Which one of the following is the capacity of a material to absorb energy when it is deformed elastically and then, upon unloading, to have this energy recovered?

Explanation:

Resilience:

• The resilience of the material is the triangular area underneath the elastic region of the curve.  Resilience generally means the ability to recover from (or to resist being affected by) some shock, insult, or disturbance.
• In physics and engineering, resilience is defined as the capacity of a material to absorb energy when it is deformed elastically and then, upon unloading to have this energy recovered.
• In other words, it is the maximum energy per volume that can be elastically stored. It is represented by the area under the curve in the elastic region in the Stress-Strain diagram. 
• This is usually measured by the modulus of resilience, which is the strain energy per unit volume required to stress the material from, zero stress to the yield stress.

Hardness:

• Hardness is the resistance to plastic deformation (e.g., a local dent or scratch). Thus, it is a measure of plastic deformation, as is the tensile strength, so they are well correlated.
• Hardness is the resistance of a material to localized deformation. The term can apply to deformation from indentation, scratching, cutting or bending.
• There are a few different hardness tests: Rockwell, Brinell, Vickers, etc. They are popular because they are easy and non-destructive (except for the small dent).

Ductility:

• The ability to deform before braking. It is the opposite of brittleness. Ductility can be given either as percent maximum elongation e_max or maximum area reduction.