What is used to drive nails in areas that require a firm grip without crushing the material?

The correct answer is a rubber mallet. This tool is specifically designed to deliver force without damaging the surface of the material being worked on. Its soft, rubbery head provides a gentle yet effective way to drive nails into surfaces where a firm grip is essential, but there is a need to avoid crushing or deforming the material.

In contrast, other options like the claw hammer and ball peen hammer have hard surfaces that can create indents or splits in softer materials, making them less suitable for applications requiring a delicate touch. The dead blow hammer also provides a solid impact but is generally used for heavier applications where the material can withstand more force, again less ideal for the situations that need both grip and material protection. Thus, the rubber mallet is the best choice for driving nails in a way that ensures a secure hold without causing damage.