Abaqus User Subroutines Reference Guide  

1.2.13 VUCREEPNETWORK
User subroutine to define time-dependent behavior (creep) for models defined within the parallel rheological framework.

Product: Abaqus/Explicit  

References

Overview

User subroutine VUCREEPNETWORK:

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 vucreepnetwork (
C Read only -
     *   nblock, networkid, nstatev, nfieldv,
     *   nprops, nDg, stepTime, totalTime, dt,
     *   jElem, kIntPt, kLayer, kSecPt, cmname,
     *   props, coordMp, tempOld, fieldOld,
     *   stateOld, tempNew, fieldNew,
     *   nIarray, i_array, nRarray, r_array,
     *   q, p, eqcs, TrCc,
C Write only -
     *   dg, stateNew )
C
      include 'vaba_param.inc'
C
C     indices for equivalent creep strain and its derivatives
      parameter( i_deqcs       = 1,
     *           i_DdeqcsDq    = 2,
     *           i_DdeqcsDeqcs = 3,
     *           i_DdeqcsDi1c  = 4 )
C
C     indices for strain invariants
      parameter( i_I1 = 1,
     *           i_I2 = 2,
     *           i_J  = 3 )
C
      dimension props(nprops),
     *  tempOld(nblock),
     *  fieldOld(nblock,nfieldv),
     *  stateOld(nblock,nstatev),
     *  tempNew(nblock),
     *  fieldNew(nblock,nfieldv),
     *  coordMp(nblock,*),
     *  jElem(nblock),
     *  i_array(nblock,nIarray),
     *  r_array(nblock,nRarray),
     *  q(nblock),
     *  p(nblock),
     *  eqcs(nblock),
     *  TrCc(nblock),
     *  stateNew(nblock,nstatev),
     *  dg(nblock,nDg)

      character*80 cmname
C
      do 100 km = 1,nblock
        user coding
  100 continue

      return
      end

Variables to be defined

dg(nblock,i_deqcs)

Equivalent creep strain increment, .

dg(nblock,i_DdeqcsDq)

The derivative: .

dg(nblock,i_DdeqcsDeqcs)

The derivative: .

dg(nblock,i_DdeqcsDi1c)

The first invariant, , of the right Cauchy-Green creep strain tensor, .

Variable that can be updated

stateNew(nblock,nstatev)

Array containing the user-defined solution-dependent state variables at this point.

Variables passed in for information

nblock

Number of material points to be processed in this call to user subroutine VUCREEPNETWORK.

networkid

Network identification number, which identifies the network for which creep is defined.

nstatev

Number of user-defined state variables that are associated with this material type (see “Allocating space” in “User subroutines: overview,” Section 18.1.1 of the Abaqus Analysis User's Guide).

nfieldv

Number of user-defined external field variables.

nprops

User-specified number of user-defined material properties.

nDg

Size of array dg.

stepTime

Value of time since the step began.

totalTime

Value of total time. The time at the beginning of the step is given by totalTime-stepTime.

dt

Time increment size.

jElem(nblock)

Array of element numbers.

kIntPt

Integration point number.

kLayer

Layer number (for composite shells).

kSecPt

Section point number within the current layer.

cmname

Material name, left justified. It is passed in as an uppercase character string. Some internal material models are given names starting with the “ABQ_” character string. To avoid conflict, “ABQ_” should not be used as the leading string for cmname.

props(nprops)

User-supplied material properties.

coordMp(nblock,*)

Material point coordinates. It is the midplane material point for shell elements and the centroid for beam elements.

tempOld(nblock)

Temperatures at the material points at the beginning of the increment.

fieldOld(nblock,nfieldv)

Values of the user-defined field variables at the material points at the beginning of the increment.

stateOld(nblock,nstatev)

State variables at the material points at the beginning of the increment.

tempNew(nblock)

Temperatures at the material points at the end of the increment.

fieldNew(nblock)

Values of the user-defined field variables at the material points at the end of the increment.

nIarray

Size of array i_array.

i_array(nblock,nIarray)

Array containing integer arguments. Currently it is not used.

nRarray

Size of array r_array.

r_array(nblock,i_I1)

The first invariant, , of the left Cauchy-Green strain tensor, .

r_array(nblock,i_I2)

The second invariant, , of the left Cauchy-Green strain tensor, .

r_array(nblock,i_J)

The determinant of the deformation gradient, .

q(nblock)

Array containing equivalent deviatoric Kirchhoff stresses.

p(nblock)

Array containing Kirchhoff pressures.

eqcs(nblock)

Array containing equivalent creep strains.

TrCc(nblock)

Array containing the first invariants, , of the right Cauchy-Green creep strain tensor, .

Example: Power-law strain hardening model

As an example of the coding of user subroutine VUCREEPNETWORK, consider the power-law strain hardening model. In this case the equivalent creep strain rate is expressed as

where

is the equivalent creep strain,

is the equivalent deviatoric Kirchhoff stress, and

A, m, and n

are material parameters.

The user subroutine would be coded as follows:

     subroutine vucreepnetwork (
C Read only -
     *   nblock, networkid, nstatev, nfieldv,
     *   nprops, nDg, stepTime, totalTime, dt,
     *   jElem, kIntPt, kLayer, kSecPt, cmname,
     *   props, coordMp, tempOld, fieldOld,
     *   stateOld, tempNew, fieldNew,
     *   nIarray, i_array, nRarray, r_array,
     *   q, p, eqcs, TrCc,
C Write only -
     *   dg, stateNew )
C
      include 'vaba_param.inc'
C
      parameter ( one = 1.d0, half = 0.5d0 )
      parameter ( eqcsSmall = 1.d-8 )
      parameter ( rMinVal = 1.d-12 )
C
      parameter( i_deqcs       = 1,
     *           i_DdeqcsDq    = 2,
     *           i_DdeqcsDeqcs = 3,
     *           i_DdeqcsDi1c  = 4 )
C
      dimension props(nprops),
     *  tempOld(nblock),
     *  fieldOld(nblock,nfieldv),
     *  stateOld(nblock,nstatev),
     *  tempNew(nblock),
     *  fieldNew(nblock,nfieldv),
     *  coordMp(nblock,*),
     *  jElem(nblock),
     *  i_array(nblock,nIarray),
     *  r_array(nblock,nRarray),
     *  q(nblock),
     *  p(nblock),
     *  eqcs(nblock),
     *  TrCc(nblock),
     *  stateNew(nblock,nstatev),
     *  dg(nblock,nDg)
C
      character*80 cmname
C
C Read properties
C
      rA = props(1)
      rN = props(2)
      rM = props(3)
C
C Update equivalent creep strain and its derivatives
C
      do k = 1, nblock
        om1 = one / ( one + rM )
        test = half - sign( half, q(k) - rMinVal )
        qInv = ( one - test ) / ( q(k) + test )
        eqcs_t = eqcs(k)
        if ( eqcs_t .le. eqcsSmall .and. q(k).gt.rMinVal ) then 
C Initial guess based on constant creep strain rate during increment
          eqcs_t = dt*(exp(log(rA)+rN*log(q(k)))*
     *             ((one+rM)*dt)**rM)
        end if
C
        test2 = half - sign( half, eqcs_t - rMinVal )
        eqcsInv = ( one - test2 ) / ( eqcs_t + test2 )
        g = dt*(exp(log(rA)+rN*log(q(k)))*
     *       ((one+rM)*(test2+eqcs_t))**rM)**om1
        dg(k,i_deqcs) = g
        dg(k,i_DdeqcsDq) = qInv * rN * om1 * g
        dg(k,i_DdeqcsDeqcs) = eqcsInv * rM * om1 * g
      end do
C
      return
      end