I'll give it a shot. This isn't 100% correct as there are numerous variables, such as friction, arrow oscillation, arrow deceleration, etc, that should be quantified. But this will give you an idea of what you're after.
Impulse = change in momentum,
therefore:
Force X Time = Arrow mass X Arrow velocity
(assuming arrow stops in target)
rearranging and correcting for units:
Force = arrow mass X arrow velocity divided by time divided by 225,400.
where Force is in lbs, arrow mass is in grains, arrow velocity at impact is in ft/s and time the force is acting upon the target is in seconds.
I would assume time of force on the target to be in the neighborhood of 0.005 seconds. Faster arrow speeds equals less time and slower arrow speeds equals more time.
So for a 650 gr arrow going 165 fps with a time of impact of 0.005 sec you get 95 lbs of impact force.
I have no idea what the guidelines of impact force would be for elk or deer.