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invariants for symmetric matrix

This commit is contained in:
Martin Diehl 2016-02-02 09:44:51 +01:00
parent b28e70e36a
commit 15e1c7edd8
1 changed files with 19 additions and 15 deletions
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@ -113,7 +113,6 @@ module math
math_equivStrain33, &
math_equivStress33, &
math_trace33, &
math_j3_33, &
math_det33, &
math_Plain33to9, &
math_Plain9to33, &
@ -969,19 +968,6 @@ real(pReal) pure function math_trace33(m)
end function math_trace33
!--------------------------------------------------------------------------------------------------
!> @brief invariant 3 of a 33 matrix
!--------------------------------------------------------------------------------------------------
real(pReal) pure function math_j3_33(m)
implicit none
real(pReal), dimension(3,3), intent(in) :: m
math_j3_33 = sum(m**3.0_pReal)/3.0_pReal
end function math_j3_33
!--------------------------------------------------------------------------------------------------
!> @brief determinant of a 33 matrix
!--------------------------------------------------------------------------------------------------
@ -2083,7 +2069,25 @@ function math_eigenvaluesSym33(m)
end function math_eigenvaluesSym33
!--------------------------------------------------------------------------------------------------
!> @brief invariants of matrix m
!> @brief invariants of symmetrix 3x3 matrix m
!--------------------------------------------------------------------------------------------------
pure function math_invariantsSym33(m)
implicit none
real(pReal), dimension(3,3) , intent(in) :: m
real(pReal), dimension(3) :: math_invariantsSym33
math_invariantsSym33(1) = math_trace33(m)
math_invariantsSym33(2) = m(1,1)*m(2,2) + m(1,1)*m(3,3) + m(2,2)*m(3,3) &
-(m(1,2)**2 + m(1,3)**2 + m(2,3)**2)
math_invariantsSym33(3) = m(1,1)*m(2,3)**2 + m(2,2)*m(1,3)**2 + m(3,3)*m(1,2)**2 &
-(m(1,1)*m(2,2)*m(3,3) + 2.0_pReal * m(1,3)*m(1,2)*m(2,3))
end function math_invariantsSym33
!--------------------------------------------------------------------------------------------------
!> @brief invariants of 3x3 matrix m
!--------------------------------------------------------------------------------------------------
pure function math_invariants33(m)