stress
Push on something and the force has to spread over the area it acts on. A thin nail and a thick post can both hold your weight, but the nail feels the load far more fiercely because the same force is packed into a much smaller patch of material. Stress is exactly this idea made into a number: force divided by the area carrying it. It is what the material actually feels, no matter how big or small the part is.
Engineering stress is written sigma = F / A0: the applied force F divided by the ORIGINAL cross-sectional area A0. The unit is the pascal, Pa = one newton per square metre; engineers usually work in megapascals, MPa = 10^6 Pa, or gigapascals, GPa = 10^9 Pa. A worked example: a round rod 10 mm in diameter has area A0 = (pi/4) x (0.010)^2 = 7.85 x 10^-5 m^2. Pull it with 7850 N and the stress is 7850 / 7.85e-5 = 100 MPa. Pulling apart is tensile stress (taken as positive), squeezing is compressive (negative), and a force acting sideways along the area gives shear stress, written tau.
Stress, not raw force, decides whether a material yields or breaks, which is why every strength is quoted as a per-area number in MPa: a value measured on a small test bar then applies to a bridge cable of any thickness. One honest catch: because engineering stress always divides by the ORIGINAL area, once a ductile bar starts to thin down (neck) the real force-per-area in that neck is higher than the number you plot. That gap is why true stress exists.
Standing on one ice skate versus one snowshoe: same body weight, but the thin blade concentrates it into a tiny area (high stress, it cuts in) while the broad shoe spreads it out (low stress, you float on the snow).
Stress = force / area, so the same force gives very different stress depending on how much material shares it.
Stress is force per unit area, not force itself — a small force on a tiny area can be a huge stress. Engineering stress uses the original area; after necking the true stress is higher than the plotted value.