The resilience of steel can be found by integrating stress-strain curve up to the

Strain Energy of the member is defined as the internal work done in deforming the body by the action of externally applied forces.

Resilience is defined as the capacity of a strained body for doing work on the removal of the straining force.

The strain energy stored in a body due to external loading, within the elastic limit, is known as resilience and the maximum energy which can be stored in a body up to the elastic limit is called proof resilience.

Modulus of resilience is defined as proof resilience per unit volume. It is the area under the stress-strain curve up to the elastic limit.

Y is the elastic limit of steel.

Toughness is the capacity of a structure to withstand an impact load i.e. the capacity to absorb energy without fracture.

Proof resilience is defined as the maximum strain energy stored in a body. So, it is the quantity of strain energy stored in a body when strained up to elastic limit (ability to store or absorb energy without permanent deformation).