Which material property allows for energy storage during elastic deformation?

The correct answer is resilience, which refers to a material's ability to absorb energy when it is deformed elastically and to release that energy upon unloading. This property is critical in applications where materials are subjected to repeated loading and unloading cycles, such as in springs or structural components that experience fluctuating loads.

Resilience is quantitatively described by the area under the stress-strain curve up to the yield point. The larger the area, the more energy the material can store during elastic deformation. Materials with high resilience can return to their original shape after the load is removed, thereby demonstrating efficient energy storage.

While elasticity is also a relevant property, as it indicates how a material will deform under stress, it does not specifically capture the aspect of energy storage. Elasticity simply refers to the material's ability to return to its original shape after being deformed, but does not quantify the energy absorbed.

Other properties such as ductility and toughness are important for different reasons. Ductility relates to a material's ability to deform plastically without fracturing, and toughness measures the energy that a material can absorb before failing, including both elastic and plastic deformation. However, neither directly addresses the specific capability of energy storage during elastic deformation like resilience does.