sam85geo,
There is no single simple solution. The "target" can vary greatly and react in a variety of ways.
For example you can have two ends of a scale. There is a lot of detail in the Asteroids - Agreed Terms thread - take, for example, iron meteorites. Asteroids themselves, are not very amenable to study, but we have lots of the pieces resulting from collisions, luckily (in most cases) delivered to us here on Earth as meteorites.
So-called iron meteorites consist almost entirely as iron/nickel, and some have differentiated, which means that they have melted and aggregated in the centre - later to be broken apart by collision. How uniform is the molten core (subsequently solidified)? What will be the result of a percussive hit? Will it react as a single body or are there planes of fracture?
At the opposite end of the scale there may be large simple aggregates. We can tell the proportion of low density "targets" and it is quite high. Depending on what you hit it with, it may explode into zillions of little bits (great meteor showers) or pass straight through.
At what angle are you going to hit it? Full on? Perpendicular - how you you plot impact course? Probably the best is at an angle from full on, i.e., approach at 5 or 10 degrees from full on. This will also slow down target a little - but before cheering too loudly look at conservation of momentum. The average case may resemble hitting a 20 ton truck, travelling at 100mph, with a rolled up newspaper.
No, do not think that a nuclear bomb will be the panacea of all ills. Before anything you need to know the course, momentum, mass (separately), and composition.
Although the Late Heavy Bombardment may be over, there is a billion year future of comets detaching from the Oort Cloud and heading inwards, not to mention perturbations of members of the Asteroid Belt to form more and closer Near Earth Objects.
Charge in, guns blazing, and all
may be well. But, where ignorance is bliss , , , , , , as the old saying goes. At least prime your bombs with investigation. And a lot of preparation will have to do with getting your approach path sorted - and 100% accurate.
Cat
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