How do you show "battle damage" to a space ship without damaging the model?   Build a second model, or a second piece of a model.

Video of the model is here...

First used in Star Trek - The Wrath of Khan, a second, more detailed portion of the Enterprise was built to show "battle damage".  This was first used on screen in the can opener shot in the nebula.  Note that only portions of the "neck" and the secondary hull were visible in this shot, although the model includes two "wings" that connect to the warp nacelles.

Here's a head-on screen cap showing the "wings"...

The model was also in Star Trek III - The Search for Spock, in the face off with the Klingon ship.  Note how the damage is visible on the lower left side, even though in theory the Enterprise was not damaged on that side in the "Wrath of Khan".

This model was reused in Star Trek VI, The Undiscovered Country.  Since the Enterprise-A from that movie was not damaged, the Wrath of Khan model was repaired... here's a screen cap that shows the model as it fires the torpedo that finally hits General Chang's ship. 

When received, this model was in fairly good shape.  However one major question - do you take the "clean side", which was battle-damaged in Wrath of Khan, and re-battle-damage it?  Both were hero shots and screen used.  In the end, the answer was no, and the model was relit but not otherwise changed.  Here are some pictures of the final product for your enjoyment...

            

 

You may note in the picture from the Undiscovered Country there's a light clearly illuminating the name "Enterprise"... sorry, but that one doesn't exist in real life.