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CCCPSubsPorous.f
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CCCPSubsPorous.f
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!-----------------------------------------------------------------------
!-----------------------------------------------------------------------
!
! Helper subroutines for CCCP
!
!-----------------------------------------------------------------------
!-----------------------------------------------------------------------
! Preprocessor definitions
!-----------------------------------------------------------------------
#ifndef SCMM_HYPO_CCCP_SUBS
#define SCMM_HYPO_CCCP_SUBS
!-----------------------------------------------------------------------
! Include files
!-----------------------------------------------------------------------
!DEC$ FREEFORM
#include './Dependencies/quartic.f90'
!DEC$ NOFREEFORM
!-----------------------------------------------------------------------
!-----------------------------------------------------------------------
! Subroutines
!-----------------------------------------------------------------------
! Subroutines should be inlined by the compiler
!-----------------------------------------------------------------------
!DIR$ ATTRIBUTES FORCEINLINE :: yieldfunction, yieldgradient, RMAP,
!DIR$& UpdateDamageHan, calcTauEff, findRoot
!-----------------------------------------------------------------------
!
!-----------------------------------------------------------------------
! SUBROUTINE yieldfunction
!-----------------------------------------------------------------------
!
!-----------------------------------------------------------------------
subroutine yieldfunction(tau_eff,tau_c,rho,m,f)
!
implicit none
!
integer, parameter :: alpha = 12
real*8, intent(in) :: tau_eff(alpha),tau_c(alpha),rho,m
real*8, intent(out) :: f
! Local variables
real*8 temp
real*8 zero,one
parameter(zero=0.d0,one=1.d0)
integer a
!-----
temp = zero
do a = 1,alpha
temp = temp+exp((rho/m)*(abs(tau_eff(a))/(tau_c(a))-one))
enddo
f = (one/rho)*log(temp)
!
return
end subroutine yieldfunction
!
!-----------------------------------------------------------------------
! SUBROUTINE calcTauEff
!-----------------------------------------------------------------------
!
!-----------------------------------------------------------------------
subroutine calcTauEff(tau,sigma,VVF,aParam,q1,q2,tau_eff)
!
use PolynomialRoots
implicit none
!
real*8, intent(in) :: tau(12),sigma(6),VVF,aParam,q1,q2
real*8, intent(out) :: tau_eff(12)
! Local variables
integer alpha, a
real*8 zero, one, half, three, oThree, precision
parameter(alpha=12,zero=0.d0,one=1.d0,half=5.d-1,three=3.d0,
. oThree=one/three,precision=epsilon(zero))
real*8 coeff(5), Sh, Seq2
complex*16 z(4)
!-----------------------------------------------------------------------
Seq2 = half*((sigma(1)-sigma(2))**2
+ +(sigma(2)-sigma(3))**2
+ +(sigma(3)-sigma(1))**2)
+ +three*sigma(4)**2+three*sigma(5)**2
+ +three*sigma(6)**2! Equivalent von Mises stress squared
Sh = (sigma(1)+sigma(2)+sigma(3))*oThree ! hydrostatic stress
!-----------------------------------------------------------------------
coeff(5) = 9.d0*q1*VVF*q2**8*Sh**8/358400000.d0
coeff(4) = three*q1*VVF*q2**6*Sh**6/320000.d0
coeff(3) = three*q1*VVF*q2**4*Sh**4/1600.d0
coeff(1) = 2.d0*q1*VVF-q1**2*VVF**2-one
!-----------------------------------------------------------------------
if(coeff(5).gt.precision)then
do a=1, alpha
coeff(2) = tau(a)**2+2.d0*aParam*VVF*Seq2/45.d0+
+ three*q1*VVF*q2**2*Sh**2/20.d0
call QuarticRoots(coeff, z)
call findRoot(tau, z, a, 4, tau_eff)
enddo
else
do a=1, alpha
tau_eff(a) = sqrt((tau(a)**2+2.d0*aParam*VVF*Seq2/45.d0+
+ three*q1*VVF*q2**2*Sh**2/20.d0)/(one+
+ q1**2*VVF**2-2.d0*q1*VVF))*sign(one,tau(a))
enddo
endif
!-----------------------------------------------------------------------
return
end subroutine calcTauEff
!
!-----------------------------------------------------------------------
! SUBROUTINE findRoot
!-----------------------------------------------------------------------
!
!-----------------------------------------------------------------------
subroutine findRoot(tau,z,a,Nroot,tau_eff)
!
implicit none
!
real*8, intent(in) :: tau(12)
complex*16, intent(in) :: z(4)
integer, intent(in) :: a, Nroot
real*8, intent(out) :: tau_eff(12)
! Local variables
integer code, i
real*8 zero, one, precision
parameter(zero=0.d0,one=1.d0,precision=epsilon(zero))
!-----------------------------------------------------------------------
code = 0
do i=1,Nroot
if((abs(aimag(z(i))).le.precision)
. .and.(dble(z(i)).gt.precision))then
tau_eff(a) = one/sqrt(dble(z(i)))*sign(one,tau(a))
code = code + 1
endif
enddo
if(code.eq.0)then
tau_eff(a) = tau(a)
#if defined SCMM_HYPO_STANDARD
call STDB_ABQERR(-1,'A real value for tau_eff was not found'
. ,,,)
#elif defined SCMM_HYPO_EXPLICIT
call XPLB_ABQERR(-1,'A real value for tau_eff was not found'
. ,,,)
#else
write(*,*) 'Warning! A real value for tau_eff was not found'
#endif
elseif(code.gt.1)then
#if defined SCMM_HYPO_STANDARD
call STDB_ABQERR(-1,'More than one root found for tau_eff'
. ,,,)
#elif defined SCMM_HYPO_EXPLICIT
call XPLB_ABQERR(-1,'More than one root found for tau_eff'
. ,,,)
#else
write(*,*) 'Warning! More than one root found for tau_eff'
write(*,*) "Number of roots", code
write(*,*) " Roots: REAL PART IMAGINARY PART"
write(*,"(2ES20.12)") (dble(z(i)), aimag(z(i)), i=1,Nroot)
#endif
endif
!-----------------------------------------------------------------------
return
end subroutine findRoot
!
!-----------------------------------------------------------------------
! SUBROUTINE yieldgradient
!-----------------------------------------------------------------------
!
!-----------------------------------------------------------------------
subroutine yieldgradient(tau,tau_eff,sigma,tau_c,VVF,rho,m,aParam,
. q1,q2,S,dfdtau_eff,dfdtau_c,dfdsigma,
. dfdsigmaskew,dfdVVF)
!
implicit none
!
integer, parameter :: alpha = 12
real*8, intent(in) :: tau(alpha),tau_eff(alpha),sigma(6),
. tau_c(alpha),VVF,rho,m,aParam,q1,q2,
. S(alpha,3,3)
real*8, intent(out) :: dfdtau_eff(alpha),dfdtau_c(alpha),
. dfdsigma(6),dfdsigmaskew(3),dfdVVF
! Local variables
real*8 dnom,temp,xmat(3,3),dgdtau_eff(12),dgdVVF(12),
. dgdsigma(12,3,3),sigXmat(3,3),Ide(3,3),Seq2,Sh
real*8 zero,one,half,two,three,oThree,precision
parameter(zero=0.d0,one=1.d0,half=5.d-1,two=2.d0,
. three=3.d0,oThree=one/three,precision=epsilon(zero))
integer a,j,i
!-----------------------------------------------------------------------
Seq2 = half*((sigma(1)-sigma(2))**2
+ +(sigma(2)-sigma(3))**2
+ +(sigma(3)-sigma(1))**2)
+ +three*sigma(4)**2+three*sigma(5)**2
+ +three*sigma(6)**2! Equivalent von Mises stress squared
Sh = (sigma(1)+sigma(2)+sigma(3))*oThree ! hydrostatic stress
!-----------------------------------------------------------------------
dnom = zero
do a = 1,alpha
temp = exp((rho/m)*(abs(tau_eff(a))/(tau_c(a))-one))
dnom = dnom+temp
dfdtau_eff(a) = temp*sign(one,tau_eff(a))/(tau_c(a))
dfdtau_c(a) = -temp*abs(tau_eff(a))/((tau_c(a)**2))
enddo
dfdtau_eff = dfdtau_eff/(m*dnom)
dfdtau_c = dfdtau_c/(m*dnom)
do a=1,alpha
if(abs(tau_eff(a)).gt.precision)then
dgdtau_eff(a) = -two*(tau(a)**2)/(tau_eff(a)**3)-
. 4.d0*aParam*VVF*Seq2/(45.d0*tau_eff(a)**3)-
. two*q1*VVF*(three*q2**2*Sh**2/(20.d0*tau_eff(a)**3)+
. three*q2**4*Sh**4/(800.d0*tau_eff(a)**5)+
. 9.d0*q2**6*Sh**6/(320000.d0*tau_eff(a)**7)+
. 9.d0*q2**8*Sh**8/(89600000.d0*tau_eff(a)**9))
dgdVVF(a) = two*aParam*Seq2/(45.d0*tau_eff(a)**2)-
. two*q1**2*VVF+two*q1+
. two*q1*(three*q2**2*Sh**2/(40.d0*tau_eff(a)**2)+
. three*q2**4*Sh**4/(3200.d0*tau_eff(a)**4)+
. three*q2**6*Sh**6/(640000.d0*tau_eff(a)**6)+
. 9.d0*q2**8*Sh**8/(716800000.d0*tau_eff(a)**8))
else
dgdtau_eff(a) = one
dgdVVF(a) = zero
endif
enddo
dfdVVF = zero
do a=1,alpha
dfdVVF = dfdVVF - dfdtau_eff(a)*dgdVVF(a)/dgdtau_eff(a)
enddo
!-----------------------------------------------------------------------
Ide(1,1) = one
Ide(1,2) = zero
Ide(1,3) = zero
Ide(2,1) = zero
Ide(2,2) = one
Ide(2,3) = zero
Ide(3,1) = zero
Ide(3,2) = zero
Ide(3,3) = one
call vec2mat(sigma,sigXmat)
!-----------------------------------------------------------------------
do j=1,3
do i=1,3
do a=1,alpha
if(abs(tau_eff(a)).gt.precision)then
dgdsigma(a,i,j) =
. two*aParam*VVF*(sigXmat(i,j)-Sh*Ide(i,j))/(15.d0*tau_eff(a)**2)+
. two*tau(a)*S(a,i,j)/tau_eff(a)**2+
. (two/three)*q1*VVF*Ide(i,j)*(
. three*q2**2*Sh/(20.d0*tau_eff(a)**2)+
. three*q2**4*Sh**3/(800.d0*tau_eff(a)**4)+
. 9.d0*q2**6*Sh**5/(320000.d0*tau_eff(a)**6)+
. 9.d0*q2**8*Sh**7/(89600000.d0*tau_eff(a)**8))
else
dgdsigma(a,i,j) = zero
endif
enddo
enddo
enddo
!-----------------------------------------------------------------------
dfdsigmaskew = zero
do a=1,alpha
dfdsigmaskew(1) = dfdsigmaskew(1)-
. half*dfdtau_eff(a)*(dgdsigma(a,3,2)-
. dgdsigma(a,2,3))/dgdtau_eff(a)
dfdsigmaskew(2) = dfdsigmaskew(2)-
. half*dfdtau_eff(a)*(dgdsigma(a,1,3)-
. dgdsigma(a,3,1))/dgdtau_eff(a)
dfdsigmaskew(3) = dfdsigmaskew(3)-
. half*dfdtau_eff(a)*(dgdsigma(a,2,1)-
. dgdsigma(a,1,2))/dgdtau_eff(a)
enddo
xmat = zero
do j=1,3
do i=1,3
do a=1,alpha
xmat(i,j) = xmat(i,j)-
. half*dfdtau_eff(a)*(dgdsigma(a,i,j)+
. dgdsigma(a,j,i))/dgdtau_eff(a)
enddo
enddo
enddo
call mat2vec(xmat,dfdsigma)
!-----------------------------------------------------------------------
!
return
end subroutine yieldgradient
!
!-----------------------------------------------------------------------
! SUBROUTINE RMAP
!-----------------------------------------------------------------------
!
!-----------------------------------------------------------------------
subroutine RMAP(f,dfdtau_eff,dfdtau_c,dfdsigma,VVF,dfdVVF,
. sigma,C11,C12,C44,hMatrix,dlambda)
!
implicit none
!
integer, parameter :: alpha = 12
real*8, intent(in) :: f,dfdtau_eff(alpha),dfdtau_c(alpha),
. dfdsigma(6),VVF,dfdVVF,sigma(6),
. C11,C12,C44,hMatrix(alpha,alpha)
real*8, intent(out) :: dlambda
! Local variables
real*8 temp1,temp2,temp3,temp(6),Seq,Sh
real*8 zero,half,one,three,four,oThree
parameter(zero=0.d0,half=5.d-1,one=1.d0,three=3.d0,
. four=4.d0,oThree=1.d0/3.d0)
integer a,b
!-----------------------------------------------------------------------
!-----------------------------------------------------------------------
temp1 = zero
temp(1) = C11*(dfdsigma(1))*(one-VVF)
+ +C12*(dfdsigma(2))*(one-VVF)
+ +C12*(dfdsigma(3))*(one-VVF)
temp(2) = C12*(dfdsigma(1))*(one-VVF)
+ +C11*(dfdsigma(2))*(one-VVF)
+ +C12*(dfdsigma(3))*(one-VVF)
temp(3) = C12*(dfdsigma(1))*(one-VVF)
+ +C12*(dfdsigma(2))*(one-VVF)
+ +C11*(dfdsigma(3))*(one-VVF)
temp(4) = four*C44*(dfdsigma(4))*(one-VVF)
temp(5) = four*C44*(dfdsigma(5))*(one-VVF)
temp(6) = four*C44*(dfdsigma(6))*(one-VVF)
do a=1,6
temp1 = temp1+temp(a)*dfdsigma(a)
enddo
!-----------------------------------------------------------------------
temp2 = zero
do b=1,alpha
do a=1,alpha
temp2 = temp2+hMatrix(a,b)*abs(dfdtau_eff(b))*dfdtau_c(a)
enddo
enddo
!-----------------------------------------------------------------------
temp3 = (one-VVF)**2*dfdVVF*(dfdsigma(1)+dfdsigma(2)+dfdsigma(3))
!-----------------------------------------------------------------------
dlambda = f/(temp1-temp2-temp3)
!-----------------------------------------------------------------------
return
end subroutine RMAP
!
!-----------------------------------------------------------------------
! SUBROUTINE UpdateDamageHan
!-----------------------------------------------------------------------
! Updates the damage variable / void volume fraction
!-----------------------------------------------------------------------
subroutine UpdateDamageHan(VVF,dfdsigma,dlambda)
!
implicit none
!
real*8, intent(inout) :: VVF
real*8, intent(in) :: dfdsigma(6),dlambda
! Local variables
real*8 one,zero
parameter(zero=0.d0,one=1.d0)
!-----------------------------------------------------------------------
VVF = VVF + (one-VVF)**2*(dfdsigma(1)+dfdsigma(2)+
. dfdsigma(3))*dlambda
VVF = max(VVF,zero)
!-----------------------------------------------------------------------
return
end subroutine UpdateDamageHan
!
!-----------------------------------------------------------------------
! End preprocessor definitions
!-----------------------------------------------------------------------
#endif
!-----------------------------------------------------------------------