Concepts & theory

Learn

From zero to laminate analysis. Start anywhere — every article says what it builds on and which tool it explains.

Follow the guided path — ground zero to composites engineer →

One ordered climb: school-level basics → foundations → the theory behind the tools → real industry applications. No background needed to start.

The lattice

Mechanical engineering as a crystal lattice — every cell is a live branch. Tap one to zoom in. This site lives in Materials Science and Mechanics of Materials, but every branch connects.

Interactive journey

From electrons to airframes — nine orders of magnitude in eight steps →

Electron shells → monomers → chains → fiber + matrix → ply → laminate → structure → product. Each level links to the tool that works there.

Start here — no background needed

Plain-language introductions for anyone from about 13 up. Read them in order and you will understand every tool on this site.

Going deeper

Builds on the foundations: how parts get made, how they fail, and where materials science touches every other field.

Anisotropy: why direction is everything in composites

A steel bar is equally strong whichever way you pull it. A carbon-fibre part can be ten times stiffer along the fibres than across them. What anisotropy is, why composites have it, and why it's a feature, not a bug.

Tool guides

The full theory behind each calculator and simulation.

Fatigue: why things break under repeated load

Most parts don't fail from one big overload — they fail from millions of small loads that each seem harmless. What fatigue is, why it's invisible until it isn't, and how the S–N curve turns cycles into a design limit.

Cure kinetics: how a thermoset hardens

A thermoset doesn't cool to solid like a plastic — it reacts to solid, and once set it can never melt again. What cure is, why it makes its own heat, and how the cure cycle races speed against a runaway exotherm.

The stress–strain curve: elastic, yield and Ramberg–Osgood

Pull a material and it stretches elastically, then yields and flows. The stress–strain curve is the fingerprint of how a material behaves — and the Ramberg–Osgood equation is how engineers turn its smooth knee into numbers.

Time, temperature and the WLF shortcut

A polymer that's rigid for a fast pull can flow like putty under a slow one — and heating it does the same thing as waiting. Time–temperature superposition is the deep idea that lets a short hot test predict decades of cold service.

Moisture in composites: the slow, hot-wet knockdown

Leave a composite in humid air and it slowly drinks water — swelling, softening, and dropping its hot-wet strength. How moisture diffuses in, why it matters most with heat, and the knockdown engineers design around.

Honeycomb sandwich panels: stiff, light, and how they fail

Two thin skins, a light honeycomb or foam core between them, and a panel many times stiffer than the same material solid. How sandwich beams bend, why the core's shear adds deflection, and the four ways a sandwich fails: facing strength, core shear, wrinkling and intracell buckling.

Beam bending and pressure vessels, explained

The two closed-form results behind most everyday structures: how a beam bends and how much it deflects, why depth beats width, the four textbook load cases, and why a pressurised cylinder is pulled apart twice as hard around its girth as along its length.

Engineering units: from psi to GPa without losing a spacecraft

SI prefixes, US customary units, why a temperature change does not convert like a temperature, and what compound units such as centipoise and BTU per hour-foot-degree really mean — plus the two famous unit mistakes that cost a spacecraft and nearly an airliner.

Mohr's circle, explained: principal stresses and maximum shear

Why the stress at a point changes with the direction you look, how Otto Mohr turned the transformation equations into one circle, and how to read principal stresses, maximum shear and the angles they act at — including the out-of-plane shear that catches people out.

Column buckling: why slender columns fail before they crush

Push on a ruler and it bows sideways long before the plastic is anywhere near breaking. Euler's buckling load, slenderness and the radius of gyration, how end conditions set the effective length, why stocky columns follow Johnson's parabola instead — and two structures that fell because a compression member buckled.

Bolted joints: why the preload does the work

A tightened bolt is a stretched spring holding the parts together. How preload shields a bolt from most of the external load, what the joint constant and property classes mean, why tightening torque is such a rough guide to tension, and how joints separate and slip.

Shaft design: why rotating shafts fail by fatigue

A shaft that turns under a steady load is bent back and forth once every revolution. How bending and torque combine, why the endurance limit is corrected for surface, size and reliability, what shoulders and keyseats do to it, and how the Goodman line decides the diameter.

Helical compression springs: rate, stress and closing solid

A coil spring is a long torsion bar wound into a helix. Why its stiffness goes with the fourth power of the wire diameter, why the inside of every coil is stressed most, what solid-safe means, and how springs fail by fatigue, buckling and surge.

Spur gears: why teeth break and surfaces pit

Gear teeth fail in two ways: they crack at the root like an overloaded cantilever, or their working surfaces pit from repeated contact. How involute teeth mesh, what module and contact ratio mean, why contact stress grows only with the square root of the load, and how the AGMA factors turn a textbook stress into a rating.

Where it is used

The same science, in the wild: how real industries choose materials, and what their numbers look like next to ours.

Toward mastery

How real design and certification work — the gap between a typical value and the number an engineer actually designs to.