To extract the deformation gradient data using Abaqus, you would indeed use the *EL PRINT command. Here's a little more information on how you can do this.
In your input file, you should include the following in the step you are interested in:
El Print, elset=ALL, position=INTEGRATION POINTS DG
This will print the deformation gradient for all elements in the model (as specified by elset=ALL) at their respective integration points.
The results will be written to the '.dat' file that Abaqus generates after an analysis. You can open this file using a text editor.
However, remember that if you have a lot of elements, the '.dat' file can get quite large and difficult to navigate. For handling such large amounts of data, using Python with the Abaqus scripting interface might be more efficient for directly reading and manipulating the output data.
Remember that the deformation gradient is printed for each element and each increment, so the data can be voluminous, especially for larger models or analyses with many increments. You might want to limit the increments for which you output results or limit the elements for which results are outputted if you only need the information for a subset of elements.