Eames Lounge Chair Busted...Need Ideas. Help!  

yes but no
You could send it off to Alfie at Hume Modern. I know he works on these, even when they are completely trashed like this. But, it's very expensive to do considered this chair is a copy. I wouldn't spend that much $$$ on a knock-off.

I am pretty handy and...
I am pretty handy and looking to do it myself. just looking for the advice on how.

I'd say
there is plenty of material there to make a glue repair. It won't look perfect, though much of the surface damage can be corrected with hot wax.
But first to make the repair. Start by unbolting the arms from the seat shell, so that they can be dealt with one at a time.
When wood is torn it cannot be expected to slip or slide back into place without first removing all the fibers that have "stretched" and dislocated within the tear(s). So a trial-and-error process of removing the bits that prevent a complete closing of the "wound" is necessary. But, sooner or later you will find that both sides of this chair will come together. Then, a clamping strategy must be devised, so that gluing can take place. Use pads of firm material that will allow clamps to apply pressure to all areas of the wound, concentrating on the breaks in the outer surface of the plywood, and a layer of something like kitchen plastic wrap so that the squeeze-out of glue will not adhere the clamping material to the chair. A liberal application of yellow wood glue to both halves of both wounds, using a brush, and a couple of hours of clamping time, and you will be ready to touch up the result. Damp glue squeeze-out under the clamp pads can be removed promptly with damp rags. Dry the result promptly, and reclamp any areas that are coming open, for another hour.
When you are done, the parts will not be as strong as original, because each ply of veneer has been cut. But it should be adequate for continued, if more careful, use. If this fault, and the lack of perfect aesthetics, are sufficient to deter you from attempting a repair, I'd congratulate you on your good sense. But if you think that possible qualified success is worth the trouble of trying, I say go for it.

We repaired our 670
using our boat building skills. Sorry, i should have documented but some of it
would be frowned upon. But...It shall not break again.

Didn't see SDR's response. And very good direction.
We did nearly all of that, but finished with a secure fiberglass and 2 part
epoxy.
(it's in the study against a corner wall. Just a favorite chair that needs to perform)
I'm not about re-sale or value at this point. I refuse to sit gently in a chair especially
if i spend a fortune on repairs. It has a few leather issues and i didn't pay top
dollar. Only the ottomon is near mint.
I don't encourage this type of repair but i did it and that was my personal choice.
I did extensive research and found this a common problem.
Also found a hidden repair that caused our break. A shock mount repaired with a pinkish
glue.
Out of character, but i don't feel i butchered it. I actually like it more now that i can enjoy
it without worry.
It is vintage and full of troubles visually but still like an old favorite t-shirt. Much nicer than
stiff and new.

After following SDR's gluing advice, how about
screwing pieces of metal strapping across the inside bottom of the plywood back shell, across the glued "wounds"? Invisible added strength.

It
couldn't hurt. I'd be more inclined to remove all finish from the area (inside surface) and glue on a plywood patch. A large glue area beats a few screws any day, in my book. But that's just me. Screwing into a half inch of wood isn't much security to my way of thinking. If they were machine screws that went all the way through the wood and into nuts (T-nuts ? a threaded strap ?) on the outside, that would be cool -- but not good-looking. I have never looked closely at the other metal fasteners on this chair. . .
Rockland, did your chair fail in the same area(s) ? Is this at all common in these chairs ? I wonder what was done the the subject chair above to cause it to break ?

Brace
on all the Plycraft chairs I've seen there has been a metal brace in the center of the backrest that connects to the seat - and absorbs a lot of the pressure from the person sitting against the backrest. I can't tell if it is present in your chair, but it doesnt appear so, which may be why it broke in the first place. I banged out a piece of steel bracing one one of my chairs where something similar had happened (not to the extent of yours 🙁 ) and it significantly helped the repairs I made to the arm screws.
I would suggest that whatever you do you add that brace to the back/seat. Good photo below.

Yeah
that makes good sense. In all cases you want to determine where the forces are and then do the simplest and most efficient thing possible to counteract or negate those forces. Your discreet brace does that perfectly.

SDR is about right on the money?
However, I would highly recommend using WEST SYSTEM brand epoxy instead of any glue out there. While there are many epoxies out there I can guarantee the repair will be stronger than the original if done WS and never break!
I have successfully repaired many chairs/furniture with this stuff.
You might ever want to convert your lounge to a one-piece shell like the plycraft I have pictured. This chair was repaired with WS with added fiberglass tape on the inside and painted black.
P.S. Always pre-clamp together before epoxy to make sure the clamping set-up and all tools are ready to go?like preparing for surgery!
http://www.westsystem.com/
Good luck!

Yes,
epoxy would be good -- though West Systems is surprisingly expensive. Epoxy has the advantage or liability of being a superb lubricant before it sets; this can be very frustrating, particularly with an awkward clamp-up.
Doing a dry clamp-up is always a good idea, regardless of technique or materials. Thanks for mentioning it. . .
Is that a repair in your photo ? Very nice !

Hi SDR, I agree the stuff is...
Hi SDR, I agree the stuff is quite expensive, however one or two paid repairs will usually cover the cost of a gallon and then I have plenty left for my own stuff.
The plycraft chair was repaired at seam with west system and fiberglass tape on inside, should be good to go, however have not assembled and used it yet.
About 7 years ago I got hooked on WS when was contracted to restore a 1960s 57' chris Craft Constellation.
The wood hull was Refastened using WS along with approx. 10,000 silicon bronze screws...now that was expensive!

I have the same knockoff lounge chair as the Original Poster
and there's no center brace (yes, we're all as individual as snowflakes! Knockoff Eames lounge? Check!). Adding a center brace, in tandem with the repair, is a good idea.
I'm curious myself, OP-- how'd you manage to do the spectacular damage (or, am I getting too personal)?

West System epoxy
and fiberglass tape is what we used.
With such an extreme splintered break it gets a bit tricky to
bring the two parts together.
I'll try and get a pic...
105 A & part B in quart size and tape is still under a 100 bucks.
A small repair kit is listed also.
http://www.westsystem.com/