Model Description
The user subroutine allows a creep law of the following general form to be defined:
where
and
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.
The left Cauchy-Green strain tensor, , is defined as
where is the deformation gradient with volume change eliminated, which is computed using
The user subroutine must define the increment of creep equivalent strain, , 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.
User Subroutine Interface
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
end
Variables to Be Defined
- outputData(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: .
Variables That Can Be Updated
- statev
An array containing the user-defined solution-dependent state variables at this point.
Variables Passed in for Information
- 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.
Example: Bergstrom-Boyce Model
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)
where
and
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
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