Hooke's Law (strain)⚠ unverified
Physics / Materials · Axial strain from stress via Hooke's law
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| stress | σ | Pa | 200000000.0 | Axial stress |
| youngs_modulus | E | Pa | 200000000000.0 | Young's modulus |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| strain | ε | — | Axial strain |
The science & history
Understanding the Parameters
- $\sigma$ — force/area in the linear range (no plasticity).
- $E$ — steel ~200 GPa; polymers much lower. Temperature- and rate-dependent in real materials.
- $\varepsilon$ — $\Delta L/L$ for small strain; inverse form is Hookes Law Strain Stress $\sigma = E\varepsilon$.
Derivation (Approaching a Proof)
Hooke’s law $\sigma = E\varepsilon$ for uniaxial stress (isotropic linear elasticity). Solving for strain gives $\varepsilon = \sigma/E$. Full 3-D Hooke’s law involves Poisson’s ratio and the full stress/strain tensors.
History
Robert Hooke (1670s) “ut tensio, sic vis”; Young’s modulus later quantified the slope.
Related Concepts: Hookes Law Strain Stress, Poissons Ratio, Strain Energy Density, Shear Stress
Notes: Registry calculator hookes-law-strain (unverified). Uniaxial linear elastic only.