Added ideas for Voigt<->Mandel transformations (PE)
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Luc Hantcherli
parent
4b69c1d738
commit
3ba46ac7d7
128
trunk/math.f90
128
trunk/math.f90
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@ -17,20 +17,34 @@
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1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,1.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,1.0_pReal /),(/3,3/))
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! *** Mandel notation ***
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integer(pInt), dimension (2,6), parameter :: mapMandel = &
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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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real(pReal), dimension(6), parameter :: nrmMandel = &
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(/1.0_pReal,1.0_pReal,1.0_pReal, 1.414213562373095_pReal, 1.414213562373095_pReal, 1.414213562373095_pReal/)
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real(pReal), dimension(6), parameter :: invnrmMandel = &
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(/1.0_pReal,1.0_pReal,1.0_pReal,0.7071067811865476_pReal,0.7071067811865476_pReal,0.7071067811865476_pReal/)
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! *** Mandel notation ***
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integer(pInt), dimension (2,6), parameter :: mapMandel = &
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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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real(pReal), dimension(6), parameter :: nrmMandel = &
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(/1.0_pReal,1.0_pReal,1.0_pReal, 1.414213562373095_pReal, 1.414213562373095_pReal, 1.414213562373095_pReal/)
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real(pReal), dimension(6), parameter :: invnrmMandel = &
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(/1.0_pReal,1.0_pReal,1.0_pReal,0.7071067811865476_pReal,0.7071067811865476_pReal,0.7071067811865476_pReal/)
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! *** Voigt notation ***
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integer(pInt), dimension (2,6), parameter :: mapMandel = &
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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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2,3, &
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1,3, &
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1,2 &
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/),(/2,6/))
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real(pReal), dimension(6), parameter :: nrmVoigt = &
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(/1.0_pReal,1.0_pReal,1.0_pReal,1.0_pReal,1.0_pReal,1.0_pReal/)
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real(pReal), dimension(6), parameter :: invnrmVoigt = &
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(/1.0_pReal,1.0_pReal,1.0_pReal,1.0_pReal,1.0_pReal,1.0_pReal/)
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CONTAINS
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@ -326,23 +340,6 @@
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END SUBROUTINE Gauss
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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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FUNCTION math_Hooke(C,e)
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use prec, only: pReal,pInt
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implicit none
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real(pReal) C(6,6), e(6), factoredE(6)
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real(pReal), dimension(6), parameter :: preFactor = (/1.0_pReal,1.0_pReal,1.0_pReal,2.0_pReal,2.0_pReal,2.0_pReal/)
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real(pReal) math_Hooke(6)
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factoredE = dot_product(preFactor,e)
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math_Hooke = matmul(C,factoredE)
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return
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END FUNCTION
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!********************************************************************
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@ -421,29 +418,52 @@
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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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forall (i=1:6,j=1:6)
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math_Mandel66to3333(mapMandel(1,i),mapMandel(2,i),mapMandel(1,j),mapMandel(2,j)) = invnrmMandel(i)*invnrmMandel(j)*m66(i,j)
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math_Mandel66to3333(mapMandel(2,i),mapMandel(1,i),mapMandel(1,j),mapMandel(2,j)) = invnrmMandel(i)*invnrmMandel(j)*m66(i,j)
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math_Mandel66to3333(mapMandel(1,i),mapMandel(2,i),mapMandel(2,j),mapMandel(1,j)) = invnrmMandel(i)*invnrmMandel(j)*m66(i,j)
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math_Mandel66to3333(mapMandel(2,i),mapMandel(1,i),mapMandel(2,j),mapMandel(1,j)) = invnrmMandel(i)*invnrmMandel(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 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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forall (i=1:6,j=1:6)
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math_Mandel66to3333(mapMandel(1,i),mapMandel(2,i),mapMandel(1,j),mapMandel(2,j)) = invnrmMandel(i)*invnrmMandel(j)*m66(i,j)
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math_Mandel66to3333(mapMandel(2,i),mapMandel(1,i),mapMandel(1,j),mapMandel(2,j)) = invnrmMandel(i)*invnrmMandel(j)*m66(i,j)
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math_Mandel66to3333(mapMandel(1,i),mapMandel(2,i),mapMandel(2,j),mapMandel(1,j)) = invnrmMandel(i)*invnrmMandel(j)*m66(i,j)
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math_Mandel66to3333(mapMandel(2,i),mapMandel(1,i),mapMandel(2,j),mapMandel(1,j)) = invnrmMandel(i)*invnrmMandel(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 Voigt matrix 6x6 back to symmetric 3x3x3x3 tensor
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!********************************************************************
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FUNCTION math_Voigt66to3333(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_Voigt66to3333
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integer(pInt) i,j
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forall (i=1:6,j=1:6)
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math_Voigt66to3333(mapVoigt(1,i),mapVoigt(2,i),mapVoigt(1,j),mapVoigt(2,j)) = invnrmVoigt(i)*invnrmVoigt(j)*m66(i,j)
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math_Voigt66to3333(mapVoigt(2,i),mapVoigt(1,i),mapVoigt(1,j),mapVoigt(2,j)) = invnrmVoigt(i)*invnrmVoigt(j)*m66(i,j)
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math_Voigt66to3333(mapVoigt(1,i),mapVoigt(2,i),mapVoigt(2,j),mapVoigt(1,j)) = invnrmVoigt(i)*invnrmVoigt(j)*m66(i,j)
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math_Voigt66to3333(mapVoigt(2,i),mapVoigt(1,i),mapVoigt(2,j),mapVoigt(1,j)) = invnrmVoigt(i)*invnrmVoigt(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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