I posted this on the e3D forum, but I thought I'd try here with the Maya experts also.
I cannot find any tutorial on this so excuse me (and re-direct) if it exists.
I am not obj savvy, but I modeled a polygon sphere, cut it in half, extruded then smoothed it (several times -- very high poly now). Next I exported it as an obj (standard settings). Okay, done.
In E3D, I imported it as an obj (Import 3D Object). It comes in with the exported part transparent. So when I toss a material onto it, the material only appears on the inner part. The extruded part is treated like transparency (glass-looking). Odd.
I'm sure I am doing something wrong, but most E3D tutorials favor Cinema 4D. I am posting here assuming that maybe I am improperly exporting my OBJs from Maya?
1) Apply an automatic UV map. I've had a similar problem where the UV's of the extruded part were completely messed up. An automatic UV map should more or less fix that problem.
2) The normals might have been flipped. Try selecting all faces and invert them.
And then export the obj again. Hope that works. If not, take a screenshot. I had a bit of difficulty understanding your problem without it, so I'm partially guessing here.