If you haven’t already, it’s probably discussing with him a little bit – at least to acknowledge that you’ve noticed he’s stressed/hurting, and that you want to be “on his team” in dealing with it.
The key is to be supportive of him, rather than adding additional demands. So I’d caution you not to present your feelings in a way that he might interpret as an additional burden, so he doesn’t end up feeling like now he has two problems to deal with. That won’t make him any more likely to share feelings with you in the future; quite the contrary.
You know how talking through your problems helps you solve them, and/or feel better for him? Because of that, if he was asking for equivalent advice, I’d say “listen to her problems!” – i.e. just do what will help you. Well, he has a different way of dealing with stress, and if you really want to help him, you should try to figure out and then focus on whatever will help him deal. In the process of helping him, you’ll likely get at least some of the emotional opening-up that you’re hoping for.
I don’t know what to suggest specifically, of course, but off the top of my head, maybe a little pampering? Like, cook his favorite comfort food for him, or take him to his favorite restaurant. Or tell him you can see how hard he’s been working and how hard on him it’s been, while you give him a great backrub. Sexual favors generally don’t hurt, either ;-)
Basically, if you want to be part of his coping strategy when times are tough, you should try to find a way to really make coping easier for him. Then he’ll turn to you.
For you, someone who’ll talk it over and be sympathetic helps; for him, apparently not so much, so you’ll need to find another way to participate. Once you’ve done that, the sharing part that you’re looking for should come more naturally to him.