I think you can make the density dependent on a predefined field. Further you can change the values of the predefined field in the subsequent steps.

Something like this:

*MATERIAL
*DENSITY, DEPENDENCIES=1
 7.E3, ,1.  
 10.E3, ,2.
.......
*INITIAL CONDITIONS, TYPE=FIELD, VARIABLE=1
 MY_NODAL_SET, 1.

*STEP
*STATIC
*FIELD, VARIABLE=1
 MY_NODAL_SET, 2.
*END STEP

You might have to use the keyword editor to add some of the above lines.

In addition *FIELD can take as an option AMPLITUDE so you can have extended control on the variation of the field values.

Hi xerf
no as far as i understand, Field can change all the material properties(strength) but it won't change the density.

Xerf
That is a reply from abaqus support concerning that issue
"Except for acoustic, heat transfer, coupled temperature-displacement, and coupled thermal-electrical elements the density is a function of the initial values of temperature and field variables and changes in volume only. There is no way to introduce a density variation in other element types"

It is not clear from your post what type of analysis you're interested in and, consequently, what type of elements you are using.

I just hope you have supplied ABAQUS support with more detailed information such that their answer is more useful than mine.

However, I could not find the information you said in ABAQUS documentation on restrictions on making the density dependent on predefined field variables (via DEPENDENCIES). (The answer from ABAQUS support seems rather "inspired" from the restriction on predefined temperature field.)

If you are interested, you can check ABAQUS Analysis User's Manual  ->Predefined fields (chapter 27.6.1 in V6.6's doc.)

Xerf
I am using pore fluid/stress analysis