Elasticity
Quick Definition
Elasticity is a material's ability to return to its original shape after a load is removed. In engineering, it is measured by a modulus such as Young's modulus. In economics, the same word means how strongly demand responds to price.
By O.E. — Partner, chairman of the board and CEO of a metal products manufacturer for 21 years; the company exports to 45 countries.
Drafted with AI assistance; calculations checked against primary sources and tested with the site's own code. About FlowUtil
Last reviewed
Elasticity explained
Load a steel rod and it stretches. Remove the load and it returns to its length. That recovery is elasticity. It has nothing to do with how stretchy a material feels: steel is far stiffer than rubber, and both are elastic within their limits. Atoms move slightly out of position, and their bonds pull them back when the load goes.
Synonyms & Related Terms
Formula
σ = E × ε
τ = G × γ
G = E ÷ (2(1 + ν))
Real-World Example
A 1 m steel rod, 10 mm across, carrying 5 kN stretches 0.32 mm at E = 200 GPa, and all of it goes away when the load comes off.
Hooke's law on a steel rod
For many solids, stress rises in step with strain at low loads: σ = E × ε. A 1 m steel rod, 10 mm across, carries 5 kN. With E = 200 GPa:
- Area: 78.5 mm²
- Stress: 5,000 ÷ 78.5 = 63.7 MPa
- Strain: 63.7 ÷ 200,000 = 0.000318, or 318 µε
- Stretch: 0.000318 × 1,000 mm = 0.32 mm
Unload it and all 0.32 mm goes away. The Young's modulus calculator finds E from test figures.
Three limits that are easy to mix up
| Term | What it marks |
|---|---|
| Proportional limit | Where stress stops being proportional to strain |
| Elastic limit | The highest stress with no permanent set |
| Yield strength | The practical limit, often at 0.2% permanent strain |
In metals these sit close together, so design usually uses yield strength. Beyond yield, dislocations move through the crystal and the change stays. That is plastic deformation.
Elastic is not always linear
Rubber recovers from huge stretches, yet its stress and strain do not follow a straight line. It is elastic but not Hookean. Concrete is close to linear only at low stress. Polymers also creep under steady load, which is called viscoelasticity.
Stiffness in shear: the shear modulus
The shear modulus G relates shear stress to shear strain: τ = G × γ. For an isotropic material it follows from E and Poisson's ratio:
G = E ÷ (2(1 + ν))
| Material | E | ν | G |
|---|---|---|---|
| Steel | 200 GPa | 0.30 | 77 GPa |
| 6061 aluminium | 68.9 GPa | 0.33 | 26 GPa |
G governs twist in shafts and the rate of a coil spring.
Elastic energy, and what it does not promise
An elastic part stores energy. A spring of 100 N/mm compressed 10 mm stores ½ × 100 × 10² = 5,000 N·mm, or 5 J. Some of that returns as motion and some is lost as heat in the system. The helical spring design calculator sizes a spring for this.
Staying below the elastic limit does not guarantee a long life. Repeated loading can still cause fatigue, so a spring can crack without ever yielding.
Why It Matters
Most service-load checks assume a part stays elastic, so deflections can be predicted and the part returns to shape. Elastic does not mean fatigue-proof, because repeated loads can crack a part below its yield strength.
Industry Applications
Sources
- ASTM International, ASTM E111 — Young's Modulus, Tangent Modulus, and Chord Modulus.
- Robert Hooke, De Potentia Restitutiva, 1678 (the law of the spring).
- The relation G = E ÷ (2(1 + ν)) is standard for isotropic elastic solids.
Related Standards
Frequently Asked Questions
What does elasticity mean?
The ability of a material to return to its shape when a load is removed.
What is the difference between elasticity and plasticity?
Elastic deformation disappears on unloading. Plastic deformation stays.
Is elasticity the same as stiffness?
No. Stiffness depends on the part's shape and size. Young's modulus describes the material.
What is the shear modulus?
The ratio of shear stress to shear strain. For steel it is about 77 GPa.
Is steel more elastic than rubber?
Steel has a much higher modulus, and rubber recovers from far larger strains. "More elastic" depends on which you mean.
What is elasticity in economics?
How much demand or supply changes when price changes. This page covers materials.
See Also
Related Glossary Terms
Stress
Stress is the internal force per unit area in a loaded material: σ = F ÷ A. Normal stress pulls or pushes across a section, and shear stress slides along it. It is measured in pascals (N/m²), MPa or psi.
Yield Strength
Yield strength is the stress at which a material stops springing back and starts to deform permanently. For metals without a sharp yield point it is defined as the stress that leaves 0.2% permanent strain — the 0.2% proof stress, R_p0.2.
Ductility
Ductility is how far a material can be stretched before it breaks. It is measured in a tensile test, as percent elongation or percent reduction of area. Steel, copper and aluminium are ductile; glass and cast iron are not.
Brittleness
Brittleness is a material's tendency to fracture with little or no plastic deformation, absorbing little energy before it breaks. It shows up as low elongation and reduction of area in a tensile test and low absorbed energy in a Charpy impact test.
Tensile Strength
Tensile strength, or ultimate tensile strength (UTS), is the highest stress a material can carry in tension: the maximum force in a tensile test divided by the original cross-section. Ductile metals reach it before they neck and break.