How do Federation shields work against physical objects?

Question

The majority of the time, in Star Trek, when shields are used, they're used against energy weapons, such as phasers. We also know that shields block transport beams. They do keep out photon torpedoes, which are composed of a casing and a warhead.

It makes sense that shields would deflect energy (they are "deflector shields"). That would tell us how they work against phasers and why transport through shields wouldn't work. How do they work against physical objects? Do they deflect them? Are the objects disintegrated on contact? Do they work to prevent entry of certain types of matter and not others?

Answer 1

From this quote, it's apparent that physical objects bounce, at least when they are of certain sizes and moving at certain velocities, but that other things might happen under other circumstances:

LAFORGE: He's making a suicide run [towards the Enterprise].
DATA: Shields have been automatically activated. Tractor beam disengaged.
WESLEY: He bounced off the shields.
RIKER: That's an interesting twist.
^{Star Trek: The Next Generation - Episode 3x11 "The Hunted"}

NB: I've found multiple versions of this script which are not all identical, and I'm not sure which one was broadcast. But bouncing off the shields occurs in all of them, and they all have Riker surprised to some extent.

That Riker found this surprising is interesting, since it suggests that he expected something else to happen. Geordi's "suicide run" makes it sound rather violent, but they might merely have expected the approaching vessel to crash into the shields rather than something more active on the part of the shields themselves.

Answer 2

Shields in the Trek universe utilize a network of oriented graviton field generators laid out throughout the ships hull. As gravitons exist in such a universe, the field magnetically or plasma web generates a field of gravitons in a distinctive shape. These particles are artificial and make a "shell" around the vessel in the form of a "bubble"

or a hull contouring shell

As stated in Star Trek: The Next Generation - Technical Manual

"To an observer aboard the starship, it appears that the intruding object has "bounced off" the shield. A zero-dimensional observer on the intruding object would, however, perceive that his/her trajectory is unaffected, but that the location of the starship has suddenly changed. This is somewhat analogous to the spatial distortion created by a natural gravity well, and is typically accompanied by a momentary discharge of Cerenkov radiation, often perceived as a brief blue flash. The deflector is also effective against a wide range of electromagnetic, nuclear, and other radiated and field energies."