The core idea
Stretch any solid object and it pushes back. Below a limit, that push-back is perfectly proportional — double the pull, double the stretch. This is Hooke's law, and the region where it holds is the elastic region: let go, and the part returns to its exact original shape. Past that limit (the yield point), it deforms permanently — it has yielded.
We quantify the pull as stress and the stretch as strain:
- Stress: σ = F / A — applied force F (N) spread over cross-sectional area A (m²). Result in pascals (Pa). This lets you compare a thin wire and a thick bar fairly: same force, smaller area, higher stress.
- Strain: ε = ΔL / L₀ — elongation ΔL divided by original length L₀. Dimensionless (e.g. 0.002 = 0.2 % stretch).
Hooke's law ties them together: σ = E · ε, where E is Young's modulus — the material's stiffness. High E (steel ≈ 200 GPa) means it barely stretches; low E (PLA ≈ 3.5 GPa) means it flexes. Note that E describes springiness, not strength — the yield point is a separate property. Rubber is flexible but tough to snap; glass is stiff and snaps easily.
Real-world example
Snap-fit clips: print them in PETG, not PLA. PETG's lower stiffness and higher ductility let a clip flex past tiny yield-free deflections thousands of times; a stiff PLA clip cracks on the second or third use. Same reasoning explains belt-tensioner springs and why printer frames use steel rods, not printed ones — the rods' high E keeps the gantry from flexing mid-print, which is what kills dimensional accuracy.
Common pitfall
Beginners equate stiff with strong. They're independent axes: a material can be stiff and brittle (PLA, glass) or springy and durable (PETG, spring steel). Ask two separate questions: Will it bend visibly? → look at E. Will it permanently bend or snap? → look at yield strength.