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<!-- source-page: 491 -->
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```python
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parameter (zero = 0.d0, half = 0.5d0, one = 1.d0, two=2.d0)
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c
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dimension rhs(nblock,ndofel), amass(nblock,ndofel,ndofel),
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* dtimeStable(nblock),
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* svars(nblock,nsvars), energy(nblock,nElEnergy),
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* props(nprops), jprops(njprops),
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* jElem(nblock), time(nTime), l(nFlags),
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* coords(nblock,nnode,ncrd), u(nblock,ndofel),
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* du(nblock,ndofel), v(nblock,ndofel), a(nblock, ndofel),
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* predef(nblock, nnode, npred, nPred), adlmag(nblock),
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* dMassScaleFactor(nblock)
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c Notes:
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c Define only nonzero entries; the arrays to be defined
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c have been zeroed out just before this call
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if (jtype .eq. 1001 .and.
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* lflags(iProcedure).eq.jDynExplicit) then
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area0 = props(1)
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eMod = props(2)
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anu = props(3)
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rho = props(4)
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eDampTra = zero
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amassFact0 = half*area0*rho
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if ( lflags(iOpCode).eq.jMassCalc ) then
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do kblock = 1, nblock
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c use original distance to compute mass
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alenX0 = (coords(kblock,2,1) - coords(kblock,1,1))
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alenY0 = (coords(kblock,2,2) - coords(kblock,1,2))
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alenZ0 = (coords(kblock,2,3) - coords(kblock,1,3))
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alen0 = sqrt(alenX0*alenX0 + alenY0*alenY0 +
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* alenZ0*alenZ0)
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am0 = amassFact0*alen0
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amass(kblock,1,1) = am0
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amass(kblock,2,2) = am0
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amass(kblock,3,3) = am0
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amass(kblock,4,4) = am0
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amass(kblock,5,5) = am0
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```
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<!-- source-page: 492 -->
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```txt
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amass(kblock,6,6) = am0
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end do
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else if ( lflags(iOpCode) .eq.
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* jIntForceAndDtStable) then
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do kblock = 1, nblock
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alenX0 = (coords(kblock,2,1) - coords(kblock,1,1))
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alenY0 = (coords(kblock,2,2) - coords(kblock,1,2))
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alenZ0 = (coords(kblock,2,3) - coords(kblock,1,3))
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alen0 = sqrt(alenX0*alenX0 + alenY0*alenY0 +
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* alenZ0*alenZ0)
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vol0 = area0*alen0
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amElem0 = two*amassFact0*alen0
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alenX = alenX0
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* + (u(kblock,4) - u(kblock,1))
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alenY = alenY0
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* + (u(kblock,5) - u(kblock,2))
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alenZ = alenZ0
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* + (u(kblock,6) - u(kblock,3))
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alen = sqrt(alenX*alenX + alenY*alenY + alenZ*alenZ)
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area = vol0/alen
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ak = area*eMod/alen
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c stable time increment for translations
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dtimeStable(kblock) = factorStable*sqrt(amElem0/ak)
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c force = E * logarithmic strain *current area
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strainLog = log(alen/alen0)
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fElasTra = eMod*strainLog*area
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forceTra = fElasTra
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c assemble internal load in RHS
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rhs(kblock,1) = -forceTra
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rhs(kblock,4) = forceTra
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c internal energy calculation
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alenOld = svars(kblock,1)
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fElasTraOld = svars(kblock,2)
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energy(kblock, iElIe) = energy(kblock, iElIe) +
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```
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<!-- source-page: 493 -->
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```fortran
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* half*(fElasTra+fElasTraOld)*(alen - alenOld)
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c update state variables
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svars(kblock,1) = alen
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svars(kblock,2) = fElasTra
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end do
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end if
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end if
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c
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return
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end
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```
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<!-- source-page: 494 -->
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<!-- source-page: 495 -->
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# 1.2.15 VUEOS: User subroutine to define equation of state material model.
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# Product: Abaqus/Explicit
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# References
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• “Equation of state,” Section 25.2.1 of the Abaqus Analysis User’s Guide
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• \*EOS
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“Equation of state material,” Section 2.2.20 of the Abaqus Verification Guide
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# Overview
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User subroutine VUEOS:
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• can be used to define the hydrodynamic material model in which the material’s volumetric response is determined by the user-defined equation of state;
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• will be called for blocks of material calculation points for which the material definition contains a user-defined equation of state;
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• can use and update solution-dependent state variables; and
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• can use any field variables that are passed in.
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# User subroutine interface
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```python
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subroutine vueos (
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C Read only (unmodifiable) variables -
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1 nblock,
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2 jElem, kIntPt, kLayer, kSecPt,
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3 steTime, totalTime, dt, cmname,
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4 nstatev, nfieldv, nprops,
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5 props, tempOld, tempNew, fieldOld, fieldNew,
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6 stateOld, charLength, coordMp,
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7 densityMean, refDensity, densityNew,
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8 dkk, Em,
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C Write only (modifiable) variables -
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8 press, dPdRho, dPdEm,
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9 stateNew )
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C
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include 'vaba_param.inc'
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C
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dimension props(nprops),
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1 tempOld(nblock),
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2 fieldOld(nblock, nfieldv),
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```
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<!-- source-page: 496 -->
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```matlab
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3 stateOld(nblock, nstatev),
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4 tempNew(nblock),
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5 fieldNew(nblock, nfieldv),
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6 charLength(nblock), coordMp(nblock, *),
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7 densityMean(nblock), refDensity(nblock),
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8 densityNew(nblock),
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9 dkk(nblock), Em(nblock),
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1 press(nblock), dPdRho(nblock), dPdEm(nblock),
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2 stateNew(nblock)
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C
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character*80 cmname
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C
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do 100 km = 1, nblock
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user coding to define/update press, dPdRho, dPdEm
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100 continue
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return
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end
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```
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# Variables to be defined
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press(nblock)
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The material point pressure stress, p.
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dPdRho(nblock)
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The derivative of the pressure with respect to the density, $\partial p / \partial \rho .$ This quantity is needed for the evaluation of the effective moduli of the material, which enters the stable time increment calculation.
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dPdEm(nblock)
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The derivative of the pressure with respect to the internal energy, $\partial p / \partial E _ { m }$ . This quantity is needed for the iterative Newton loop used outside of the user subroutine to solve for pressure.
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# Variable that can be updated
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stateNew(nblock,nstatev)
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State variables at each material point at the end of the increment. You define the size of this array by allocating space for it (see “User subroutines: overview,” Section 18.1.1 of the Abaqus Analysis User’s Guide, for more information).
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<!-- source-page: 497 -->
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# Variables passed in for information
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nblock
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Number of material points to be processed in this call to VUEOS.
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jElem(nblock)
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Array of element numbers.
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kIntPt
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Integration point number.
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kLayer
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Layer number.
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kSecPt
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Section point number within the current layer.
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stepTime
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Value of time since the step began.
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totalTime
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Value of total time. The time at the beginning of the step is given by totalTime - stepTime.
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dt
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Time increment size.
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cmname
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User-specified 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, you should not use “ABQ\_” as the leading string for cmname.
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nstatev
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Number of user-defined state variables that are associated with this material type (you define the number as described in “Allocating space” in “User subroutines: overview,” Section 18.1.1 of the Abaqus Analysis User’s Guide).
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nfieldv
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Number of user-defined external field variables.
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nprops
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User-specified number of user-defined material properties.
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props(nprops)
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User-supplied material properties.
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<!-- source-page: 498 -->
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tempOld(nblock)
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Temperatures at each material point at the beginning of the increment.
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tempNew(nblock)
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Temperatures at each material point at the end of the increment.
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fieldOld(nblock,nfieldv)
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Values of the user-defined field variables at each material point at the beginning of the increment.
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fieldNew(nblock,nfieldv)
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Values of the user-defined field variables at each material point at the end of the increment.
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stateOld(nblock,nstatev)
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State variables at each material point at the beginning of the increment.
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charLength(nblock)
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Characteristic element length, which is either the default value based on the geometric mean or the user-defined characteristic element length defined in user subroutine VUCHARLENGTH. The default value is a typical length of a line across an element for a first-order element; it is half the same typical length for a second-order element. For beams, pipes, and trusses, the default value is a characteristic length along the element axis. For membranes and shells it is a characteristic length in the reference surface. For axisymmetric elements it is a characteristic length in the r–z plane only. For cohesive elements it is equal to the constitutive thickness.
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coordMp(nblock,\*)
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Material point coordinates.
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densityMean(nblock)
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The mean density.
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refDensity(nblock)
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The reference density.
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densityNew(nblock)
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The current density for this increment.
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dkk(nblock)
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The volumetric strain increment.
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Em(nblock)
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The element specific internal energy (per unit mass)
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Example: User subroutine VUEOS to reproduce results obtained with \*EOS, TYPE=USUP
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As a simple example of coding of user subroutine VUEOS, consider the following form of the Mie-Grüneisen equation of state with 0.0 and a linear dependency between pressure and internal energy:
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<!-- source-page: 499 -->
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$$
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p = \rho_ {0} c _ {0} ^ {2} \eta (1 - \frac {\Gamma_ {0} \eta}{2}) + \Gamma_ {0} \rho_ {0} E _ {m},
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$$
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where $\eta = 1 - \rho _ { 0 } / \rho .$ . Therefore, the results obtained with user subroutine VUEOS should be the same as the results obtained with the linear $U _ { s } - U _ { p }$ type of EOS already available in “Equation of state material,” Section 2.2.20 of the Abaqus Verification Guide.
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The code in user subroutine VUEOS must return the pressure, , as in the above equation; the derivative of the pressure with respect to the density, $\partial p / \partial \rho ;$ and the derivative of the pressure with respect to the energy, $\partial p / \partial E _ { m }$ . For the case considered here, these values are
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$$
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\frac {\partial p}{\partial \rho} = \frac {\rho_ {0} ^ {2} c _ {0} ^ {2}}{\rho^ {2}} (1 - \Gamma_ {0} \eta),
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$$
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$$
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\frac {\partial p}{\partial E _ {m}} = \Gamma_ {0} \rho_ {0}.
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$$```fortran
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subroutine vueos (
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C Read only (unmodifiable) variables -
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1 nblock,
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2 jElem, kIntPt, kLayer, kSecPt,
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3 steTime, totalTime, dt, cmname,
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4 nstatev, nfieldv, nprops,
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5 props, tempOld, tempNew, fieldOld, fieldNew,
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6 stateOld, charLength, coordMp,
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7 densityMean, refDensity, densityNew,
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8 dkk, Em,
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C Write only (modifiable) variables -
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8 press, dPdRho, dPdEm,
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9 stateNew)
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C
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include 'vaba_param.inc'
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C
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dimension props(nprops),
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1 tempOld(nblock),
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2 fieldOld(nblock,nfieldv),
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3 stateOld(nblock,nstatev),
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4 tempNew(nblock),
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5 fieldNew(nblock,nfieldv),
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6 charLength(nblock), coordMp(nblock,*),
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7 densityMean(nblock), refDensity(nblock),
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8 densityNew(nblock),
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9 dkk(nblock), Em(nblock),
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1 press(nblock), dPdRho(nblock), dPdEm(nblock),
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```
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<!-- source-page: 500 -->
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```txt
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2 stateNew(nblock)
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C
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character*80 cmname
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C
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parameter ( zero = 0.d0, one = 1.d0, half = 0.5d0 )
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C
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c0 = props(1)
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gamma0 = props(2)
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c02 = c0*c0
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C
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do k=1, nblock
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rho0 = refDensity(k)
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eta = one - rho0/densityNew(k)
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f1 = rho0*c02*eta*(one-half*gamma0*eta)
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f2 = gamma0*rho0
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press(k) = f1 + f2*Em(k)
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C dP/dEm
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dPdEm(k) = f2
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C dP/dRho
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dPdRho(k) = c02*(rho0/densityNew(k))**2*(one-gamma0*eta)
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end do
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C
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return
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end
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```
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Reference in New Issue
Block a user