To write data from GiD to a calculations program, it is necessary to create a 'problem type' for it.
A 'problem type' is basically a collection of text files, copied inside a common directory with .gid extension. This files define your material fields, conditions, the template to write your calculation file, etc.
It is quite easy write a simple 'problem type'. The first step is to check one of the examples that are included in the GiD distribution like 'problem_type_solid1.gid'. Studying it and modifying accordingly to suit your needs you will get a GiD that can write the files that your calculations code can read.
Check also in the Help menu the 'Customization manual' and the 'Defining a problemtype' tutorial chapter of the 'User manual'.
Some problemtypes can be downloaded from the 'Data->Problem type->Internet retrieve' GiD menu, or from the GiD web page https://www.gidhome.com/gid-plus/modules