I usually do that in Abaqus viewer during post processing, via Python script. Before running my model, I specify I want it to save the Sate Variables (SDV's) and the I read them and export them to a txt. file.
Here's the code I use to export Mises Stress, Triaxiality and some state variables from a particular Integration point of a particular element in the region o interest in my model (frame-by-frame in the load-step):
for frame in frames:
# getting frame ID and time at this frame
frameID = frame.frameId
time = frame.frameValue
# getting quantities at the integration point closest to the origin:
Guys, Thanks for your information. I also want to know how I can write the output just for centroid of each element. That command writes it for all the integration points.