(3.0)/cOverA
case (2)
characteristicShear(s1:e1) = 1.0/cOverA
case (3)
characteristicShear(s1:e1) = (4.0*cOverA**2-9.0)/sqrt(48.0)/cOverA
case (4)
characteristicShear(s1:e1) = 2.0*(cOverA**2-2.0)/3.0/cOverA
end select
enddo
write(6,*)'characteristic shear, 1, 0, -1, 1, -1, 0, 1, 2, = ',characteristicShear(4)
write(6,*)'characteristic shear, -1, -1, 2, 6, 1, 1, -2, 1, =',characteristicShear(7)
write(6,*)'characteristic shear, 1, 0, -1, -2, 1, 0, -1, 1, =',characteristicShear(13)
write(6,*)'characteristic shear, 1, 1, -2, -3, 1, 1, -2, 2, =',characteristicShear(19)
do i = 1, sum(active)
forall(j=1:3, k=1:3) SchmidMatrix(j,k,i) = direction_vector(j,i) * normal_vector(k,i)
enddo enddo
end program corresponcence_matrix do i = 1, sum(active)
corresponcenceMatrix(1:3,1:3,i) = matmul(math_axisAngleToR(normal_vector(1:3,i),pi),&
I3+characteristicShear(i)*SchmidMatrix(1:3,1:3,i))
enddo
write(6,*)'correspondence matrix for 1, 0, -1, 1, -1, 0, 1, 2 =====',corresponcenceMatrix(1:3,1:3,4)
write(6,*)'ooooooooooooooooooooooooooooooooooooooooooooooo'
write(6,*)'correspondence matrix for -1, -1, 2, 6, 1, 1, -2, 1 =====',corresponcenceMatrix(1:3,1:3,7)
write(6,*)'ooooooooooooooooooooooooooooooooooooooooooooooo'
write(6,*)'correspondence matrix for 1, 0, -1, -2, 1, 0, -1, 1 =====',corresponcenceMatrix(1:3,1:3,13)
write(6,*)'ooooooooooooooooooooooooooooooooooooooooooooooo'
write(6,*)'correspondence matrix for 1, 1, -2, -3, 1, 1, -2, 2 =====',corresponcenceMatrix(1:3,1:3,19)
end program corresponcence_matrix

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