*deck,usermat
USERDISTRIB parallel
gal
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
gal July, 1999
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"
#include "ansysdef.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 (3,3),
defGrad_t(3,3),
&
tsstif (2)
c
EXTERNAL
usermat3d, usermatps, usermatbm, usermat1d
EXTERNAL
myuserfunc
integer myvar
&
DOUBLE PRECISION var0, var1, var2, var3, var4, var5,
var6, var7, var8
integer iott,wrinqr
external wrinqr
c
c*************************************************************************
c
iott = wrinqr(WR_OUTPUT)
write(iott,*) ' ************************************************'
write(iott,*) ' * #DEBUG# UserMatLib.dll USERMAT
*'
write(iott,*) ' ************************************************'
myvar = 99
call myuserfunc(myvar)
IF(ncomp .GE. 4) THEN
c ***
3d, plane strain and axisymmetric example
call usermat3d (
&
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)
ELSE IF(nDirect.eq. 2 .and. ncomp .EQ. 3) THEN
plane stress example
call usermatps (
&
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 ***
ELSE IF(ncomp .EQ. 3) THEN
3d beam example
call usermatbm (
&
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 ***
ELSE IF(ncomp .EQ. 1) THEN
1d beam example
call usermat1d (
&
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,
c ***
&
&
&
tsstif, epsZZ,
var1, var2, var3, var4, var5,
var6, var7, var8)
END IF
return
end
*deck,usermat1d
USERDISTRIB parallel
gal
subroutine usermat1d(
&
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 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
gal July, 1999
c
c
The following demonstrates a USERMAT subroutine for
c
a plasticity model of 1D truss element (LINK180).
c
The plasticity model is the same as TB, BISO.
c
c
See "ANSYS user material subroutine USERMAT" for detailed
c
description of how to write a USERMAT routine.
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
ustatev(1)
- equivalent plastic strain
c
ustatev(2) - ustatev(1+ncomp)
- plastic strain vector
c
ustatev(nStatev)
- von-Mises stress
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"
#include "ansysdef.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 (3,3),
defGrad_t(3,3),
&
tsstif (2)
c
c***************** User defined part *************************************
c
c --- parameters
c
INTEGER
mcomp
DOUBLE PRECISION ZERO, HALF, ONE, TWO, SMALL
PARAMETER
(ZERO
= 0.d0,
&
&
&
&
&
&
HALF
ONE
TWO
SMALL
mcomp
)
= 0.5d0,
= 1.d0,
= 2.d0,
= 1.d-08,
= 1
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 beginnig of time
increment
c
pleq
(dp,sc
,l)
equivalent plastic strain at end of time
increment
c
dpleq
(dp,sc
,l)
incremental 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 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 slop
c
twoG
(dp,sc
,l)
two time of shear moduli
c
c
DOUBLE PRECISION sigElp(mcomp), dsdeEl(mcomp,mcomp)
&
DOUBLE PRECISION var0, var1, var2, var3, var4, var5,
var6, var7, var8
DOUBLE PRECISION qEl,
pleq_t, sigy_t , sigy,
&
dpleq, pleq,
signTens,
&
young, posn,
sigy0,
dsigdep,
&
twoG, fratio
c*************************************************************************
c
integer iott,wrinqr
external wrinqr
c
c*************************************************************************
c
iott = wrinqr(WR_OUTPUT)
write(iott,*) ' ************************************************'
write(iott,*) ' * #DEBUG# UserMatLib.dll USERMAT1D
*'
write(iott,*) ' ************************************************'
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 plastic slope
dsigdep = young*prop(4)/(young-prop(4))
twoG
= young / (ONE+posn)
c *** define tsstif(1) since it is used for calculation of hourglass stiffness
tsstif(1) = HALF * twoG
c
c *** calculate elastic stiffness matrix
c
dsdeEl(1,1)= young
c
c *** calculate the trial stress and
c
copy elastic moduli dsdeEl to material Jacobian matrix
sigElp(1)
= stress(1)
dsdePl(1,1) = dsdeEl(1,1)
sigElp(1)
= sigElp(1) + dsdeEl(1,1) * dStrain(1)
c *** sign of predicted stress
signTens = sign (ONE, sigElp(1))
c *** compute von-mises equivalent stress
qEl = abs(sigElp(1))
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
c *** initial guess of incremental equivalent plastic strain
dpleq
= (qEl - sigy) / young
pleq
= pleq_t + dpleq
sigy
= sigy0 + dsigdep * pleq
c
c *** update plastic strains, stresses
epsPl(1) = epsPl(1) + dpleq * signTens
stress(1) = signTens * sigy
c
c *** update plastic strains
epseq = pleq
c *** Update state variables
ustatev(1) = pleq
ustatev(2) = epsPl(1)
c *** Update plastic work
sedPl = sedPl + HALF * (sigy_t + sigy) * dpleq
c
c *** Material Jcobian matrix
c
dsdePl(1,1) = dsdeEl(1,1) * dsigdep /(dsdeEl(1,1) + dsigdep)
c *** Allow a small number for Jcobian matrix if it is an ideal plasticity
if(dsdePl(1,1).LE.ZERO) dsdePl(1,1) = SMALL*dsdeEl(1,1)
c
goto 600
500 continue
c *** Update stress in case of elastic/unloading
stress(1) = sigElp(1)
600 continue
c *** elastic strain energy
sedEl = HALF * stress(1) * (Strain(1)+dStrain(1)-epsPl(1))
c *** update state variables
ustatev(nStatev) = sigy
c
return
end
*deck,usermat3d
USERDISTRIB parallel
gal
subroutine usermat3d(
&
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 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
gal July, 1999
c
c
The following demonstrates a USERMAT subroutine for
c
a plasticity model of 3D solid elements or plane elements
c
in plane strain or axisymmetric stress state. The plasticity
c
model is the same as TB, BISO.
c
See "ANSYS user material subroutine USERMAT" for detailed
c
description of how to write a USERMAT routine.
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 variable
c
ustatev(1)
- equivalent plastic strain
c
ustatev(2) - statev(1+ncomp)
- plastic strain vector
c
ustatev(nStatev)
- von-Mises stress
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"
#include "ansysdef.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 (3,3),
defGrad_t(3,3),
&
tsstif (2)
c
c***************** User defined part *************************************
c
c --- parameters
c
INTEGER
mcomp
DOUBLE PRECISION HALF, THIRD, ONE, TWO, SMALL, ONEHALF,
&
PARAMETER
&
&
&
&
&
&
&
&
&
&
&
&
ZERO, TWOTHIRD, ONEDM02, ONEDM05, sqTiny
(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,
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 beginnig of time
increment
c
pleq
(dp,sc
,l)
equivalent plastic strain at end of time
increment
c
dpleq
(dp,sc
,l)
incremental 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 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 slop
c
twoG
(dp,sc
,l)
two time of shear moduli
c
threeG
(dp,sc
,l)
three time of shear moduli
c
c --- temperary variables for solution purpose
c
i, j
c
threeOv2qEl, oneOv3G, qElOv3G, con1, con2, fratio
c
EXTERNAL
vzero, vmove, get_ElmData
DOUBLE PRECISION sigElp(mcomp), dsdeEl(mcomp,mcomp), G(mcomp),
&
sigDev(mcomp), JM
(mcomp,mcomp), dfds(mcomp),
&
sigi (mcomp), strainEl(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,
&
dpleq, pleq,
&
young, posn,
&
elast1,elast2,
&
twoG, threeG,
pleq_t,
sigy_t , sigy,
sigy0,
dsigdep,
oneOv3G, qElOv3G, threeOv2qEl,
&
fratio, con1,
con2, dperr(3)
c*************************************************************************
c
integer iott,wrinqr
external wrinqr
c
c*************************************************************************
c
iott = wrinqr(WR_OUTPUT)
write(iott,*) ' ************************************************'
write(iott,*) ' * #DEBUG# UserMatLib.dll USERMAT3D
*'
write(iott,*) ' ************************************************'
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 *** plastic strain tensor
call vmove(ustatev(2), epsPl(1), ncomp)
c *** calculate plastic slope
dsigdep = young*prop(4)/(young-prop(4))
twoG
= young / (ONE+posn)
threeG
= ONEHALF * twoG
elast1=young*posn/((1.0D0+posn)*(1.0D0-TWO*posn))
elast2=HALF*twoG
c *** define tsstif(1) since it is used for calculation of hourglass stiffness
tsstif(1) = elast2
c
c *** calculate elastic stiffness matrix (3d)
c
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
c *** get initial stress
call vzero(sigi(1),ncomp)
i = ncomp
call get_ElmData ('ISIG', elemId,kDomIntPt, i, sigi)
c
c *** calculate the trial stress and
c
copy elastic moduli dsdeEl to material Jacobian matrix
do i=1,ncomp
strainEl(i) = Strain(i) + dStrain(i) - epsPl(i)
end do
call vzero(sigElp, 6)
do i=1,ncomp
do j=1,ncomp
dsdePl(j,i) = dsdeEl(j,i)
sigElp(i) = sigElp(i)+dsdeEl(j,i)*strainEl(j)
end do
sigElp(i) = sigElp(i) + sigi(i)
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
= qElOv3G - sigy * oneOv3G
pleq
= pleq_t + dpleq
sigy
= sigy0 + dsigdep * pleq
c
c ***
update stresses
DO i = 1 , ncomp
stress(i) = sigElp(i) - TWOTHIRD * (qEl-sigy) * 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
do i=1,ncomp
ustatev(i+1) = epsPl(i)
end do
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
sedEl = ZERO
DO i = 1 , ncomp
sedEl = sedEl + stress(i)*(Strain(i)+dStrain(i)-epsPl(i))
END DO
sedEl
= sedEl * HALF
ustatev(nStatev) = sigy
c
return
end
*deck,usermatbm
USERDISTRIB parallel
gal
subroutine usermatbm(
&
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 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
gal July, 1999
c
c
The following demonstrates a USERMAT subroutine for
c
a plasticity model in 3D beam(188, 189). The plasticity
c
model is the same as TB, BISO.
c
See "ANSYS user material subroutine USERMAT" for detailed
c
description of how to write a USERMAT routine.
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)
statev
c
ustatev(1)
- equivalent plastic strain
c
ustatev(2) - ustatev(1+ncomp) - plastic strain vector
c
ustatev(nStatev)
- von-Mises stress
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
c
ncomp
4
for plane strain, axisymmetric (nShear = 1)
c
ncomp
3
for plane stress (nShear = 1)
c
ncomp
3
for 3D beam (nShear = 2), beam188/189
c
ncomp
1
for 1D beam, link180
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 and 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, axisymmetric
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
c
dsdePl
| 1111
1122
1112 |
c
dsdePl
| 2211
2222
2212 |
c
dsdePl
| 1211
1222
1212 |
c
3d beam plasticity
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"
#include "ansysdef.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), sigi(ncomp),
&
Strain (ncomp ), dStrain (ncomp ),
&
epsPl
(ncomp ), prop
(nProp ),
&
coords (3),
&
defGrad (3,3),
defGrad_t(3,3),
&
tsstif (2)
c
c***************** User defined part *************************************
c
c --- parameters
c
INTEGER
NEWTON, mcomp
DOUBLE PRECISION HALF, ONE, TWO, SMALL, SQTWOTHIRD,
&
ZERO, TWOTHIRD, ONEDM02, ONEDM05, sqTiny
PARAMETER
(ZERO
= 0.d0,
&
HALF
= 0.5d0,
&
ONE
= 1.d0,
&
TWO
= 2.d0,
&
SMALL
= 1.d-08,
&
sqTiny
= 1.d-20,
&
ONEDM02
= 1.d-02,
&
ONEDM05
= 1.d-05,
&
TWOTHIRD
= 2.0d0/3.0d0,
&
SQTWOTHIRD = 0.816496580927726030d0,
&
NEWTON
= 20,
&
mcomp
= 3
&
)
c
c --- local variables
c
c
sigElp
(dp,ar(3 ),l)
trial stress
c
dsdeEl
(dp,ar(3,3),l)
elastic moduli
c
pleq_t
(dp,sc
,l)
equivalent plastic strain at beginnig of time
increment
c
pleq
(dp,sc
,l)
equivalent plastic strain at end of time
increment
c
dpleq
(dp,sc
,l)
incremental equivalent plastic strain
c
gamma
(dp,sc
,l)
variable for solving incremental equivalent
plastic strain
c
dgamma
(dp,sc
,l)
correction of gamma
c
sigy_t
(dp,sc
,l)
yield stress at beginnig of time increments
c
sigy
(dp,sc
,l)
yield stress at end of time 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 slop
c
twoG
(dp,sc
,l)
two time of shear moduli
c
funcf
(dp,sc
,l)
nonlinear function to be solved for gamma
c
dFdep
(dp,sc
,l)
derivative of nonlinear function over gamma
c
c --- temperary variables for solution purpose
c
i, j
c
c1, c2, c3, fratio
c
wk1(3), wk2(3), wk3(3), wk4(3) vector working arrays
c
EXTERNAL
vmove, vzero, vapb1, vamb1,get_ElmData
DOUBLE PRECISION sigElp(mcomp), dsdeEl(mcomp,mcomp),
&
wk1(3), wk2(3), wk3(3), wk4(3)
&
DOUBLE PRECISION var0, var1, var2, var3, var4, var5,
var6, var7, var8
INTEGER
i, j, k
DOUBLE PRECISION pleq_t, sigy_t , sigy,
&
cpleq, dpleq,
pleq,
&
young, posn,
sigy0,
&
gamma, dgamma, dfdga,
&
funcFb,funcFb2, funcf,
twoG,
et,
dsigdep,
dplga,
fratio,
dFdep,
&
c1, c2, c3, c4, c5
DOUBLE PRECISION pv(3)
data pv/TWOTHIRD, TWO, TWO/
c*************************************************************************
c
integer iott,wrinqr
external wrinqr
c
c*************************************************************************
c
iott = wrinqr(WR_OUTPUT)
write(iott,*) ' ************************************************'
write(iott,*) ' * #DEBUG# UserMatLib.dll USERMATBM
*'
write(iott,*) ' ************************************************'
keycut
= 0
c *** equivalent plastic strain at beginning of time step
pleq_t
= ustatev(ncomp+1)
pleq
= pleq_t
c *** get Young's modulus and Poisson's ratio, initial yield stress and slope of stressstrain
young
= prop(1)
posn
= prop(2)
sigy0
= prop(3)
et
= prop(4)
c *** calculate plastic slope
dsigdep = young * et/(young - et)
twoG
= young / (ONE+posn)
c *** define tsstif(1) since it is used for calculation of hourglass stiffness
tsstif(1) = HALF * twoG
c
c *** calculate elastic stiffness matrix
c
call vzero(dsdeEl(1,1), ncomp * ncomp)
c1 = twoG * HALF
dsdeEl (1,1) = young
dsdeEl (2,2) = c1
dsdeEl (3,3) = c1
DO i = 1, ncomp
wk3(i) = dsdeEl(i,i)
END DO
c *** calculate predicted strain
call vmove(Strain(1), wk1(1), ncomp)
call vapb1(wk1(1), dStrain(1), ncomp)
call vamb1(wk1(1), ustatev(1), ncomp)
c
c *** get initial stress
call vzero(sigi(1),ncomp)
i = ncomp
call get_ElmData ('ISIG', elemId,kDomIntPt, i, sigi)
c
c *** calculate the trial stress and
c
copy elastic moduli dsdeEl to material Jacobian matrix
call vmove(dsdeEl(1,1), dsdePl(1,1), ncomp * ncomp)
do i=1,ncomp
sigElp(i) = wk3(i) * wk1(i) + sigi(i)
end do
c
funcFb2 = ZERO
DO i = 1, ncomp
funcFb2 = funcFb2 + pv(i) * sigElp(i) * sigElp(i)
END DO
funcFb = sqrt(funcFb2)
c *** compute current yield stress
sigy
= sigy0 + dsigdep * pleq
c
fratio = funcFb/sigy - SQTWOTHIRD
c *** check for yielding
IF (fratio .LE. -SMALL) GO TO 500
sigy_t = sigy
DO i = 1, ncomp
wk3(i) = wk3(i) * pv(i)
END DO
gamma
dplga
dfdga
dpleq
pleq
= ZERO
= ZERO
= ZERO
= ZERO
= pleq_t
c *** Local New-Raphson procedure for solving the gamma and
c
thus the incremental equivalent plastic strain
DO k=1,NEWTON
funcFb2 = ZERO
dfdga
= ZERO
DO j = 1 , ncomp
c1 = ONE + gamma * wk3(j)
c1 = ONE / c1
c2 = sigElp(j) * c1
wk4(j) = c2
funcFb2 = funcFb2 + pv(j) * c2 * c2
c2 = c2 * c2 * c1 * wk3(j) * pv(j)
dfdga
= dfdga - c2
END DO
funcFb
= sqrt(funcFb2)
c ***
derivative of funcFb w.r.t. gamma
dfdga
= dfdga / funcFb
c ***
c ***
c ***
c ***
c ***
c ***
c ***
calculate the incremental equivalent plastic strain
dpleq
= gamma * SQTWOTHIRD * funcFb
update the total equivalent plastic strain
pleq
= pleq_t + dpleq
current yield stress
sigy
= sigy0 + dsigdep * pleq
calculate the residual
funcf
= funcFb - SQTWOTHIRD * sigy
derivative of incremental equivalent plastic strain w.r.t. gamma
dplga
= SQTWOTHIRD * (gamma * dfdga + funcFb)
derivative of residual function w.r.t. gamma
dFdep
= dfdga - SQTWOTHIRD * dsigdep * dplga
correction of gamma
dgamma
= -funcf / dFdep
c ***
c
c ***
&
&
&
&
gamma
= gamma
+ dgamma
check for negative gamma
gamma
= max (gamma, sqTiny)
fratio
= funcf/ sigy
Check for convergence of local New-Raphson iteration
IF (((abs(fratio) .LT. ONEDM05 ) .AND.
(abs(dgamma) .LT. ONEDM02*gamma)) .OR.
((abs(fratio) .LT. ONEDM05 ) .AND.
(dgamma
.LE. sqTiny ) .AND.
( gamma
.LE. sqTiny ))) GO TO 100
END DO
c
c *** Uncovergence, set keycut to 1 for bisection/cutback the load increment
keycut
= 1
GO TO 990
100 CONTINUE
c
c *** update stresses
call vmove(wk4(1), stress(1), ncomp)
c *** calculate incremental plastic strain
DO j = 1, ncomp
wk2(j) = gamma * pv(j) * wk4(j)
END DO
c *** update plastic strains
call vapb1(epsPl(1),wk2(1),ncomp)
c *** Update state variables
ustatev(ncomp+1) = pleq
do i=1,ncomp
ustatev(i) = epsPl(i)
end do
c *** update plastic work
sedPl
= sedPl + HALF * (sigy_t+sigy) * dpleq
c1
= TWOTHIRD * dsigdep
c3
= c1 * funcFb2 / (ONE - c1 * gamma)
DO j = 1 , ncomp
c1 = ONE / (ONE + gamma * wk3(j))
wk3(j) = wk3(j) * c1 / pv(j)
END DO
DO j = 1 , ncomp
wk4(j) = wk4(j) * pv(j)
END DO
DO j = 1 , ncomp
c3 = c3 + wk4(j) * wk4(j) * wk3(j)
END DO
DO j = 1 , ncomp
wk4(j) = wk4(j) * wk3(j)
END DO
c3
= ONE / c3
DO i=1,ncomp
dsdePl(i,i) = wk3(i)
END DO
c *** Calculate the plastic Jacobian
DO i=1,ncomp
DO j=1,ncomp
dsdePl(i,j) =
END DO
END DO
dsdePl(i,j) - c3 * wk4(i) * wk4(j)
goto 600
500 continue
c *** Update stress in case of elastic/unloading
call vmove(sigElp(1),stress(1),ncomp)
600 continue
c *** elastic strain energy
sedEl = ZERO
DO i = 1 , ncomp
sedEl = sedEl + stress(i)*(Strain(i)+dStrain(i)-epsPl(i))
END DO
sedEl = sedEl * HALF
ustatev(nStatev) = funcFb / SQTWOTHIRD
990
c
CONTINUE
return
end
*deck,usermatps
USERDISTRIB parallel
gal
subroutine usermatps(
&
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 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
gal July, 1999
c
c
The following demonstrates a USERMAT subroutine for
c
a plasticity model of plane stress state (such as PLANE182,
c
PLANE183 or SHELL181). The plasticity model is the same
c
as ANSYS TB, BISO.
c
c
See "ANSYS user material subroutine USERMAT" for detailed
c
description of how to write a USERMAT routine.
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
ustatev(1)
- equivalent plastic strain
c
ustatev(2) - ustatev(1+ncomp)
- plastic strain vector
c
ustatev(nStatev)
- von-Mises stress
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"
#include "ansysdef.inc"
c
INTEGER
&
&
&
&
matId, elemId,
kDomIntPt, kLayer, kSectPt,
ldstep,isubst,keycut,
nDirect,nShear,ncomp,nStatev,nProp
DOUBLE PRECISION
&
&
Time,
sedEl,
dTime,
sedPl,
Temp,
epseq,
dTemp,
epsZZ
DOUBLE PRECISION
&
&
&
&
&
&
&
stress (ncomp ), ustatev (nStatev),
dsdePl (ncomp,ncomp), sigi(ncomp),
Strain (ncomp ), dStrain (ncomp ),
epsPl
(ncomp ), prop
(nProp ),
coords (3),
defGrad (3,3),
defGrad_t(3,3),
tsstif (2)
c
c***************** User defined part *************************************
c
c --- parameters
c
INTEGER
NEWTON, mcomp
DOUBLE PRECISION HALF, THIRD, ONE, TWO, SMALL,
&
SQTWOTHIRD, SQTWO1,
&
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,
&
TWOTHIRD
= 2.0d0/3.0d0,
&
SQTWOTHIRD = 0.816496580927726030d0,
&
SQTWO1
= 0.707106769084930420d0,
&
NEWTON
= 20,
&
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
pleq_t
(dp,sc
,l)
equivalent plastic strain at beginnig of time
increment
c
pleq
(dp,sc
,l)
equivalent plastic strain at end of time
increment
c
dpleq
(dp,sc
,l)
incremental equivalent plastic strain
c
gamma
(dp,sc
,l)
variable for solving incremental equivalent
plastic strain
c
dgamma
(dp,sc
,l)
correction of gamma
c
sigy_t
(dp,sc
,l)
yield stress at beginnig of time increments
c
sigy
(dp,sc
,l)
yield stress at end of time 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 slop
c
twoG
(dp,sc
,l)
two time of shear moduli
c
funcf
(dp,sc
,l)
nonlinear function to be solved for dpleq
c
dFdep
(dp,sc
,l)
derivative of nonlinear function over dpleq
c
c --- temperary variables for solution purpose
c
i, j
c
con1eOv2qEl, oneOv3G, qElOv3G, con1, con2, fratio
c
EXTERNAL
vmove, vzero, vapb1, get_ElmData
DOUBLE PRECISION sigElp(mcomp), dsdeEl(mcomp,mcomp),
&
wk1(3), wk2(3), wk3(3), wk4(3)
&
DOUBLE PRECISION var0, var1, var2, var3, var4, var5,
var6, var7, var8
INTEGER
i, j, k
DOUBLE PRECISION pleq_t, sigy_t , sigy,
&
dpleq,
pleq,
twoG,
et,
&
young, posn,
sigy0,
dsigdep, tEo1pm,
&
gamma, dgamma, dfdga,
dplga,
&
funcFb,funcFb2, funcf,
dFdep,
fratio,
&
con1, con2,
con3, con4,
&
con2p1, ocon2p1,
&
ocon2p2, con4p1, ocon4p1, ocon4p2,
&
c1, c2, c3,c4, c5,dperr(3)
c*************************************************************************
c
integer iott,wrinqr
external wrinqr
c
c*************************************************************************
c
iott = wrinqr(WR_OUTPUT)
write(iott,*) ' ************************************************'
write(iott,*) ' * #DEBUG# UserMatLib.dll USERMATPS
*'
write(iott,*) ' ************************************************'
keycut
= 0
c *** equivalent plastic strain at beginning of time step
pleq_t
= ustatev(1)
pleq
= pleq_t
c *** get Young's modulus and Poisson's ratio, initial yield stress and slope of stressstrain
young
= prop(1)
posn
= prop(2)
sigy0
= prop(3)
et
= prop(4)
c *** calculate plastic slope
dsigdep = young * et/(young - et)
twoG
= young / (ONE+posn)
tEo1pm
= THIRD * young /(ONE - posn)
c *** define tsstif(1) since it is used for calculation of hourglass stiffness
tsstif(1) = HALF * twoG
c
c *** calculate elastic stiffness matrix (3d)
c
c1 = ONE - posn * posn
c2 = young / c1
c3 = posn * c2
dsdeEl (1,1) = c2
dsdeEl (1,2) = c3
dsdeEl (1,3) = ZERO
dsdeEl (2,2) = c2
dsdeEl (2,3) = ZERO
dsdeEl (3,3) = HALF * twoG
do i=1,ncomp-1
do j=i+1,ncomp
dsdeEl(j,i)=dsdeEl(i,j)
end do
end do
call vmove(ustatev(2), epsPl(1), ncomp)
c *** calculate elastic strain
do i=1,ncomp
wk1(i) = Strain(i) - epsPl(i) + dStrain(i)
end do
c
c *** get initial stress
call vzero(sigi(1),ncomp)
i = ncomp
call get_ElmData ('ISIG', elemId,kDomIntPt, i, sigi)
c
c *** calculate the trial stress and
c
copy elastic moduli dsdeEl to material Jacobian matrix
do i=1,ncomp
sigElp(i) = ZERO
do j=1,ncomp
dsdePl(j,i) = dsdeEl(j,i)
sigElp(i) = sigElp(i) + dsdeEl(j,i) * wk1(j)
end do
sigElp(i) = sigElp(i) + sigi(i)
end do
c
wk1(1)
= SQTWO1 * ( sigElp(1) + sigElp(2) )
wk1(2)
= SQTWO1 * (-sigElp(1) + sigElp(2) )
wk1(3)
= sigElp(3)
c
funcFb2 = THIRD * wk1(1) * wk1(1) +
&
wk1(2) * wk1(2) + TWO * wk1(3) * wk1(3)
funcFb
= sqrt(funcFb2)
c *** compute current yield stress
sigy
= sigy0 + dsigdep * pleq
c
fratio = funcFb/sigy - SQTWOTHIRD
c *** check for yielding
IF (fratio .LE. -SMALL) GO TO 500
sigy_t = sigy
gamma
dplga
dfdga
con1
con2
= ZERO
= ZERO
= ZERO
= THIRD * wk1(1) * wk1(1)
= wk1(2) * wk1(2) + TWO * wk1(3) * wk1(3)
con3
con4
funcf
dfdga
dFdep
dgamma
gamma
gamma
= - con1 * tEo1pm
= - con2 * twoG
= funcFb - SQTWOTHIRD * sigy
= (con3 + con4) / funcFb
= dfdga - TWOTHIRD * dsigdep * funcFb
= -funcf / dFdep
= gamma
+ dgamma
= max (gamma, sqTiny)
DO k=1,NEWTON
con2p1
con4p1
ocon2p1
ocon2p2
ocon4p1
ocon4p2
funcFb2
funcFb
c
c ***
c ***
c ***
c ***
c ***
&
c ***
c ***
= ONE + tEo1pm * gamma
= ONE + twoG * gamma
= ONE / con2p1
= ocon2p1 * ocon2p1
= ONE / con4p1
= ocon4p1 * ocon4p1
= con1 * ocon2p2 + con2 * ocon4p2
= sqrt(funcFb2)
calculate the incremental equivalent plastic strain
dpleq
= gamma * SQTWOTHIRD * funcFb
update the total equivalent plastic strain
pleq
= pleq_t + dpleq
current yield stress
sigy
= sigy0 + dsigdep * pleq
calculate the residual
funcf
= funcFb - SQTWOTHIRD * sigy
derivative of funcFb w.r.t. gamma
dfdga
= ( con3 * ocon2p2 * ocon2p1
+ con4 * ocon4p2 * ocon4p1) / funcFb
derivative of incremental equivalent plastic strain w.r.t. gamma
dplga
= SQTWOTHIRD * (gamma * dfdga + funcFb)
derivative of residual function w.r.t. gamma
dFdep = dfdga - SQTWOTHIRD * dsigdep * dplga
fratio
= funcf/ sigy
dgamma
gamma
gamma
= -funcf / dFdep
= gamma
+ dgamma
= max (gamma, sqTiny)
c
&
&
&
&
IF (((abs(fratio) .LT. ONEDM05 ) .AND.
(abs(dgamma) .LT. ONEDM02*gamma)) .OR.
((abs(fratio) .LT. ONEDM05 ) .AND.
(dgamma
.LE. sqTiny ) .AND.
( gamma
.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
c1 = ONE / ( ONE + gamma * tEo1pm)
c2 = ONE / ( ONE + gamma * twoG )
stress(1) = SQTWO1 * (c1 * wk1(1) - c2 * wk1(2))
stress(2) = SQTWO1 * (c1 * wk1(1) + c2 * wk1(2))
stress(3) = c2 * wk1(3)
c
wk1(1)
= SQTWO1 * ( stress(1) + stress(2))
wk1(2)
= SQTWO1 * (-stress(1) + stress(2))
wk1(3)
= stress(3)
con1 = SQTWO1 * gamma
c *** calculate incremental plastic strain, wk2(i)
wk2(1)
= con1 * ( THIRD * wk1(1) - wk1(2))
wk2(2)
= con1 * ( THIRD * wk1(1) + wk1(2))
wk2(3)
= TWO * gamma * wk1 (3)
c ***
update plastic strains
call vapb1(epsPl(1),wk2(1),ncomp)
epseq
= pleq
ustatev(1) = pleq
c *** calculate plastic work
sedPl
= sedPl + HALF * (sigy_t+sigy) * dpleq
c *** consistent tangent stiffness matrix
con3
= TWOTHIRD*dsigdep*funcFb2/(ONE-TWOTHIRD*dsigdep*gamma)
call vmove(wk1(1),wk4(1),3)
c1 = wk4(1)
c2 = wk4(2)
c3 = wk4(3)
c4 = tEo1pm / (ONE + tEo1pm * gamma)
c5 = twoG / (ONE + twoG * gamma)
wk4(1) = SQTWO1 * ( c4 * c1 - c5 * c2)
wk4(2) = SQTWO1 * ( c4 * c1 + c5 * c2)
wk4(3) = c5 * c3
call vmove(wk4(1),wk3(1),3)
c1 = wk3(1)
c2 = wk3(2)
wk3(1) = SQTWO1 * ( c1+c2)
wk3(2) = SQTWO1 * (-c1+c2)
con3
&
= con3 + THIRD*wk1(1)*wk3(1)+
wk1(2)*wk3(2)+TWO*wk1(3)*wk3(3)
c1 = 3.0d0 * tEo1pm / (ONE + tEo1pm * gamma)
c2 = twoG / (ONE + twoG * gamma)
call vzero(dsdePl(1,1),9)
dsdePl(1,1) = HALF * (c1 + c2)
dsdePl(2,1) = HALF * (c1 - c2)
dsdePl(1,2) = dsdePl(2,1)
dsdePl(2,2) = dsdePl(1,1)
dsdePl(3,3) = HALF * c2
con3
= ONE / con3
DO i=1,3
DO j=1,3
dsdePl(i,j) = dsdePl(i,j) - con3 * wk4(i) * wk4(j)
END DO
END DO
goto 600
500 continue
c *** Update stress in case of elastic/unloading
call vmove(sigElp(1),stress(1),ncomp)
600 continue
c *** elastic strain and put into epsZZ
epsZZ
= -posn/young * (stress(1) + stress(2))
c *** add plastic strain to total strain epsZZ
epsZZ
= epsZZ - (epsPl(1) + epsPl(2))
c *** elastic strain energy
sedEl = ZERO
DO i = 1 , ncomp
sedEl = sedEl + stress(i)*(Strain(i)+dStrain(i)-epsPl(i))
END DO
sedEl
= sedEl * HALF
ustatev(nStatev) = sigy
do i=1,ncomp
ustatev(i+1) = epsPl(i)
end do
990
c
CONTINUE
return
end