Apply a tensile force to a round rod and watch it actually elongate. Stress σ = F/A and strain ε (bilinear elastic-plastic) update live, the rod stretches proportionally (exaggerated for visibility), and the operating point moves along the material's real σ-ε curve.
This simulator applies a real tensile force to a round rod of chosen material, diameter, and length, then computes the resulting stress, strain, and physical elongation — and animates the rod actually stretching. The operating point moves live along a bilinear elastic-plastic idealization of the material's stress-strain curve, so you can see exactly when the rod crosses from fully recoverable elastic deformation into permanent plastic set.
A stress-strain curve explainer teaches the shape of the σ-ε curve itself — comparing how steel, concrete, aluminum, and wood behave qualitatively. This simulator instead starts from a real applied load: you pick a material, a rod diameter, and a length, apply a tensile force in kip, and the tool computes actual numbers — stress σ = F/A, strain ε from the bilinear elastic-plastic model, and elongation δ = ε·L0 in inches — then animates the rod visibly stretching by that amount (exaggerated for clarity, since real elastic strains are far too small to see at true scale). It is a load-to-deformation simulator, not a curve-shape reference.
Below the yield stress Fy, stress and strain are linearly related by Hooke's Law: ε = σ/E, where E is the modulus of elasticity. This deformation is fully recoverable — remove the load and the rod returns exactly to its original length. Once stress exceeds Fy, this simulator switches to a reduced hardening modulus Et (typically 2-4% of E for structural metals), so strain grows much faster per unit of additional stress: ε = Fy/E + (σ − Fy)/Et. This bilinear kinematic hardening idealization is a standard simplification used throughout mechanical and structural analysis (including finite element software) to approximate real strain-hardening behavior with two straight-line segments instead of a full nonlinear curve.
Elongation δ = ε·L0 tells you how much a tension member actually grows under load — critical for fit-up tolerances, bolt preload retention, and serviceability limits on cables, tie rods, and hangers. Because δ scales with strain, it grows dramatically once a member yields: a rod carrying twice its yield force can elongate ten times or more compared to the same rod held just below yield, which is exactly why ductile materials give visible warning (large, obvious stretch) before eventual fracture — a key safety feature exploited throughout structural and mechanical design codes.
Real elastic strains in metals are extremely small — typically 0.001 to 0.002 in/in even near yield, meaning a 24-inch rod elongates only about 0.03 to 0.05 inches. That is imperceptible on screen, so the animation applies a visual amplification factor to the true elongation so you can actually see the rod lengthen. The numeric elongation readout (in inches) is always the real, unscaled value.
Once stress exceeds the yield stress Fy, the material begins to deform plastically — atomic planes slip past one another (dislocation motion) rather than just stretching elastic bonds. This deformation is permanent: if you remove the load after yielding, the rod does not return to its original length: it retains a permanent set. The bilinear model captures this transition with a reduced stiffness (Et) beyond yield.
Force at yield onset is simply Fy × A, the yield stress multiplied by the rod's cross-sectional area. It tells you the maximum tensile force the rod can carry while remaining fully in the elastic range. Increasing the rod diameter raises this force substantially since area scales with diameter squared (A = π/4·d²), so doubling the diameter quadruples the load capacity at yield.
Yield stress Fy is an intrinsic material property driven by atomic bonding and microstructure — titanium alloys (Ti-6Al-4V, Fy ≈ 120 ksi) can carry over three times the load of mild steel (A36, Fy ≈ 36 ksi) at the same cross-section before yielding, while annealed copper (Fy ≈ 10 ksi) yields at a much lower stress. Modulus of elasticity E (stiffness) is largely independent of yield strength — steel alloys all share E ≈ 29,000 ksi regardless of their yield strength grade, because E depends on atomic bonding stiffness, not alloying for strength.
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