Strain & Poisson's Ratio
Compute axial strain from original length and deformation, transverse strain from Poisson's ratio, and the new cross-sectional area.
Inputs
Formula
ε = ΔL/L₀; εt = −ν·ε; A' = A₀ + ΔA
Fundamentals
Poisson's ratio is the ratio of transverse to axial strain under uniaxial load — an elastic constant.
$\nu=-\varepsilon_\text{lat}/\varepsilon_\text{long}$, $\varepsilon_\text{long}$ axial, $\varepsilon_\text{lat}$ transverse strain. Isotropic materials $0<\nu<0.5$; rubber ≈0.5, cork ≈0.
History
Poisson's ratio was predicted by S. Poisson (1829) from molecular theory and later confirmed by experiment.
Engineering applications
Used for lateral strain, volume change and stress-strain analysis of isotropic materials.
Glossary
| Poisson $\nu$ | Absolute ratio of transverse to axial strain. |
| Axial strain | Strain along the load direction. |
| Transverse strain | Strain normal to load (opposite sign). |
How to use
- Fill in Orig. length L₀, Deformation ΔL, Poisson ν, Orig. area A₀, Area change ΔA in the Inputs section (watch the unit on each field).
- Click Calculate; the tool evaluates the formula shown above.
- Read Axial strain ε, Transverse strain εt, New area A' in the results area.
Formula notesPoisson ratio ν = −ε_lateral / ε_longitudinal; axial strain ε = σ/E, lateral contracts by ν.
Formula · Worked Example · Knowledge
Formula
Axial strain $\varepsilon=\Delta L/L_0$, transverse strain $\varepsilon_t=-\nu\varepsilon$; Poisson's ratio $\nu$ is their ratio (metals ≈0.3).
Worked Example
L₀=100 mm, ΔL=0.1 mm, ν=0.3 → ε=0.001, ε_t=−0.0003.
Key Points
- ν is a material constant with E describing deformation.
- Tension lengthens axially, shrinks transversely.
- Rubber ν≈0.5 (near-incompressible), cork ν≈0.
Parameters
Inputs
| Parameter | Symbol | Unit | Default |
|---|---|---|---|
| Orig. length L₀ (mm) | L0 | mm | 100 |
| Deformation ΔL (mm) | dL | mm | 0.1 |
| Poisson ν | nu | 0.3 | |
| Orig. area A₀ (mm²) | A0 | mm² | 200 |
| Area change ΔA (mm²) | dA | mm² | 0 |
Outputs
| Result | Symbol | Unit |
|---|---|---|
| Axial strain ε | eps | |
| Transverse strain εt | epst | |
| New area A' | A1 | mm² |
Applications
- Common engineering use cases
FAQ
What formula does this tool use?
This tool computes per ISO / AGMA / ASME standard formulas: ε = ΔL/L₀; εt = −ν·ε; A' = A₀ + ΔA
How accurate are the results?
Results match input precision, based on SI units and common engineering approximations; for critical duty re-check with a safety factor.
Where is it used?
Common engineering use cases