Strain

Strain is deformation per unit length. Learn normal and shear strain, microstrain, the stress–strain curve, ductility, lateral strain and Poisson's ratio, and how strain gauges measure it.

Every loaded part deforms, even if you can't see it. Strain measures that deformation as a fraction of the original size — a dimensionless number that lets you compare a 10 mm bolt and a 100 m bridge.

Strain is what engineers actually measure (with strain gauges and extensometers); stress is then calculated from it.

An analogy

Stretching a rubber band: pulling 10 cm to 11 cm is a 10 % strain. A steel bar would reach about 0.12 % before yielding — tiny, but measurable.

Measuring deformation

Strain = change in length / original length. It has no units, but engineers write it as %, mm/m or microstrain (µε). 1000 µε = 0.1 % = 1 mm per metre. Steel at 150 MPa strains about 750 µε.

The stress–strain curve

A tensile test plots stress vs strain. Key points: proportional limit, yield point (or 0.2 % offset proof stress), ultimate strength and fracture. Ductile metals stretch 15–40 % before breaking; brittle materials (cast iron, glass) under 1 %. Ductility gives warning before failure.

Poisson's effect

Stretching a bar makes it thinner. The ratio of lateral to axial strain is Poisson's ratio: ≈ 0.3 for metals, 0.2 for concrete, ≈ 0.5 for rubber (volume-preserving).

True strain and large deformation

Engineering strain uses original length; true (logarithmic) strain ε_t = ln(1 + ε) integrates instantaneous changes. Forming processes, crash simulation and rubber design use true stress–strain and hyperelastic material models.

Formulas

• Normal strain: ε = δ / L
• Lateral strain: ε_lat = −ν · ε_axial
• Volumetric strain (bar): ε_v = ε(1 − 2ν)
• Strain gauge: ΔR / R = GF · ε (GF ≈ 2)

Worked example: Strain from elongation

Given: Bar 2 m long; Stretches 1.2 mm

Find: Strain.

• ε = 1.2/2000 = 0.0006
• = 600 µε = 0.06 %

Answer: 600 µε

Worked example: Diameter change

Given: Ø20 mm bar with ε = 800 µε; ν = 0.3

Find: Change in diameter.

• ε_lat = −0.3 × 800 = −240 µε
• Δd = −240 × 10⁻⁶ × 20 = −0.0048 mm

Answer: Diameter shrinks 4.8 µm

Common mistakes

• Wrong: Treating strain as having units of mm. — Right: Strain is dimensionless (mm/mm); elongation δ has units.
• Wrong: Assuming volume is constant in elastic deformation. — Right: Only when ν = 0.5; metals change volume slightly (ν ≈ 0.3).

Applications

• Load cells: Strain gauges on an elastic element in a Wheatstone bridge measure weight and force.
• Structural health monitoring: Fibre-optic and foil gauges track strain on bridges, wind turbine blades and aircraft.
• Metal forming: Forming limit diagrams in terms of strain predict sheet-metal tearing.

Key takeaways

• ε = δ/L, dimensionless; think in µε.
• Stress–strain curve: elastic, yield, hardening, fracture.
• Lateral strain = −ν × axial strain.
• Strain gauges: ΔR/R = GF·ε.

Going further

• Strain rosettes: Three gauges at 0/45/90° give the full 2D strain state, from which principal strains and stresses follow.
• Digital image correlation: DIC tracks a speckle pattern with cameras to map full-field strain on test specimens.
• Temperature compensation: Half- and full-bridge gauge arrangements cancel thermal output so only mechanical strain is read.