MAT-01

Hooke's law

σ = E ε in the linear elastic regime.

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ElasticityHooke 1678ISO 6892

Governing equation

\sigma = E\varepsilon

where

E: Young 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-01 — Hooke's law) is the form associated with Hooke 1678 · ISO 6892. Working symbols: $E$ , $\varepsilon$ $\rightarrow$ $\sigma$ . Hooke's 'ut tensio, sic vis' is the constitutive statement of linear elasticity and defines Young's modulus E = σ/ε.

Purpose

Purpose: compute

\sigma

from

E

\varepsilon

in Materials via

\sigma = E\varepsilon

σ = E ε in the linear elastic regime. 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 = 200.000\,\mathrm{MPa}

. Uniaxial, small strain, isothermal. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Young modulus E200 GPaStrain \varepsilon0.001 —

Outputs

Stress \sigma200.000 MPa

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Narration of this film

Uniaxial, small strain, isothermal.

Hooke's 'ut tensio, sic vis' is the constitutive statement of linear elasticity and defines Young's modulus E = σ/ε.

Reading speed

Watch on YouTube