Elastic strain energy
The energy stored in a material when elastically deformed. For a material under stress, elastic strain energy per unit volume is the area under the stress-strain curve in the elastic region. For a spring stretched by extension x, elastic strain energy is E = ½kx².
Formula
E = ½kx² = ½Fx (spring); energy/volume = ½σε
Real World
Archery bows — including those used by GB Olympic archers at Paris 2024 — store elastic strain energy in the limbs when drawn; that stored energy converts to kinetic energy of the arrow on release.
Exam Focus
The area under a force-extension graph (not stress-strain) gives total elastic strain energy in joules — use ½Fx only when the graph is linear (Hooke's law obeyed).
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