Thermal Expansion

Most materials expand when heated and contract when cooled. For small temperature changes, the fractional change in length (strain) is approximately proportional to the temperature change. This property is crucial in engineering, physics, and many practical applications where temperature fluctuations occur, and neglecting it can cause significant structural issues.

Experiment Simulation

Use the Thermal Expansion module to observe these effects in action. Try setting alpha or deltaT to 0 to see that the length and volume remain completely unchanged, proving the dependence on both factors. Try a negative temperature change (cooling) to see the material contract rather than expand. Finally, compare the "Isotropic cube" expansion to the "Rod" expansion to visualize the difference between one-dimensional and three-dimensional scaling.

1. Set Geometry to Isotropic cube, Initial length L0 to 2, Expansion coefficient alpha to 20 and Temperature change deltaT to 50. Read strain 0.001, length 2.002 m, V = 8.024024008 m^3, Vlin = 8.024 m^3 and positive remainder 0.000024008 m^3.
2. Set Initial length L0 to 1, Expansion coefficient alpha to 10 and Temperature change deltaT to -100. Read strain -0.001, length 0.999 m, V = 0.997002999 m^3 and Vlin = 0.997 m^3.
3. Set Geometry to Rod, Initial length L0 to 5, Expansion coefficient alpha to 0 and Temperature change deltaT to 50. Length stays 5 m and change is 0; the corresponding cube comparison stays 125 m^3.
4. Set Temperature change deltaT to 0. All changes vanish while the initial length and volume remain.
5. Set Initial length L0 to 0. The positive-length error replaces all computations. Restore L0 = 2, choose Isotropic cube, set alpha = 30 and deltaT = 100. Read strain 0.003 and a nonzero volume remainder 0.000216216 m^3.
6. Set Initial length L0 = 1, Expansion coefficient alpha = 0.01 and Temperature change deltaT = 1. The small positive remainder is approximately 3.00000001e-16 m^3; it is not replaced with zero.
7. Pan and choose Reset view. Inputs remain unchanged. The upper body keeps actual relative dimensions; the separately labelled lower inset magnifies strain by 100.