Product: Abaqus/Standard
User subroutine UCREEPNETWORK:
is intended to provide creep laws for nonlinear viscoelastic networks for models defined using the parallel rheological framework (see “Parallel rheological framework,” Section 22.8.2 of the Abaqus Analysis User's Guide);
can use and update solution-dependent state variables; and
can be used in conjunction with user subroutine USDFLD to redefine any field variables before they are passed in.
The user subroutine allows a creep law of the following general form to be defined:
is the identity tensor,
is the right Cauchy-Green creep strain tensor,
is the equivalent creep strain rate,
is the equivalent creep strain,
is the first invariant of 
,
is the second invariant of ,
is the determinant of the deformation gradient, 
,
is the Kirchhoff pressure,
is the equivalent deviatoric Kirchhoff stress,
t
is the time,
is the temperature, and
FV
are field variables.
, is defined as
is the deformation gradient with volume change eliminated, which is computed using
, as a function of the time increment, 
, and the variables used in the definition of 
, as well as the derivatives of the equivalent creep strain increment with respect to those variables. If any solution-dependent state variables are included in the definition of , they must also be integrated forward in time in this user subroutine. subroutine ucreepnetwork (
C Must be updated
* outputData,
C Can be updated
* statev,
C Information (Read only)
* nOutput,
* nstatv,
* networkid,
* coords,
* temp,
* dtemp,
* nfield,
* predef,
* dpred,
* nprops,
* props,
* i_array,
* niarray,
* r_array,
* nrarray,
* c_array,
* ncarray)
C
include 'aba_param.inc'
C
parameter( io_creep_equiv_creepinc = 1,
* io_creep_deqcreepinc_deqcreep = 2,
* io_creep_deqcreepinc_dqtild = 3,
* io_creep_deqcreepinc_dinv1crp = 4,
* io_creep_deqcreepinc_dinv1 = 5,
* io_creep_deqcreepinc_dinv2 = 6,
* io_creep_deqcreepinc_ddetf = 7,
* io_creep_deqcreepinc_dpress = 8 )
C
parameter( i_creep_kstep = 1,
* i_creep_kinc = 2,
* i_creep_noel = 3,
* i_creep_npt = 4,
* i_creep_layer = 5,
* i_creep_kspt = 6,
* i_creep_lend = 7 )
C
parameter( ir_creep_step_time = 1,
* ir_creep_total_time = 2,
* ir_creep_creep_time = 3,
* ir_creep_timeinc = 4,
* ir_creep_equiv_creep_strain = 5,
* ir_creep_qtild = 6,
* ir_creep_inv1crp = 7,
* ir_creep_inv1 = 8,
* ir_creep_inv2 = 9,
* ir_creep_detf = 10,
* ir_creep_press = 11 )
C
parameter( ic_creep_material_name = 1 )
C
dimension
* statev(nstatv),
* predef(nfield),
* dpred(nfield),
* coords(*),
* props(nprops),
* outputData(nOutput),
* i_array(niarray),
* r_array(nrarray)
character*80 c_array(ncarray)
C
user coding to define outputData(io_creep_equiv_creepinc),
outputData(io_creep_deqcreepinc_deqcreep),
outputData(io_creep_deqcreepinc_dqtild),
outputData(io_creep_deqcreepinc_dinv1crp),
outputData(io_creep_deqcreepinc_dinv1),
outputData(io_creep_deqcreepinc_dinv2),
outputData(io_creep_deqcreepinc_ddetf) and
outputData(io_creep_deqcreepinc_dpress)
return
endoutputData(io_creep_equiv_creepinc)
Equivalent creep strain increment, 
.
outputData(io_creep_deqcreepinc_deqcreep)
The derivative: 
.
outputData(io_creep_deqcreepinc_dqtild)
The derivative: 
.
outputData(io_creep_deqcreepinc_dinv1crp)
The derivative: 
.
outputData(io_creep_deqcreepinc_dinv1)
The derivative: 
.
outputData(io_creep_deqcreepinc_dinv2)
The derivative: 
.
outputData(io_creep_deqcreepinc_ddetf)
The derivative: 
.
outputData(io_creep_deqcreepinc_dpress)
The derivative: 
.
statev
An array containing the user-defined solution-dependent state variables at this point.
nOutput
Size of array outputData.
nstatv
Number of solution-dependent state variables associated with this material.
networkid
Network identification number, which identifies the network for which creep is defined.
coords
An array containing the current coordinates at this point.
temp
Temperature at the end of the increment.
dtemp
Increment of temperature.
nfield
Number of field variables.
predef
An array of interpolated values of predefined field variables at this point at the end of the increment, based on the values read in at the nodes and, optionally, redefined in user subroutine USDFLD.
dpred
An array of increments of predefined field variables.
nprops
User-specified number of property values associated with this creep model.
props
An array of user-specified property values that are used to define the creep model.
i_array(i_creep_kstep)
Step number.
i_array(i_creep_kinc)
Increment number.
i_array(i_creep_noel)
Element number.
i_array(i_creep_npt)
Integration point.
i_array(i_creep_layer)
Layer number (for layered solids).
i_array(i_creep_kspt)
Section point number within the current layer.
i_array(i_creep_lend)
Start/end of increment flag. The value of 0 denotes the beginning of the increment, and the value of 1 denotes the end of the increment.
niarray
Size of array i_array.
r_array(ir_creep_step_time)
Value of step time at the end of the increment.
r_array(ir_creep_total_time)
Value of total time at the end of the increment.
r_array(ir_creep_creep_time)
Value of creep time at the end of the increment.
r_array(ir_creep_timeinc)
Time increment.
r_array(ir_creep_equiv_creep_strain)
Equivalent creep strain.
r_array(ir_creep_qtild)
Equivalent deviatoric Kirchhoff stress.
r_array(ir_creep_inv1crp)
The first invariant, 
, of the right Cauchy-Green creep strain tensor, 
.
r_array(ir_creep_inv1)
The first invariant, 
, of the left Cauchy-Green strain tensor, 
.
r_array(ir_creep_inv2)
The second invariant, 
, of the left Cauchy-Green strain tensor, .
r_array(ir_creep_detf)
The determinant of the deformation gradient, 
.
r_array(ir_creep_press)
Kirchhoff pressure.
nrarray
Size of array r_array.
c_array(ic_creep_material_name)
User-specified material name, left justified. Some internal material models are given names starting with the “ABQ_” character string. To avoid conflict, you should not use “ABQ_” as the leading string for the material name.
ncarray
Size of array c_array.
As an example of the coding of user subroutine UCREEPNETWORK, consider the Bergstrom-Boyce model. In this case the equivalent creep strain rate is expressed as (see “Parallel rheological framework,” Section 22.8.2 of the Abaqus Analysis User's Guide)
is the right Cauchy-Green creep strain tensor,
is the equivalent deviatoric Kirchhoff stress, and
A, m, C, and E
are material parameters.
The user subroutine would be coded as follows:
subroutine ucreepnetwork (
C Must be updated
* outputData,
C Can be updated
* statev,
C Information (Read only)
* nOutput,
* nstatv,
* networkid,
* coords,
* temp,
* dtemp,
* nfield,
* predef,
* dpred,
* nprops,
* props,
* i_array,
* niarray,
* r_array,
* nrarray,
* c_array,
* ncarray)
C
include 'aba_param.inc'
C
parameter( io_creep_equiv_creepinc = 1,
* io_creep_deqcreepinc_deqcreep = 2,
* io_creep_deqcreepinc_dqtild = 3,
* io_creep_deqcreepinc_dinv1crp = 4,
* io_creep_deqcreepinc_dinv1 = 5,
* io_creep_deqcreepinc_dinv2 = 6,
* io_creep_deqcreepinc_ddetf = 7,
* io_creep_deqcreepinc_dpress = 8 )
C
parameter( i_creep_kstep = 1,
* i_creep_kinc = 2,
* i_creep_noel = 3,
* i_creep_npt = 4,
* i_creep_layer = 5,
* i_creep_kspt = 6,
* i_creep_lend = 7 )
C
parameter( ir_creep_step_time = 1,
* ir_creep_total_time = 2,
* ir_creep_creep_time = 3,
* ir_creep_timeinc = 4,
* ir_creep_equiv_creep_strain = 5,
* ir_creep_qtild = 6,
* ir_creep_inv1crp = 7,
* ir_creep_inv1 = 8,
* ir_creep_inv2 = 9,
* ir_creep_detf = 10,
* ir_creep_press = 11 )
C
parameter( ic_creep_material_name = 1 )
C
C model parameters
parameter ( zero=0.0d0,half=0.5d0,one=1.0d0,two=2.0d0,
& three=3.0d0,five=5.0d0,six=6.0d0 )
C
dimension
* statev(nstatv),
* predef(nfield),
* dpred(nfield),
* coords(*),
* props(nprops),
* outputData(nOutput),
* i_array(niarray),
* r_array(nrarray)
character*80 c_array(ncarray)
C
C Bergstrom-Boyce Model
C
A = props(1)
dm = props(2)
C = props(3)
E = props(4)
C
dI1 = r_array(ir_creep_inv1crp)
dLamb = (dI1/three)**half
sigmaB = r_array(ir_creep_qtild)
dt = r_array(ir_creep_timeinc)
C
C deq
deq = dt*A*(dLamb-one+E)**C*sigmaB**dm
C
C d(deq)/(dI1crp)
deqdi1 = deq*C/(dLamb-one+E)/dLamb/six
C
C d(eq)/d(eq)
deqeq = zero
C
C d(eq)/d(q)
deqdq = dm*dt*A*(dLamb-one+E)**C*sigmaB**(dm-one)
C
C set output
outputData(io_creep_equiv_creepinc) = deq
outputData(io_creep_deqcreepinc_deqcreep) = deqeq
outputData(io_creep_deqcreepinc_dqtild) = deqdq
outputData(io_creep_deqcreepinc_dinv1crp) = deqdi1
outputData(io_creep_deqcreepinc_dinv1) = zero
outputData(io_creep_deqcreepinc_dinv2) = zero
outputData(io_creep_deqcreepinc_ddetf) = zero
outputData(io_creep_deqcreepinc_dpress) = zero
C
return
end