This simulator draws the full stress–strain curve of a tensile test, tracing how a material responds as it is stretched from zero up to fracture. The elastic region follows Hooke's law (σ = E·ε), while the plastic region uses a power-law hardening model (σ = σ_y + K·εₚⁿ) that bends over toward the ultimate tensile strength before necking and failure. It compares five materials — steel, aluminium, rubber, bone and polymer — so you can see why Young's modulus and ductility differ so dramatically across them.
A stress–strain diagram alongside an animated specimen. The elastic portion is linear (σ = E·ε); past the yield point σ_y it follows power-law hardening up to the ultimate tensile strength, then drops as the bar necks and fractures. Markers flag the yield and UTS points, and the shaded area under the curve gives toughness in MJ/m³.
Pick a material preset, or adjust the sliders for Young's modulus E (GPa), yield strength σ_y, UTS, fracture strain ε_f and the strain-hardening exponent n. Drag the applied-strain slider to load the specimen by hand, or press Auto test to ramp it to fracture; Stop, Reset and Show all materials toggle the overlay of the other four curves.
Steel and rubber sit at opposite ends of stiffness: structural steel has a Young's modulus near 200 GPa, while rubber is around 0.01 GPa — roughly twenty-thousand times more compliant. That is why rubber can stretch several times its length elastically while steel deforms only a fraction of a percent before yielding.
It is a plot of stress (force per unit area, here in MPa) against strain (the fractional change in length, shown as a percentage) measured during a tensile test. The shape of the curve reveals a material's stiffness, yield point, ultimate strength and ductility, summarising almost everything an engineer needs to know about its mechanical behaviour.
The elastic region uses Hooke's law, σ = E·ε, giving a straight line whose slope is Young's modulus E. Beyond the yield strain it switches to a power-law hardening expression, σ = σ_y + K·εₚⁿ, which rises toward the UTS. Past about 80 per cent of the strain to UTS the stress falls off to mimic necking and fracture.
E (GPa) sets the elastic slope, σ_y (MPa) is the yield strength where plastic flow begins, and UTS is the peak engineering stress. Fracture strain ε_f (%) fixes where the specimen breaks, and the strain-hardening exponent n shapes how steeply the plastic region climbs. Applied strain drives the live test point along the curve.
The presets use realistic textbook values and the equations are standard idealisations, so the trends and comparisons are sound. However, it plots engineering stress rather than true stress, ignores effects like strain rate, temperature and anisotropy, and uses a simplified post-UTS drop, so it is best treated as a teaching tool rather than a substitute for real test data.
Toughness is the total energy a material absorbs per unit volume before fracturing, expressed in MJ/m³. Because energy equals stress integrated over strain, it equals the area beneath the stress–strain curve. The simulator fills that area and reports the running value, which is why a ductile material with modest strength can absorb more energy than a strong but brittle one.