An additional complication is the behaviour of the bullet itself on impact, which is not only difficult to model but can vary a lot according to the construction of the bullet, it's geometry and mass, and the angle and energy of impact.
For example a low-velocity, unjacketed lead bullet might squash against the impact surface with little or no penetration, which is a reasonable approximation of an inelastic collision and so the best modelling approach might be to consider its momentum and here it is certainly possible, although not trivial, to construct fairly credible finite element model based on dynamic stress and strain. Indeed you may even be able to get meaningful order of magnitude numbers with manual calculations.
On the other hand a high-velocity, armour-piercing bullet might well pass through cleanly and transfer relatively little energy to the target.
A third case is that fragmentation or tumbling of the bullet or target. In high energy impacts you may even observe fluid-type behaviour.
In addition to the actual contact surface between the bullet and the target there will also be shock waves that propagate through the target, which can cause high stresses and failures (eg. spalling) and can eject material from the back side of the target even if the bullet itself does not penetrate it.
In general the big difficulty with modeling this sort of situation is that you are dealing with strain rates far outside the assumptions underlying the material properties and equations used for static and most dynamic modelling.
To put it another way firing a bullet at a target is a fundamentally different condition from pushing it through a target slowly regardless of how much force is applied. Indeed in practical impact testing it is more usual to think in terms of energy than stress and strain.
In fact when it gets right down to real world applications standards for body armour will usually specify resistance to specific rounds (in terms of caliber, propellant and bullet type) at a specific range. Simply because there isn't a measurable physical property which is generally descriptive of this sort of performance.
You also need to think carefully about what you are trying to determine. In the context of armour something which generates a wide cone of debris and fragmentation on impact may actually be far worse than just allowing the bullet to pass through intact.