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### Modulus of Resilience Formulae and Calculator

Strength of Materials and Applications

Modulus of Resilience Equation and Calculator

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 within 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.

Eq. 1

${U}_{r}=\frac{{\sigma}^{2}}{2\xb7E}$ = ${\sigma}_{y}\xb7\frac{{\epsilon}_{y}}{2}$Where :

*U _{r} =* The modulus of resilience (J/m

^{3})

*σ*= The uniaxial tensile yield strength (Pa)

_{y}E = Young's modulus (Pa)

*ε*= strain (unit/unit)

_{y}Reference:

- Campbell, Flake C. (2008). Elements of Metallurgy and Engineering Alloys. ASM International. p. 206. ISBN 9780871708670.
- O.Balkan and H.Demirer (2010). "Polym. Compos". Polymer Composites. 31: 1285. ISSN 1548-0569.
- 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

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