fixed error in _identity (wrong delta-function)
added _exp33 for matrix exponential added trace33 for matrix trace
This commit is contained in:
Philip Eisenlohr
parent
a5629304dc
commit
1b2edd7e7d
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@ -143,10 +143,12 @@ real(pReal), dimension(4,36), parameter, private :: &
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qsort, &
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math_range, &
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math_identity2nd, &
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math_civita, &
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math_identity4th, &
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math_delta, &
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math_civita, &
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math_vectorproduct, &
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math_tensorproduct, &
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math_norm3, &
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math_mul3x3, &
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math_mul6x6, &
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math_mul33xx33, &
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@ -158,18 +160,22 @@ real(pReal), dimension(4,36), parameter, private :: &
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math_mul33x3, &
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math_mul33x3_complex, &
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math_mul66x6 , &
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math_qConj, &
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math_qRot, &
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math_trace33, &
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math_det33, &
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math_norm33, &
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math_transpose33, &
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math_skew33, &
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math_exp33 , &
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math_inv33, &
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math_invert33, &
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math_invSym3333, &
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math_invert, &
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math_symmetric33, &
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math_symmetric66, &
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math_skew33, &
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math_deviatoric33, &
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math_equivStrain33
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math_equivStrain33, &
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math_qConj, &
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math_qRot
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#ifdef Spectral
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public :: math_curlFFT, &
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math_divergenceFFT, &
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@ -183,8 +189,7 @@ real(pReal), dimension(4,36), parameter, private :: &
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mesh_index
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#endif
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private :: math_partition, &
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math_delta
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private :: math_partition
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contains
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@ -427,7 +432,8 @@ end function math_delta
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!--------------------------------------------------------------------------------------------------
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!> @brief fourth rank identity tensor of specified dimension
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!> @brief symmetric fourth rank identity tensor of specified dimension
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! from http://en.wikipedia.org/wiki/Tensor_derivative_(continuum_mechanics)#Derivative_of_a_second-order_tensor_with_respect_to_itself
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!--------------------------------------------------------------------------------------------------
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pure function math_identity4th(dimen)
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@ -437,7 +443,7 @@ pure function math_identity4th(dimen)
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real(pReal), dimension(dimen,dimen,dimen,dimen) :: math_identity4th
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forall (i=1_pInt:dimen,j=1_pInt:dimen,k=1_pInt:dimen,l=1_pInt:dimen) math_identity4th(i,j,k,l) = &
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0.5_pReal*(math_I3(i,k)*math_I3(j,k)+math_I3(i,l)*math_I3(j,k))
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0.5_pReal*(math_I3(i,k)*math_I3(j,l)+math_I3(i,l)*math_I3(j,k))
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end function math_identity4th
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@ -673,6 +679,35 @@ pure function math_mul66x6(A,B)
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end function math_mul66x6
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!--------------------------------------------------------------------------------------------------
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!> @brief 3x3 matrix exponential up to series approximation order n (default 5)
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!--------------------------------------------------------------------------------------------------
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pure function math_exp33(A,n)
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implicit none
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integer(pInt) :: i,order
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integer(pInt), intent(in), optional :: n
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real(pReal), dimension(3,3), intent(in) :: A
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real(pReal), dimension(3,3) :: B,math_exp33
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real(pReal) :: invfac
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order = 5
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if (present(n)) order = n
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B = math_identity2nd(3) ! init
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invfac = 1.0_pReal ! 0!
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math_exp33 = B ! A^0 = eye2
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do i = 1_pInt,n
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invfac = invfac/real(i) ! invfac = 1/i!
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B = math_mul33x33(B,A)
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math_exp33 = math_exp33 + invfac*B ! exp = SUM (A^i)/i!
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enddo
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end function math_exp33
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!--------------------------------------------------------------------------------------------------
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!> @brief random quaternion
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!--------------------------------------------------------------------------------------------------
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@ -1020,8 +1055,8 @@ pure function math_deviatoric33(m)
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integer(pInt) :: i
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real(pReal) :: hydrostatic
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hydrostatic = (m(1,1) + m(2,2) + m(3,3)) / 3.0_pReal
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math_deviatoric33 = m
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hydrostatic = (m(1,1) + m(2,2) + m(3,3)) / 3.0_pReal
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forall (i=1_pInt:3_pInt) math_deviatoric33(i,i) = m(i,i) - hydrostatic
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end function math_deviatoric33
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@ -1050,6 +1085,21 @@ pure function math_equivStrain33(m)
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end function math_equivStrain33
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!--------------------------------------------------------------------------------------------------
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!> @brief trace of a 33 matrix
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!--------------------------------------------------------------------------------------------------
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pure function math_trace33(m)
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implicit none
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real(pReal), dimension(3,3), intent(in) :: m
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real(pReal) :: math_trace33
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math_trace33 = m(1,1) + m(2,2) + m(3,3)
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end function math_trace33
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!--------------------------------------------------------------------------------------------------
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!> @brief determinant of a 33 matrix
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!--------------------------------------------------------------------------------------------------
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@ -1083,7 +1133,7 @@ end function
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!--------------------------------------------------------------------------------------------------
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!> @brief euclidic norm of a 3 vector
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!> @brief euclidian norm of a 3 vector
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!--------------------------------------------------------------------------------------------------
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pure function math_norm3(v)
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