C.4. USERMAT.F List File for This Example
subroutine usermat(
& matId, elemId,kDomIntPt, kLayer, kSectPt,
& ldstep,isubst,keycut,
& nDirect,nShear,ncomp,nStatev,nProp,
& Time,dTime,Temp,dTemp,
& stress,ustatev,dsdePl,sedEl,sedPl,epseq,
& Strain,dStrain, epsPl, prop, coords,
& var0, defGrad_t, defGrad,
& tsstif, epsZZ,
& var1, var2, var3, var4, var5,
& var6, var7, var8)
c*************************************************************************
c *** primary function ***
c
c user defined material constitutive model
c
c Attention:
c User must define material constitutive law properly
c according to the stress state such as 3D, plane strain
c and axisymmetry, plane stress and 3D/1D beam.
c
c a 3D material constitutive model can use for
c plane strain and axisymmetry cases.
c
c When using shell elements, a plane stress algorithm
c must be use.
c
c
c The following demonstrates a USERMAT subroutine for
c a plasticity model, which is the same as TB, BISO,
c for different stress states.
c See "ANSYS user material subroutine USERMAT" for detailed
c description of how to write a USERMAT routine.
c
c This routine calls four routines,
c usermat3d.F, usermatps.F usermatbm.F and usermat1d.F, w.r.t.
c the corresponding stress states.
c Each routine can be also a usermat routine for the specific
c element.
c
c*************************************************************************
c
c input arguments
c ===============
c matId (int,sc,i) material #
c elemId (int,sc,i) element #
c kDomIntPt (int,sc,i) "k"th domain integration point
c kLayer (int,sc,i) "k"th layer
c kSectPt (int,sc,i) "k"th Section point
c ldstep (int,sc,i) load step number
c isubst (int,sc,i) substep number
c nDirect (int,sc,in) # of direct components
c nShear (int,sc,in) # of shear components
c ncomp (int,sc,in) nDirect + nShear
c nstatev (int,sc,l) Number of state variables
c nProp (int,sc,l) Number of material ocnstants
c
c Temp (dp,sc,in) temperature at beginning of
c time increment
c dTemp (dp,sc,in) temperature increment
c Time (dp,sc,in) time at beginning of increment (t)
c dTime (dp,sc,in) current time increment (dt)
c
c Strain (dp,ar(ncomp),i) Strain at beginning of time increment
c dStrain (dp,ar(ncomp),i) Strain increment
c prop (dp,ar(nprop),i) Material constants defined by TB,USER
c coords (dp,ar(3),i) current coordinates
c defGrad_t(dp,ar(3,3),i) Deformation gradient at time t
c defGrad (dp,ar(3,3),i) Deformation gradient at time t+dt
c
c input output arguments
c ======================
c stress (dp,ar(nTesn),io) stress
c ustatev (dp,ar(nstatev),io) user state variables
c sedEl (dp,sc,io) elastic work
c sedPl (dp,sc,io) plastic work
c epseq (dp,sc,io) equivalent plastic strain
c tsstif (dp,ar(2),io) transverse shear stiffness
c tsstif(1) - Gxz
c tsstif(2) - Gyz
c tsstif(1) is also used to calculate hourglass
c stiffness, this value must be defined when low
c order element, such as 181, 182, 185 with uniform
c integration is used.
c var? (dp,sc,io) not used, they are reserved arguments
c for further development
c
c output arguments
c ================
c keycut (int,sc,io) loading bisect/cut control
c 0 - no bisect/cut
c 1 - bisect/cut
c (factor will be determined by ANSYS solution control)
c dsdePl (dp,ar(ncomp,ncomp),io) material jacobian matrix
c epsZZ (dp,sc,o) strain epsZZ for plane stress,
c define it when accounting for thickness change
c in shell and plane stress states
c
c*************************************************************************
c
c ncomp 6 for 3D (nshear=3)
c ncomp 4 for plane strain or axisymmetric (nShear = 1)
c ncomp 3 for plane stress (nShear = 1)
c ncomp 3 for 3d beam (nShear = 2)
c ncomp 1 for 1D (nShear = 0)
c
c stresss and strains, plastic strain vectors
c 11, 22, 33, 12, 23, 13 for 3D
c 11, 22, 33, 12 for plane strain or axisymmetry
c 11, 22, 12 for plane stress
c 11, 13, 12 for 3d beam
c 11 for 1D
c
c material jacobian matrix
c 3D
c dsdePl | 1111 1122 1133 1112 1123 1113 |
c dsdePl | 2211 2222 2233 2212 2223 2213 |
c dsdePl | 3311 3322 3333 3312 3323 3313 |
c dsdePl | 1211 1222 1233 1212 1223 1213 |
c dsdePl | 2311 2322 2333 2312 2323 2313 |
c dsdePl | 1311 1322 1333 1312 1323 1313 |
c plane strain or axisymmetric (11, 22, 33, 12)
c dsdePl | 1111 1122 1133 1112 |
c dsdePl | 2211 2222 2233 2212 |
c dsdePl | 3311 3322 3333 3312 |
c dsdePl | 1211 1222 1233 1212 |
c plane stress (11, 22, 12)
c dsdePl | 1111 1122 1112 |
c dsdePl | 2211 2222 2212 |
c dsdePl | 1211 1222 1212 |
c 3d beam (11, 13, 12)
c dsdePl | 1111 1113 1112 |
c dsdePl | 1311 1313 1312 |
c dsdePl | 1211 1213 1212 |
c 1d
c dsdePl | 1111 |
c
c*************************************************************************
#include "impcom.inc"
c
INTEGER
& matId, elemId,
& kDomIntPt, kLayer, kSectPt,
& ldstep,isubst,keycut,
& nDirect,nShear,ncomp,nStatev,nProp
DOUBLE PRECISION
& Time, dTime, Temp, dTemp,
& sedEl, sedPl, epseq, epsZZ
DOUBLE PRECISION
& stress (ncomp ), ustatev (nStatev),
& dsdePl (ncomp,ncomp),
& Strain (ncomp ), dStrain (ncomp ),
& epsPl (ncomp ), prop (nProp ),
& coords (3),
& defGrad_t(3,3), defGrad(3,3),
& tsstif (2)
c
c***************** User defined part *************************************
c
c --- parameters
c
INTEGER NEWTON, mcomp
DOUBLE PRECISION HALF, THIRD, ONE, TWO, SMALL, ONEHALF,
& ZERO, TWOTHIRD, ONEDM02, ONEDM05, sqTiny
PARAMETER (ZERO = 0.d0,
& HALF = 0.5d0,
& THIRD = 1.d0/3.d0,
& ONE = 1.d0,
& TWO = 2.d0,
& SMALL = 1.d-08,
& sqTiny = 1.d-20,
& ONEDM02 = 1.d-02,
& ONEDM05 = 1.d-05,
& ONEHALF = 1.5d0,
& TWOTHIRD = 2.0d0/3.0d0,
& NEWTON = 10,
& mcomp = 6
& )
c
c --- local variables
c
c sigElp (dp,ar(6 ),l) trial stress
c dsdeEl (dp,ar(6,6),l) elastic moduli
c sigDev (dp,ar(6 ),l) deviatoric stress tensor
c dfds (dp,ar(6 ),l) derivative of the yield function
c JM (dp,ar(6,6),l) 2D matrix for a 4 order tensor
c pEl (dp,sc ,l) hydrostatic pressure stress
c qEl (dp,sc ,l) von-mises stress
c pleq_t (dp,sc ,l) equivalent plastic strain at
c beginnig of time increment
c pleq (dp,sc ,l) equivalent plastic strain at end
c of time increment
c dpleq (dp,sc ,l) incremental equivalent plastic strain
c cpleq (dp,sc ,l) correction of incremental
c equivalent plastic strain
c sigy_t (dp,sc ,l) yield stress at beginnig of time increments
c sigy (dp,sc ,l) yield stress at end of time
c increment
c young (dp,sc ,l) Young's modulus
c posn (dp,sc ,l) Poiss's ratio
c sigy0 (dp,sc ,l) initial yield stress
c dsigdep (dp,sc ,l) plastic slope
c twoG (dp,sc ,l) two time of shear moduli
c threeG (dp,sc ,l) three time of shear moduli
c funcf (dp,sc ,l) nonlinear function to be solved
c for dpleq
c dFdep (dp,sc ,l) derivative of nonlinear function
c over dpleq
c
c --- temporary variables for solution purpose
c i, j
c threeOv2qEl, oneOv3G, qElOv3G, con1, con2, fratio
c
DOUBLE PRECISION sigElp(mcomp), dsdeEl(mcomp,mcomp), G(mcomp),
& sigDev(mcomp), JM (mcomp,mcomp), dfds(mcomp)
DOUBLE PRECISION var0, var1, var2, var3, var4, var5,
& var6, var7, var8
DATA G/1.0D0,1.0D0,1.0D0,0.0D0,0.0D0,0.0D0/
c
INTEGER i, j
DOUBLE PRECISION pEl, qEl, pleq_t, sigy_t , sigy,
& cpleq, dpleq, pleq,
& young, posn, sigy0, dsigdep,
& elast1,elast2,
& twoG, threeG, oneOv3G, qElOv3G, threeOv2qEl,
& funcf, dFdep, fratio, con1, con2
c*************************************************************************
c
keycut = 0
dsigdep = ZERO
pleq_t = ustatev(1)
pleq = pleq_t
c *** get Young's modulus and Poisson's ratio, initial yield stress and others
young = prop(1)
posn = prop(2)
sigy0 = prop(3)
c *** calculate the plastic slope
dsigdep = young*prop(4)/(young-prop(4))
twoG = young / (ONE+posn)
threeG = ONEHALF * twoG
c
c *** calculate elastic stiffness matrix (3D)
c
c
elast1=young*posn/((1.0D0+posn)*(1.0D0-TWO*posn))
elast2=young/(TWO*(1.0D0+posn))
dsdeEl(1,1)=(elast1+TWO*elast2)*G(1)*G(1)
dsdeEl(1,2)=elast1*G(1)*G(2)+elast2*TWO*G(4)*G(4)
dsdeEl(1,3)=elast1*G(1)*G(3)+elast2*TWO*G(5)*G(5)
dsdeEl(1,4)=elast1*G(1)*G(4)+elast2*TWO*G(1)*G(4)
dsdeEl(1,5)=elast1*G(1)*G(5)+elast2*TWO*G(1)*G(5)
dsdeEl(1,6)=elast1*G(1)*G(6)+elast2*TWO*G(4)*G(5)
dsdeEl(2,2)=(elast1+TWO*elast2)*G(2)*G(2)
dsdeEl(2,3)=elast1*G(2)*G(3)+elast2*TWO*G(6)*G(6)
dsdeEl(2,4)=elast1*G(2)*G(4)+elast2*TWO*G(1)*G(4)
dsdeEl(2,5)=elast1*G(2)*G(5)+elast2*TWO*G(1)*G(5)
dsdeEl(2,6)=elast1*G(2)*G(6)+elast2*TWO*G(2)*G(6)
dsdeEl(3,3)=(elast1+TWO*elast2)*G(3)*G(3)
dsdeEl(3,4)=elast1*G(3)*G(4)+elast2*TWO*G(5)*G(6)
dsdeEl(3,5)=elast1*G(3)*G(5)+elast2*TWO*G(5)*G(3)
dsdeEl(3,6)=elast1*G(3)*G(6)+elast2*TWO*G(6)*G(3)
dsdeEl(4,4)=elast1*G(4)*G(4)+elast2*(G(1)*G(2)+G(4)*G(4))
dsdeEl(4,5)=elast1*G(4)*G(5)+elast2*(G(1)*G(6)+G(5)*G(4))
dsdeEl(4,6)=elast1*G(4)*G(6)+elast2*(G(4)*G(6)+G(5)*G(2))
dsdeEl(5,5)=elast1*G(5)*G(5)+elast2*(G(1)*G(3)+G(5)*G(5))
dsdeEl(5,6)=elast1*G(5)*G(6)+elast2*(G(4)*G(3)+G(5)*G(6))
dsdeEl(6,6)=elast1*G(6)*G(6)+elast2*(G(2)*G(3)+G(6)*G(6))
do i=1,ncomp-1
do j=i+1,ncomp
dsdeEl(j,i)=dsdeEl(i,j)
end do
end do
c
c *** calculate the trial stress and
c copy elastic moduli dsdeEl to material Jacobian matrix
do i=1,ncomp
sigElp(i) = stress(i)
do j=1,ncomp
dsdePl(j,i) = dsdeEl(j,i)
sigElp(i) = sigElp(i)+dsdeEl(j,i)*dStrain(j)
end do
end do
c *** hydrostatic pressure stress
pEl = -THIRD * (sigElp(1) + sigElp(2) + sigElp(3))
c *** compute the deviatoric stress tensor
sigDev(1) = sigElp(1) + pEl
sigDev(2) = sigElp(2) + pEl
sigDev(3) = sigElp(3) + pEl
sigDev(4) = sigElp(4)
sigDev(5) = sigElp(5)
sigDev(6) = sigElp(6)
c *** compute von-mises stress
qEl =
& sigDev(1) * sigDev(1)+sigDev(2) * sigDev(2)+
& sigDev(3) * sigDev(3)+
& TWO*(sigDev(4) * sigDev(4)+ sigDev(5) * sigDev(5)+
& sigDev(6) * sigDev(6))
qEl = sqrt( ONEHALF * qEl)
c *** compute current yield stress
sigy = sigy0 + dsigdep * pleq
c
fratio = qEl / sigy - ONE
c *** check for yielding
IF (sigy .LE. ZERO.or.fratio .LE. -SMALL) GO TO 500
c
sigy_t = sigy
threeOv2qEl = ONEHALF / qEl
c *** compute derivative of the yield function
DO i=1, ncomp
dfds(i) = threeOv2qEl * sigDev(i)
END DO
oneOv3G = ONE / threeG
qElOv3G = qEl * oneOv3G
c *** initial guess of incremental equivalent plastic strain
dpleq = (qEl - sigy) * oneOv3G
pleq = pleq_t + dpleq
c
c *** Newton-Raphson procedure for return mapping iteration
DO i = 1,NEWTON
sigy = sigy0 + dsigdep * pleq
funcf = qElOv3G - dpleq - sigy * oneOv3G
dFdep = - ONE - dsigdep * oneOv3G
cpleq = -funcf / dFdep
dpleq = dpleq + cpleq
c --- avoid negative equivalent plastic strain
dpleq = max (dpleq, sqTiny)
pleq = pleq_t + dpleq
fratio = funcf/qElOv3G
c *** check covergence
IF (((abs(fratio) .LT. ONEDM05 ) .AND.
& (abs(cpleq ) .LT. ONEDM02 * dpleq)) .OR.
& ((abs(fratio) .LT. ONEDM05 ) .AND.
& (abs(dpleq ) .LE. sqTiny ))) GO TO 100
END DO
c
c *** Uncovergence, set keycut to 1 for bisect/cut
keycut = 1
GO TO 990
100 CONTINUE
c
c *** update stresses
con1 = twoG * dpleq
DO i = 1 , ncomp
stress(i) = sigElp(i) - con1 * dfds(i)
END DO
c
c *** update plastic strains
DO i = 1 , nDirect
epsPl(i) = epsPl(i) + dfds(i) * dpleq
END DO
DO i = nDirect + 1 , ncomp
epsPl(i) = epsPl(i) + TWO * dfds(i) * dpleq
END DO
epseq = pleq
c *** Update state variables
ustatev(1) = pleq
c *** Update plastic work
sedPl = sedPl + HALF * (sigy_t+sigy)*dpleq
c
c *** Material Jcobian matrix
c
IF (qEl.LT.sqTiny) THEN
con1 = ZERO
ELSE
con1 = threeG * dpleq / qEl
END IF
con2 = threeG/(threeG+dsigdep) - con1
con2 = TWOTHIRD * con2
DO i=1,ncomp
DO j=1,ncomp
JM(j,i) = ZERO
END DO
END DO
DO i=1,nDirect
DO j=1,nDirect
JM(i,j) = -THIRD
END DO
JM(i,i) = JM(i,i) + ONE
END DO
DO i=nDirect + 1,ncomp
JM(i,i) = HALF
END DO
DO i=1,ncomp
DO j=1,ncomp
dsdePl(i,j) = dsdeEl(i,j) - twoG
& * ( con2 * dfds(i) * dfds(j) + con1 * JM(i,j) )
END DO
END DO
c
goto 600
500 continue
c *** Update stress in case of elastic/unloading
do i=1,ncomp
stress(i) = sigElp(i)
end do
600 continue
c *** Claculate elastic work
sedEl = ZERO
DO i = 1 , ncomp
sedEl = sedEl + stress(i)*(Strain(i)+dStrain(i)-epsPl(i))
END DO
sedEl = sedEl * HALF
c
990 CONTINUE
c
return
end
