Final answer:
Rubber is the material that best maintains structure and shape while allowing for extensive flexibility due to its elastic behavior. This elasticity is a result of the ability of rubber's polymer chains to revert to their original shape after being deformed and then having the deforming force removed.
Step-by-step explanation:
The question asks about a material that maintains structure and shape while permitting extensive flexibility. Considering the properties of materials like metal, wood, plastic, and rubber, rubber is the one that has the ability to return to its original shape after being stretched or deformed, which is a characteristic of elastic behavior. While metals may be ductile and plastic, becoming easier to deform as they are stretched towards their breaking point, and plastics can show varied behavior from being quite rigid to very flexible, it is rubber that best exemplifies the ability to undergo significant flexing while maintaining shape due to the elasticity of polymers, particularly when external forces are removed.
Elasticity in materials like rubber is often the result of stretching polymer chains under an applied force. When the force is removed, the material returns to its original shape which is a distinctive feature of elastic materials, such as rubber. This is contrasted with the permanent deformation, or plasticity, that occurs in materials like metals and plastics when they are subjected to stresses beyond their elastic limits.