In this context, what do you mean by "animated model"? What animations are in place that you're concerned about?
To attempt an answer, I imagine that the spike-strip would simply be a trigger object (and not a "solid" physics object) that would produce a temporary change in the velocity, handling characteristics and perhaps other properties of the car that hits it (perhaps via a state change, or perhaps an modifying class aggregated in the "car" object, or some other means); the specifics of this would likely depend on how you've modelled your driving physics, I imagine.
I agree with Thaumaturge, spikes implementation depends on how you model your car and physics. In order to help you, it would be nice to tell us exactly what language / engine you're using, is it 2D ? (Box2D, Farseer) 3D ? (Havok, Bullet Physics, Newton).
Spikes are better off without a physical presence, in the case of Box2D, they would be implemented as sensors. When colliding with the tires, you can make the car less responsive to input, you can modify the friction of the tires to make them stick more to the ground. I guess there's some tweaking to do here to get the right effect.
We're discussing gameplay mechanics but it seems to me that OP is more concerned by graphics and animation of the tires. We can go as far as implementing it using soft bodies but that would be overkill, I would say fake it : make 2 models or 2 textures for the tires, then change the model (or texture) once a tire hits the spike strip. You can also create a smoke particle system and maybe throw in some sound effects to make it more realistic.