This simulator heats a bar mounted on a precision expansion bench. Compare material, length, diameter and end-restraint conditions while a displacement indicator and load cell reveal free expansion, gap closure against a stop, and the elastic stress demand that builds up once a restrained bar can no longer expand freely.
• A real-time 3D workbench (a heated bar, a fixed support, a movable end with an optional gap and stop, a displacement indicator and a load cell) with home view, focus-selected-part, auto-rotate, expand, show/hide outer shell and hide-labels scene tools; motion amplification affects only the 3D graphics, not the physical displacement values reported. • Experiment controls: bar material, bar length, bar diameter, target temperature, end-restraint condition (free, gapped, or fully restrained) and gap size sliders, plus pause/resume, single-step and 60 s-step buttons, six playback speeds, and restart/heat-cool-bar/stop actions. • A Curves & measurements analysis tab with two live charts (temperature response; restraint response versus temperature), the underlying thermal-strain and thermoelastic-stress equations, and snapshot readouts (temperature, free expansion, end displacement, elastic trial stress and elastic trial force — tension positive, compression negative). • An Experiments tab with four guided fixtures (measuring free steel expansion, heating a fully restrained bar, closing a 0.5 mm gap before restraint engages, and cooling a bar away from a stop) and a Model verification bench with a timestamped event log and copyable trial report. • A Learn & assess tab with four guided lessons, a knowledge-check quiz with reset, and a written model-scope statement linking to a thermal-expansion reference.
When a bar is free to expand, heating it produces a linear thermal strain ε = αΔT, where α is the material's coefficient of thermal expansion — this strain shows up entirely as a change in length, with no internal stress developing, demonstrated in the measure-free-steel-expansion experiment. Once the bar is fully restrained and cannot change length at all, that same thermal strain must instead be accommodated elastically: it converts directly into elastic stress, σ = EαΔT, where E is the material's elastic modulus — shown in the restrained-heating experiment, where displacement stays at zero while trial stress climbs with temperature.
A gapped restraint condition sits between these two extremes: the bar first expands freely until it closes a finite gap against a stop, and only after contact does further heating convert to stress rather than displacement — the close-a-0.5-mm-gap experiment traces exactly this transition point. The cool-away-from-a-stop experiment shows the reverse: once contact is lost during cooling, the bar again behaves as free, and elastic trial stress returns to zero.
This is a one-dimensional, small-strain thermoelastic bar model with uniform temperature and rigid supports, using constant representative material properties; the illustrative elastic limits shown do not specify any particular real alloy or temper. Temperature follows an imposed exponential approach to the target value — heat capacity, convective heat-transfer coefficient and frame expansion are not solved as a coupled thermal problem. The model excludes plastic deformation, buckling, temperature gradients along the bar, friction and any external gauge loading. Stress and force values above the illustrative elastic limit represent elastic trial demands only, not actual post-yield material predictions. Motion amplification in the 3D view affects only the graphics. Controls reset to a stress-free 20 °C trial, and the simulation stops automatically after one simulated hour.
No. A freely expanding bar accommodates all of its thermal strain as a length change, with no internal stress developing at all. Stress only appears when expansion is at least partially restrained — demonstrated by comparing the free-expansion and restrained-heating experiments directly.
The trial stress follows σ = EαΔT, where E is the material's elastic modulus, α is its coefficient of thermal expansion, and ΔT is the temperature change. Since the bar cannot change length at all, the thermal strain that would otherwise appear as expansion instead converts entirely into elastic stress.
The bar first expands freely, exactly as an unrestrained bar would, until it closes the specified gap against a stop. Only after that contact point does further heating begin converting to elastic stress rather than additional displacement — traced directly in the gap-closure experiment.
No. Stress and force values above the illustrative elastic limit shown represent elastic trial demands calculated from the linear thermoelastic equations only — they are not predictions of actual post-yield behavior, plastic deformation, or failure for any specific real alloy or temper.