vol_elem_mat_matous.f90

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SUBROUTINE vol_elem_mat_matous(glb)
!
!     Forms the material compliance matix, [C] for an isotropic material
!                    -1
!     Note: [E] = [C]    and {epsilon} = [C]{sigma}
!

  USE rocstar_rocfrac

  IMPLICIT NONE
  TYPE(rocfrac_global) :: glb

  REAL*8 :: e_l, nu_l

  INTEGER :: i,j                 ! loop counter

!-----Create material constant matrices



  ALLOCATE(glb%L_tensor(1:6,1:6,1:glb%NumMatVol_Part))
  ALLOCATE(glb%M_tensor(1:6,1:6,1:glb%NumMatVol_Part))

  glb%L_tensor = 0.d0
  glb%M_tensor = 0.d0

  DO i = 1, glb%NumMatVol_Part


! -- [E]
!!$     ci(1,i) = e(i)*(1.d0 - xnu(i))/ &
!!$          ( (1.d0+xnu(i))*(1.d0-2.d0*xnu(i)) )
!!$     ci(2,i) = e(i)*xnu(i)/( (1.d0+xnu(i))*(1.d0-2.d0*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)

! -- [C]
     glb%M_tensor(1,1,i) = 1.d0 / glb%E1(i)
     glb%M_tensor(1,2,i) = - glb%nu12(i) / glb%E2(i)
     glb%M_tensor(1,3,i) = - glb%nu13(i) / glb%E3(i)
     glb%M_tensor(2,1,i) = glb%M_tensor(1,2,i) 
     glb%M_tensor(2,2,i) = 1.d0 / glb%E2(i)
     glb%M_tensor(2,3,i) = - glb%nu23(i) / glb%E3(i)
     glb%M_tensor(3,1,i) = glb%M_tensor(1,3,i)
     glb%M_tensor(3,2,i) = glb%M_tensor(2,3,i)
     glb%M_tensor(3,3,i) = 1.d0 / glb%E3(i)
     glb%M_tensor(4,4,i) = 1.d0/glb%G12(i)
     glb%M_tensor(5,5,i) = 1.d0/glb%G13(i)
     glb%M_tensor(6,6,i) = 1.d0/glb%G23(i)

! -- 

     CALL invert2(glb%M_tensor(:,:,i), glb%L_tensor(:,:,i), 6)


     print*,' Stiffness Matrix of Material',i
     DO j= 1, 6
        print*,glb%L_tensor(j,:,i)
     ENDDO
     
     print*,' Compliance Matrix of Material',i
     DO j= 1, 6
        print*,glb%M_tensor(j,:,i)
     ENDDO



!!$     PRINT*, 'E = 1/M(1,1) = ', E_l
!!$     PRINT*, 'G = 1/M(4,4) = ', 1.d0/glb%M_tensor(4,4,i)
!!$     PRINT*, 'nu = -M(1,2)*E = ', nu_l

     ! not true for othotropic material: fix

     glb%ShrMod(i) = 1.d0/glb%M_tensor(4,4,i)
     glb%PoisRat(i) = -glb%M_tensor(1,2,i)*1.d0/glb%M_tensor(1,1,i)
     glb%BulkMod(i) = glb%E1(i)/(3.*(1.-2.*glb%PoisRat(i)))

  ENDDO

!  PRINT*,'HOMOGENEOUS MEDIUM : matrix[2], fiber[1] | cm =', cm, ': cf =', cb, ' : cd =', cd
  print*,'Comparison medium Lo = a1*Lm + a2*L2 : a1 =',glb%alpha1, ' | a2 =', glb%alpha2

  
  CALL compositestiffnes(glb%L_tensor(:,:,1), glb%L_tensor(:,:,2), glb%M_tensor(:,:,1), glb%M_tensor(:,:,2), glb%cm, glb%c2, &
       glb%alpha1, glb%alpha2, glb%L_bar, glb%M_bar, glb%Lo)

  print*,'Stiffness Matrix of Homogeneous Medium'

  DO j= 1, 6
     print*,glb%L_bar(j,:)
  ENDDO

  print*,'Compliance Matrix of Homogeneous Medium'

    DO j= 1, 6
     print*,glb%M_bar(j,:)
  ENDDO

  print*,''

  print*,'E = 1/M(1,1) = ', 1.d0/glb%M_bar(1,1), 'G = 1/M[4][4] = ', &
       1.d0/glb%M_bar(4,4), 'nu = -M(1,2)*E =,', -glb%M_bar(1,2)*1./glb%M_bar(1,1)

  e_l = 1.d0/glb%M_bar(1,1)
  nu_l = -glb%M_bar(1,2)*1.d0/glb%M_bar(1,1)

  print*,e_l*(1.d0-nu_l),glb%rho(1),(1.d0+nu_l)/(1.d0-2.d0*nu_l)
  glb%cd_fastest = sqrt( e_l*(1.d0-nu_l)/glb%rho(1)/(1.d0+nu_l)/(1.d0-2.d0*nu_l) )

!  ALLOCATE( glb%cd(1:4,1:glb%NumElVol) )

  print*,'done'

  RETURN
END SUBROUTINE vol_elem_mat_matous