Stress, strain, and why things break
Stiffness is not strength, strength is not toughness — the three ideas behind every material choice ever made.
Stress and strain
Stress is how concentrated a force is: force divided by the area that carries it, measured in megapascals (MPa). Standing on one heel of an ice skate puts far more stress on the floor than standing flat, even though your weight is unchanged. Strain is the response: how much the material stretches, as a fraction of its length. Pull a 100 mm strip until it is 101 mm long and the strain is 1%.
For small loads, stress and strain are proportional: σ = E·ε, known as Hooke's law. The proportionality constant E is Young's modulus — the material's stiffness, in gigapascals (GPa). Rubber has E near 0.01 GPa, plastics sit around 1–4, glass fiber near 70, carbon fiber above 200, and steel about 210 GPa. Every modulus number in this site's database is exactly this E.
Stiffness, strength, toughness — three different virtues
Stiffness (E) says how hard it is to stretch or bend. Strength says how much stress the material survives before it permanently deforms or breaks — that is the tensile strength column in the database, in MPa. Toughness says how much energy it absorbs before fracturing.
They do not travel together. A ceramic tile is stiff and fairly strong but shatters — stiff, not tough. A polycarbonate riot shield is less stiff but absorbs enormous impacts — tough. Polystyrene (a CD case) and polycarbonate have nearly the same stiffness, yet one cracks if you look at it wrong and the other stops hammers. Choosing a material means deciding which virtue your design actually needs.
Ductile or brittle, and the safety factor
Ductile materials (most metals, many plastics) stretch and yield before breaking — they give warning. Brittle materials (glass, ceramics, thermosets like polystyrene) fail suddenly at their strength limit. Composites are their own case: strong yet brittle-ish in failure, which is why composite design leans on careful analysis.
Because real loads, real materials, and real manufacturing all scatter, engineers never design right up to the limit. They divide the material's strength by a safety factor — typically 1.5 for aircraft, 2 or more elsewhere. The strength ratio SR reported by this site's laminate calculator is precisely this idea: SR = 1.8 means the laminate holds 1.8× the applied load before first damage.
Teaching illustration of σ = E·ε with a brittle break. A stiff-but-weak material breaks at tiny strain; a compliant-but-strong one stretches far. Real curves bend — measured values live in the materials database.
1. A material with a very high Young's modulus E is necessarily…
2. A 200 mm strip is stretched to 202 mm. The strain is…
3. The laminate calculator reports SR = 1.8. That means…