Strain Energy: 
When a force is applied to an elastic body it causes a linear deformation and as a result of this deformation the point of application of a force undergoes a displacement. Thus the work is done by a force this work is stored in the elastic body as strain energy. When external force is removed this stored energy takes back the material to original position according to the principle of conservation of energy the work done by external force is equal to strain energy.
Resilience: Strain energy stored within the elastic limit is called resilience.
Proof resilience: The maximum energy stored within the elastic limit is called proof resilience it is the strain energy corresponding to stress at elastic limit.
Modulus of resilience: The proof resilience per unit volume of a body is called modulus of resilience.
Toughness: Maximum strain energy stored upto fracture/rupture point is called toughness.
Modulus of Toughness: Maximum strain energy stored per unit volume upto fracture/rupture point is called modulus of toughness.