how abaqus obtain DSTRAN by using UMAT for non-isothermal case

Hi, all,

I recently encounted a big question regarding to the temperature dependent UMAT case. 

I used the UMAT for non-isothermal elasticity as followed. The DDSDDE calculating part is not shown here.

You can see that I output  ETHERM(K1),EELAS(K1),STRAN(K1),DSTRAN(K1) at the beginning of the code.

And this UMAT also saves ETHERM and EELAS to state variable array.

Job set up is no loading and using the static general step. But essentially it is a free expansion with thermal expansion coef of 6e-6 and temperature from 0 to 80, which is reflected in UMAT only. After Abaqus completes the job, these resluts are all correct, SDV(1-6)=EELAS=0, SDV(7-9)=ETHERM=4.8e-4. And the DSTRAN is 4.8e-4 as well.

 My question is that how abaqus knows DSTRAN here, since I did not apply any mechanical loading and not tell abaqus that this is a thermal expansion analysis here. I think DSTRAN is supposed to be given by specific dispalcement or thermal expasion. 

 
Could someone help me with that? I have been struggling with this for a while.

       SUBROUTINE UMAT(STRESS, STATEV, DDSDDE, SSE, SPD, SCD, RPL,
     1 DDSDDT, DRPLDE, DRPLDT, STRAN, DSTRAN, TIME, DTIME, TEMP, DTEMP,
     2 PREDEF, DPRED, CMNAME, NDI, NSHR, NTENS, NSTATV, PROPS, NPROPS,
     3 COORDS, DROT, PNEWDT, CELENT, DFGRD0, DFGRD1, NOEL, NPT, LAYER,
     4 KSPT, KSTEP, KINC)
C
      INCLUDE 'ABA_PARAM.INC'
C
      CHARACTER*8 CMNAME
C
      DIMENSION STRESS(NTENS), STATEV(NSTATV), DDSDDE(NTENS, NTENS),
     1 DDSDDT(NTENS), DRPLDE(NTENS), STRAN(NTENS), DSTRAN(NTENS),
     2 PREDEF(1), DPRED(1), PROPS(NPROPS), COORDS(3), DROT(3, 3),
     3 DFGRD0(3, 3), DFGRD1(3, 3)

       DIMENSION EELAS(6), ETHERM(6), DTHERM(6), DELDSE(6,6)
C
       PARAMETER(ZERO=0.D0, ONE=1.D0, TWO=2.D0, THREE=3.D0, SIX=6.D0)
C ----------------------------------------------------------------
C     UMAT FOR ISOTROPIC THERMO-ELASTICITY WITH LINEARLY VARYING
C     MODULI - CANNOT BE USED FOR PLANE STRESS
C ----------------------------------------------------------------
C     PROPS(1) - E(T0)
C     PROPS(2) - NU(T0)
C     PROPS(3) - T0
C     PROPS(4) - E(T1)
C     PROPS(5) - NU(T1)
C     PROPS(6) - T1
C     PROPS(7) - ALPHA
C     PROPS(8) - T_INITIAL
C     ELASTIC PROPERTIES AT START OF INCREMENT
C

        WRITE (6,*) 'ENTER UMAT'

       DO K1=1, NTENS
       WRITE(6,*) ETHERM(K1),EELAS(K1),STRAN(K1),DSTRAN(K1)
       END DO
 
C
C     CALCULATE THERMAL EXPANSION
C

       DO K1=1,NDI
     ETHERM(K1)=PROPS(7)*(TEMP-PROPS(8))
     DTHERM(K1)=PROPS(7)*DTEMP

       END DO
       DO K1=NDI+1,NTENS
     ETHERM(K1)=ZERO
     DTHERM(K1)=ZERO
       END DO
C
C     CALCULATE STRESS, ELASTIC STRAIN AND THERMAL STRAIN
C
       DO K1=1, NTENS
     DO K2=1, NTENS
       STRESS(K2)=STRESS(K2)+DDSDDE(K2,K1)*(DSTRAN(K1)-DTHERM(K1))+DELDSE(K2,K1)*(STRAN(K1)-ETHERM(K1))
         END DO
       ETHERM(K1)=ETHERM(K1)+DTHERM(K1)
       EELAS(K1)=STRAN(K1)+DSTRAN(K1)-ETHERM(K1)
       END DO

C
C     STORE ELASTIC AND THERMAL STRAINS IN STATE VARIABLE ARRAY
C
       DO K1=1, NTENS
     STATEV(K1)=EELAS(K1)
     STATEV(K1+NTENS)=ETHERM(K1)
       END DO
       RETURN   
       END
 

Thanks for helping.

Chen

Email: chen1164@purdue.edu