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Hooke's law for solids
Beginner
Stress is proportional to strain in the elastic region.
For small deformations stress ∝ strain; the constant is the elastic modulus. It holds below the proportional limit.
Rubber doesn't obey it well.
It's a limit, not a universal law.
In more detail
Hooke's law for solids states that stress is proportional to strain within the elastic limit, σ = Eε. The constant E is Young's modulus for tensile stress.
Real-world uses
- Designing springs, beams and cables within their linear range.
- Testing materials to find their stiffness.
- Engineers designing steel springs and beams rely on Hooke's law in the elastic region to predict how much they will deform.
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Frequently asked questions
Does Hooke's law apply beyond the limit?
No. Beyond the elastic limit, stress and strain are no longer proportional.
Is it the same as the spring law?
It is the same principle applied to materials, with the spring constant derived from the geometry.
Where does Hooke's law stop being valid?
At the elastic limit, beyond which the stress and strain are no longer proportional and the material may deform permanently.
Related topics in Fluids & Elasticity
Elasticity · Stress · Strain · Young's modulus · Bulk modulus · Shear modulus