MP/Source/vol_elem_mat.f90

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SUBROUTINE vol_elem_mat(e,xnu,ci,cj,numat_vol,Integration,MatOrtho)

!!****f* Rocfrac/Rocfrac/Source/vol_elem_mat.f90
!!
!!  NAME
!!    VOL_ELEM_MAT
!!
!!  FUNCTION
!!
!!     Forms the material compliance matix, [C] for an isotropic material
!!                    -1
!!     Note: [E] = [C]    and {epsilon} = [C]{sigma}
!!
!!  INPUTS
!!
!!     e -- Young's modulus
!!    xnu -- Possion's ratio
!!   numat_vol -- number of volumetric elements
!!   Integration -- = 1 pseudo-Reduced integration (split Cijkl)
!!                  = 0 Cijkl
!!
!!  OUTPUT
!!     ci -- elastic stiffness constants
!!     cj -- split stiffness constants
!!
!!****
!!
      IMPLICIT NONE
      INTEGER :: numat_vol         ! number of materials
!      INTEGER :: nplane            ! type of material
!                                   !   0 = isotropic
!                                   !   1 = orthotropic
!--   young's moduli
      REAL*8, DIMENSION(1:numat_vol) :: e
!--   Poisson's ratios
      REAL*8, DIMENSION(1:numat_vol) :: xnu
!--   elastic stiffness constants [E]
      REAL*8, DIMENSION(1:9,1:numat_vol) :: ci
!--   elastic stiffness constants [E]
      REAL*8, DIMENSION(1:9,1:numat_vol) :: cj
! --  
      REAL*8 :: xmu, xlambda
      REAL*8 :: caux
      integer :: integration

      INTEGER :: i                 ! loop counter

      INTEGER, DIMENSION(1:numat_vol) :: matortho

!-----Create material constant matrices
      DO i = 1, numat_vol
!----- (isotropic)
         IF ( ( integration.EQ.0 ) ) THEN !.AND. ( MatOrtho(i) == 0 ) ) THEN

            caux = e(i) / ( (1.d0+xnu(i))*(1.d0-2.d0*xnu(i)) )

! -- [E]
!
!        [ c1 c2 c4 ..    ] 
!        [    c3 c5 ..    ]
!        [       c6 ..    ]
!        [         c7     ]
!        [           c8   ]
!        [             c9 ]

            ci(1,i) = caux*(1.d0 - xnu(i))
            ci(2,i) = caux*xnu(i)
            ci(3,i) = ci(1,i)
            ci(4,i) = ci(2,i)
            ci(5,i) = ci(2,i)
            ci(6,i) = ci(1,i)
            ci(7,i) = e(i)/( 2.d0 * (1.d0 + xnu(i)) )
            ci(8,i) = ci(7,i)
            ci(9,i) = ci(7,i)


            cj(:,i) = 0.d0

         ELSE IF(integration.EQ.1)THEN

! -- pseudo-Reduced integration (split Cijkl)
            ! mu
            xmu = e(i)/( 2.d0 * (1.d0 + xnu(i)) )
            ! lambda
            xlambda = e(i)*xnu(i)/( (1.d0+xnu(i))*(1.d0-2.d0*xnu(i)) )

! -- [Emu]
            ci(1,i) = 2.d0*xmu
            ci(2,i) = 0.d0
            ci(3,i) = ci(1,i)
            ci(4,i) = ci(2,i)
            ci(5,i) = ci(2,i)
            ci(6,i) = ci(1,i)
            ci(7,i) = xmu
            ci(8,i) = ci(7,i)
            ci(9,i) = ci(7,i)

! -- [Elambda]

            cj(1,i) = xlambda 
            cj(2,i) = xlambda
            cj(3,i) = cj(1,i)
            cj(4,i) = cj(2,i)
            cj(5,i) = cj(2,i)
            cj(6,i) = cj(1,i)
            cj(7,i) = 0.d0
            cj(8,i) = cj(7,i)
            cj(9,i) = cj(7,i)
            
!----- (orthotropic, not yet implemented)
!         ELSEIF (nplane.GE.1) THEN
!            PRINT*,'ERROR: Material properties not yet implemented'
!            PRINT*,'       Your Choices are: '
!            PRINT*,'                         nplane = 0, isotropic'
!            STOP
         ENDIF
      ENDDO

      RETURN
    END