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. It can be calculated by integrating the stress–strain curve from zero to the elastic limit. 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.^{[1]} This analysis is not valid for non-linear elastic materials like rubber, for which the approach of area under the curve until elastic limit must be used.

## Unit of resilienceEdit

Modulus of resilience (*U*_{r}) 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).

Like the unit of tensile toughness (*U*_{T}), the unit of resilience can be easily calculated by using area underneath the stress–strain (*σ*–*ε*) curve, which gives resilience value, as given below:^{[2]}

*U*_{r}= Area underneath the stress–strain (*σ*–*ε*) curve up to yield =*σ*×*ε**U*_{r}[=] Pa × % = (N·m^{−2})·(unitless)*U*_{r}[=] N·m·m^{−3}*U*_{r}[=] J·m^{−3}

## See alsoEdit

## ReferencesEdit

- Guha S. Quantification of inherent energy resilience of process systems for optimization of energy usage. Environ Prog Sustainable Energy. 2019;e13308. https://doi.org/10.1002/ep.13308
- Guha S. Quantification of inherent energy resilience of process systems pertaining to a gas sweetening unit. International Journal of Industrial Chemistry (2020) 11:71–90 https://doi.org/10.1007/s40090-020-00203-3