User subroutine UEXPAN

Zhiwei,

Depending upon your problem, you need to do coding to provide ABAQUS with the EXPAN (thermal strain increment) and DEXPANDT (thermal strain dependent on temperature).

You can get help of solution dependent variable (SDV's) to solve for above two quantities at end of each increment. which can be defined in inp file as initial condition. 

Typical code looks like this (From ABBQUS help): 

!=========================== 

SUBROUTINE UEXPAN(EXPAN,DEXPANDT,TEMP,TIME,DTIME,PREDEF,
1 DPRED,STATEV,CMNAME,NSTATV,NOEL)
C
INCLUDE 'ABA_PARAM.INC'
C
CHARACTER*80 CMNAME
C
DIMENSION EXPAN(*),DEXPANDT(*),TEMP(2),TIME(2),PREDEF(*),
1 DPRED(*),STATEV(NSTATV)
! user coding to define EXPAN, DEXPANDT and update
! STATEV if necessary.
RETURN 

      END 

!============================ 

(*) values depend upon problem. Based on your problem, the USR is invokes once or twice for each increment. Basically all it is doing is calculting thermal strain increment (thermal expansion coefficient) which might be dependent on quantities such as rate of cooling, temperature etc.

Hope it helps.

~Jay