CauchyStressPrinc.f90

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SUBROUTINE cauchystressprinc(ndime,xmu,xlamb,detf,stret,princ,sigma,sprin)

!!****f* Rocfrac/Rocfrac/Source/CauchyStressPrinc.f90
!!
!!  NAME
!!     CauchyStressPrinc
!!
!!  FUNCTION
!!
!!     Determines the Cauchy stress tensor for materials defined in
!!     principal directions
!!
!!  INPUTS
!!
!!     ndime  -->  number of dimensions
!!     xmu    -->  mu coefficient
!!     xlamb  -->  lambda coefficient
!!     detf   -->  determinant of F, i.e. J
!!     stret  -->  vector containing the stretches
!!     btens  -->  matrix containing the the principal directions
!!
!!  OUTPUT
!!     sigma  -->  Cauchy stress tensor
!!     sprin  -->  principal stresses
!!
!!****

  IMPLICIT DOUBLE PRECISION (a-h,o-z)
  dimension sigma(3,3),princ(3,3),stret(3),sprin(3)
      
!
!     Obtains the principal stress using equation (5.103) (5.90)
!
  detfinv = 1.d0/detf

  DO id=1,ndime
     sprin(id) = detfinv*(xlamb*log(detf) + 2.d0*xmu*log(stret(id)))
  ENDDO
!
!     Obtains the Cartesian Cauchy stress tensor using equation (5.47)
!
  DO jd=1,ndime      
     DO kd=1,ndime
        sum=0.0d0
        DO id=1,ndime
           sum=sum+sprin(id)*princ(jd,id)*princ(kd,id)
        ENDDO
        sigma(jd,kd)=sum
     ENDDO
  ENDDO
  RETURN
END SUBROUTINE cauchystressprinc