Elastic Potential Energy Density (u = ½σε = ½Yε² = σ²/(2Y))
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u = ½σε = ½Yε² = σ²/(2Y)
What each symbol means
| Symbol | What it stands for |
|---|---|
| Y | Young's modulus (Pa) |
| u | Elastic potential energy per unit volume (J/m³) |
| ε | Strain (dimensionless) |
| σ | Stress (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).