added Mandel notation transformations for sym 3x3x3x3 and 3x3 tensors
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Philip Eisenlohr
parent
dfd73a72ea
commit
9241c7de91
179
trunk/math.f90
179
trunk/math.f90
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@ -19,6 +19,24 @@
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CONTAINS
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! *** Initialize random number generator ***
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! *** for later use in mpie_fiber and mpie_disturbOri ***
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SUBROUTINE math_init ()
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use prec, only: pReal,pInt
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implicit none
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integer (pInt) seed
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call random_seed()
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call get_seed(seed)
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call halton_seed_set(seed)
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call halton_ndim_set(3)
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END SUBROUTINE
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SUBROUTINE math_invert3x3(A, InvA, DetA, err)
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! Bestimmung der Determinanten und Inversen einer 3x3-Matrix
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@ -219,17 +237,13 @@
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! Triangulation
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DO J = I + 1, 6
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Quote = A(J,I) / A(I,I)
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DO K = I + 1, 6
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A(J,K) = A(J,K) - Quote * A(I,K)
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END DO
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DO K = 1, 6
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B(J,K) = B(J,K) - Quote * B(I,K)
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END DO
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END DO
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! Bestimmung des groessten Pivotelementes
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@ -257,17 +271,12 @@
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! R U E C K W A E R T S A U F L O E S U N G
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DO I = 6, 1, -1
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DO L = 1, 6
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DO J = I + 1, 6
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B(I,L) = B(I,L) - A(I,J) * B(J,L)
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END DO
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B(I,L) = B(I,L) / A(I,I)
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END DO
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END DO
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! Sortieren der Unbekanntenvektoren?
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@ -275,16 +284,12 @@
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IF (SortX) THEN
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DO L = 1, 6
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StoreA(1:6) = B(1:6,L)
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DO I = 1, 6
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J = XNr(I)
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B(J,L) = StoreA(I)
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END DO
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END DO
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END IF
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! Determinante
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@ -305,27 +310,6 @@
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END SUBROUTINE Gauss
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! *** Initialize random number generator ***
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! *** for later use in mpie_fiber and mpie_disturbOri ***
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SUBROUTINE math_init ()
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use prec, only: pReal,pInt
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implicit none
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integer (pInt) seed
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call random_seed()
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call get_seed(seed)
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call halton_seed_set(seed)
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call halton_ndim_set(3)
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END SUBROUTINE
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!********************************************************************
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! calculate v6 stress from M6x6 stiffness and v6 strain
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!********************************************************************
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@ -363,6 +347,133 @@
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END FUNCTION
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!********************************************************************
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! convert a symmetric 3x3 matrix into Mandel vector 6x1
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!********************************************************************
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FUNCTION math_Mandel33to6(m33)
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use prec, only: pReal,pInt
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implicit none
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real(pReal), dimension(3,3) :: m33
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real(pReal), dimension(6) :: math_Mandel33to6
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integer(pInt) i
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real(pReal), dimension(6), parameter :: nrm = &
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(/1.0_pReal,1.0_pReal,1.0_pReal,dsqrt(2.0_pReal),dsqrt(2.0_pReal),dsqrt(2.0_pReal)/)
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integer(pInt), dimension (2,6), parameter :: map = &
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reshape((/&
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1,1, &
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2,2, &
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3,3, &
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1,2, &
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2,3, &
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1,3 &
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/),(/2,6/))
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forall (i=1:6) math_Mandel33to6(i) = nrm(i)*m33(map(1,i),map(2,i))
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return
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END FUNCTION
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!********************************************************************
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! convert Mandel 6x1 back to symmetric 3x3 matrix
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!********************************************************************
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FUNCTION math_Mandel6to33(v6)
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use prec, only: pReal,pInt
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implicit none
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real(pReal), dimension(6) :: v6
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real(pReal), dimension(3,3) :: math_Mandel6to33
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integer(pInt) i,j
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real(pReal), dimension(6), parameter :: nrm = &
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(/1.0_pReal,1.0_pReal,1.0_pReal,dsqrt(0.5_pReal),dsqrt(0.5_pReal),dsqrt(0.5_pReal)/)
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integer(pInt), dimension (2,6), parameter :: map = &
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reshape((/&
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1,1, &
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2,2, &
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3,3, &
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1,2, &
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2,3, &
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1,3 &
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/),(/2,6/))
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forall (i=1:6)
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math_Mandel6to33(map(1,i),map(2,i)) = nrm(i)*v6(i)
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math_Mandel6to33(map(2,i),map(1,i)) = nrm(i)*v6(i)
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end forall
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return
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END FUNCTION
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!********************************************************************
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! convert symmetric 3x3x3x3 tensor into Mandel matrix 6x6
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!********************************************************************
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FUNCTION math_Mandel3333to66(m3333)
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use prec, only: pReal,pInt
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implicit none
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real(pReal), dimension(3,3,3,3) :: m3333
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real(pReal), dimension(6,6) :: math_Mandel3333to66
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integer(pInt) i,j
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real(pReal), dimension(6), parameter :: nrm = &
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(/1.0_pReal,1.0_pReal,1.0_pReal,dsqrt(2.0_pReal),dsqrt(2.0_pReal),dsqrt(2.0_pReal)/)
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integer(pInt), dimension (2,6), parameter :: map = &
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reshape((/&
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1,1, &
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2,2, &
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3,3, &
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1,2, &
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2,3, &
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1,3 &
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/),(/2,6/))
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forall (i=1:6,j=1:6) math_Mandel3333to66(i,j) = &
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nrm(i)*nrm(j)*m3333(map(1,i),map(2,i),map(1,j),map(2,j))
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return
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END FUNCTION
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!********************************************************************
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! convert Mandel matrix 6x6 back to symmetric 3x3x3x3 tensor
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!********************************************************************
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FUNCTION math_Mandel66to3333(m66)
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use prec, only: pReal,pInt
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implicit none
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real(pReal), dimension(6,6) :: m66
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real(pReal), dimension(3,3,3,3) :: math_Mandel66to3333
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integer(pInt) i,j
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real(pReal), dimension(6), parameter :: nrm = &
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(/1.0_pReal,1.0_pReal,1.0_pReal,dsqrt(0.5_pReal),dsqrt(0.5_pReal),dsqrt(0.5_pReal)/)
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integer(pInt), dimension (2,6), parameter :: map = &
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reshape((/&
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1,1, &
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2,2, &
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3,3, &
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1,2, &
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2,3, &
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1,3 &
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/),(/2,6/))
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forall (i=1:6,j=1:6)
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math_Mandel66to3333(map(1,i),map(2,i),map(1,j),map(2,j)) = nrm(i)*nrm(j)*m66(i,j)
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math_Mandel66to3333(map(2,i),map(1,i),map(1,j),map(2,j)) = nrm(i)*nrm(j)*m66(i,j)
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math_Mandel66to3333(map(1,i),map(2,i),map(2,j),map(1,j)) = nrm(i)*nrm(j)*m66(i,j)
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math_Mandel66to3333(map(2,i),map(1,i),map(2,j),map(1,j)) = nrm(i)*nrm(j)*m66(i,j)
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end forall
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return
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END FUNCTION
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!********************************************************************
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! convert a symmetric 3,3 matrix into an array of 6
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!********************************************************************
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