Subject 08 · Materials

Solid Deformation

Begin with a spring, then remove the effects of sample geometry to compare materials fairly. Each lesson links an equation to a responsive graph, a misconception check, and a worked example.

TENSIONσ / εRESPONSE

F = kxHooke's Law & Extension

Measure extension, identify the proportional region, and read stiffness from graph gradient.

→02

W = ∫F dxElastic Energy & Force-Extension Graphs

Use graph area to calculate deformation work, recoverable energy, and spring combinations.

→03

E = σ/εStress, Strain & Young Modulus

Remove geometry from the comparison and predict elastic extension.

→04

UTS = max σStress-Strain Curves

Locate elastic response, yield, UTS, necking, and fracture on one tensile test.

→05

Recover or retain?Elastic, Plastic, Brittle & Ductile Behaviour

Compare recovery, permanent strain, fracture style, and rubber hysteresis.

→06

x = FL/EAMaterial Selection & Deformation Modelling

Turn a design brief into stiffness, stress, geometry, and model-limit checks.

→07

U = ∫F dxDeformation Calculus

Differentiate force–extension curves for stiffness and integrate them for stored energy, from springs to a rod's own weight.

→Play

free game · σ = F/ABridge Load Tester

One dial sets the cable diameter, then a convoy crosses. Find the thinnest cable that neither breaks nor lets the deck drop too far. Four spans, free, no account needed.

→Slides

Members · classroom mode, full screenPresent this chapter

Full-screen slides for the classroom, built from the lessons themselves: pick a lesson, then reveal its idea, formulae, quick check, and worked examples one step at a time.

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One connected model

Force and extension describe a sample. Stress and strain describe the material response. A design must check stiffness, strength, behaviour, geometry, and where the chosen model stops applying.