When you say "exchange", what do you really mean? If you wish to extract data from an .odb, you may need to write a python script unless you have data in a .dat or .fil files, which you can import in to MATLAB using regular file and text commands.
For instance. I have a static step time = 5 seconds. I would like to export the maximum Von Mises value of a given section at t= 2.4s to Matlab, work the value there and bring it back to Abaqus at step time=2.5 s.
In any case, you'll need a Python script to extract the max. von Mises stress. ABAQUS has a scripting manual. If you are comfortable with Python, it won't take long before you have a working script. Besides, you may not even have to write an entire script because .rpy files record everything that you are doing in ABAQUS/CAE. More often than not, you can simply copy the contents of the .rpy file to get your Python code.