In material science, resilience is the ability of a material to absorb energy when it is deformed elastically, and release that energy upon unloading.
Proof resilience is defined as the maximum energy that can be absorbed up to the elastic limit, without creating a permanent distortion.
The modulus of resilience is defined as the maximum energy that can be absorbed per unit volume without creating a permanent distortion.
In uniaxial tension, under the assumptions of linear elasticity, where Ur is the modulus of resilience, σy is the yield strength, εy is the yield strain, and E is the Young's modulus.
Modulus of resilience (Ur) is measured in a unit of joule per cubic meter (J·m−3) in the SI system, i.e. elastical deformation energy per surface of test specimen (merely for gauge-length part).