• id: JME-08-N11
• title: Energy Stored in a Deformed Elastic Body
• tags: elastic-energy, energy-density, wire

When a body is elastically deformed, work is done against internal restoring forces and stored as elastic potential energy. For a wire: $U = \frac{1}{2} F \cdot \Delta L = \frac{1}{2} \frac{F^2 L}{AY} = \frac{1}{2} \frac{YA(\Delta L)^2}{L}$

Energy density (energy per unit volume): $u = \frac{1}{2} \sigma \varepsilon = \frac{\sigma^2}{2Y} = \frac{1}{2} Y \varepsilon^2$

This equals the area under the stress-strain curve up to the given point. On the full stress-strain curve, the total area represents the toughness (total energy absorbed before fracture).