Elastic Potential Energy Density (u = ½σε = ½Yε² = σ²/(2Y))

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u = ½σε = ½Yε² = σ²/(2Y)

What each symbol means

SymbolWhat it stands for
YYoung's modulus (Pa)
uElastic potential energy per unit volume (J/m³)
εStrain (dimensionless)
σStress (Pa)

When to use this

Energy stored per unit volume in a deformed elastic body within Hooke's law regime. Total elastic PE = u × volume = ½ × stress × strain × AL. Analogous to ½kx² for a spring. Derived from work W = ∫F dl with F = YA(l/L).