MAT-09

Hooke's law

σ = E ε in the linear elastic range.

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Mechanics of materialsHooke

Governing equation

\sigma=E\varepsilon

where

E: Young's modulus (GPa)
\varepsilon: Strain (—)
\sigma: Stress (MPa)

Lecture brief

Historical brief

Hooke (1678), Hall–Petch grain size, Arrhenius activation and Paris fatigue-crack growth are the spine of materials selection. The sheets relate stress, microstructure and life. This sheet (MAT-09 — Hooke's law) is the form associated with Hooke. Working symbols: $E$ , $\varepsilon$ $\rightarrow$ $\sigma$ . E is the slope of the uniaxial stress–strain curve before yield.

Purpose

Purpose: compute

\sigma

from

E

\varepsilon

in Materials via

\sigma=E\varepsilon

σ = E ε in the linear elastic range. Use it when a real materials question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

E = 200.000\,\mathrm{GPa}

\varepsilon = 0.001\,\mathrm{—}

, the governing relation

\sigma=E\varepsilon

yields

\sigma = 200.00\,\mathrm{MPa}

. A spring of continuum, a proportional arrow. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Young's modulus E200 GPaStrain \varepsilon0.001 —

Outputs

Stress \sigma200.00 MPa

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Narration of this film

A spring of continuum, a proportional arrow.

E is the slope of the uniaxial stress–strain curve before yield.

Reading speed

Watch on YouTube