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Elastic potential energy density
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Energy stored per unit volume.
u = ½σεThe energy stored per unit volume is u = ½σε = ½Yε². Total energy is u × volume.
A steel wire stretched to ε = 10⁻³: 100 kJ/m³.
Spring energy ½kx² follows.
In more detail
The elastic potential energy density in a stressed material is ½σε, the energy stored per unit volume. It is the area under the stress-strain curve in the elastic region.
Real-world uses
- Springs and elastic materials store energy per unit volume for shock absorption.
- Designers estimate energy capacity of elastic components.
- Engineers estimate how much energy a spring or a bar can store per unit volume before it is damaged.
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Frequently asked questions
What is the unit?
Joules per cubic metre, equivalent to pascals.
Why is it the area under the curve?
Because energy is the integral of stress over strain, which gives this area.
Why is energy density useful?
It lets you compare materials for energy storage, since it shows how much energy each unit volume can hold.
Related topics in Fluids & Elasticity
Shear modulus · Stress–strain curve · Poisson's ratio · Bending of beams · Torsion of a cylinder