Thanks for the file.
I was able to get it working, but there are several issues I had to fix manually:
6878 OBJ test
1) commas as decimal separator
In the OBJ file, vertices/normals/faces are defined using commas instead of points as the decimal separator:
v -0,235776457135308 0,064 0,871102222521133
While the issue of , vs . as the decimal mark is a matter of international standards, it seems to be cause issues with encoding the OBJ file. Do you think this is an issue with your OBJ plugin, or does SolidWorks have a global preference for this? Or maybe a language setting?
2) spaces in texture names / MTL file
It's best to avoid spaces and special characters in all file names:
map_Kd corten texture matter.jpg
There were still issues automatically applying the textures...I'm looking into it...but it's still good practice.